Edge Intelligence for Satellite-based Earth Observation: Scheduling Image Acquisition and Processing Beatriz Soret, Antonio M. Mercado-Martı́nez, Antonio Jurado-Navas, Nicolai D. Lyholm, Marco Moretti, Petar Popovski, and Israel Leyva-Mayorga
arXiv:2604.05937v1 [cs.NI] 7 Apr 2026
April 8, 2026
Abstract Modern Earth Observation (EO) missions generate massive volumes of imagery that challenge existing downlink and ground-processing capabilities, particularly for time-critical applications. This work investigates how a low Earth orbit (LEO) satellite constellation equipped with heterogeneous edge computing resources can enable real-time semantic processing of data acquired by EO satellites. We introduce an energy-aware framework that optimizes the use of resources accounting for data acquisition, computing, and communication constraints. Although we focus on maritime surveillance, the formulation is task-agnostic and accommodates a broad class of semantic and goal-oriented inference problems. Specifically, we formulate two coupled optimization problems: (i) observation scheduling, which selects image acquisition opportunities while accounting for turbulence-induced image degradation and energy budget, and (ii) processing scheduling, which allocates semantic workloads across onboard and ground processors. We evaluate these mechanisms for the task of detection and localization of vessels, for which we quantify the benefits of turbulence-aware observation scheduling for preserving image quality and experimentally characterize the execution-time distribution of YOLOv8 on different computing platforms. Results demonstrate that task- and turbulence- aware observation scheduling can significantly improve the quality and quantity of observed targets. Furthermore, cooperative edge processing within the constellation substantially reduces power consumption compared to traditional downlink-centric architectures. These findings highlight the potential of distributed edge intelligence to enhance the responsiveness and autonomy of future satellite-based EO systems.
1
Introduction
We are witnessing a surge in satellite-based Earth Observation (EO) [1], driven by scientific, commercial, and geopolitical factors, with the number of satellites expected to triple by 2033 [2]. This growth reflects the essential role of EO in providing critical information for climate and environmental monitoring [3] [4], maritime surveillance [5], disaster management [6], and beyond. Historically, EO applications have downloaded vast amounts of collected raw, or minimally processed, data to a server on ground, to be stored and processed at some point in the future. This is changed radically by making the EO data part of real-time computation-communication loops within the emerging trend towards on-board intelligence. There are several drivers of this trend: (i) Satellite and space technologies are drastically reducing the cost of the missions through specialized yet affordable spacecrafts, leading to a densification of low Earth orbit (LEO) satellite networks and increasing the volume of EO data generated in orbit. B. Soret, A. M. Mercado-Martı́nez, and A. Jurado-Navas are with the Telecommunications Research Institute (TELMA), Universidad de Málaga, Málaga, Spain. N. D. Lyholm, P. Popovski and I. Leyva-Mayorga are with the Connectivity Section, Aalborg University, Aalborg, Denmark. Marco Moretti is with the University of Pisa, Pisa, Italy and also with the National Inter-University Consortium for Telecommunications (CNIT), 43124 Parma, Italy. This work was partially funded by ESA SatNEx V (prime contract no. 4000130962/20/NL/NL/FE). The view expressed herein can in no way be taken to reflect the official opinion of the European Space Agency. The work of B. Soret, A.M. Mercado-Martı́nez and A. Jurado-Navas is further supported by the Spanish Ministerio de Ciencia e Innovación under grant PID2022-136269OB-I00 funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”. The work of A.M. MercadoMartı́nez is also supported by Grant DGP PRED 2024 01603, funded by the Consejerı́a de Universidad, Investigación e Innovación of Junta de Andalucı́a and the European Union. The work of Petar Popovski and Israel Leyva-Mayorga is partially supported by the Velux Foundation, Denmark, through the Villum Investigator Grant WATER, nr. 37793. The work of Marco Moretti is also partially supported by the Italian Ministry of Education and Research (MUR) in the Framework of the FoReLab Project (Departments of Excellence).
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Figure 1: Scenario overview: EO satellites capture images of a set of tracked objects (vessels), with image quality affected by atmospheric turbulence. Raw images are transmitted to the edge layer via ISLs for semantic compression (vessel detection and localization), and processed data transmitted to ground via DL. Both the EO satellites and the edge constellation operate within the LEO layer. (ii) Edge computing enables the use of the computing capabilities of the network infrastructure to analyze information closer to the source, resulting in reduced latency and bandwidth. In the case of space, LEO satellite edge nodes can process raw EO data before being sent to the ground, de-congesting the communication network, specifically the feeder link connecting the space segment to the ground segment [7]. (iii) Artificial Intelligence (AI) and Deep Learning are driving remarkable progress in data processing, including image and video, by transforming raw data into actionable intelligence. When combined with Semantic Communications (SemCom) [8] principles, these methods extract and transmit the informative content (meaning, relevance and mission value), which allows a great reduction in data volume [9]. Although semantic compression and feature extraction have already been adopted in space missions, such as ESA’s Sentinel-2, they typically operate in isolation at the source, without considering the endto-end communication context or task-specific objectives. In contrast, the SemCom concept is a broader paradigm that envisions the joint optimization of sensing, processing, transmission, and interpretation, guided by a shared Knowledge Base (KB) and aligned with the semantic goals of the application at the intelligent communicating nodes [10]. Together, these developments form the foundation for edge intelligence in EO [11, 12], where satellites do not simply observe the Earth, but understand it, enabling dynamic, efficient, and autonomous sensing and processing, considering the final goal of the EO task. In this paper, we focus on two core procedures for this vision: (1) Scheduling of observations, which determines what to observe, when, by which satellites, and under which acquisition parameters. The latter includes adjusting the attitude control subsystem at the spacecrafts for dynamic adjustment of pointing, accounting for impairments caused by the atmospheric turbulence. (2) Scheduling of processing, which allocates data processing and communication tasks between satellite edge nodes and ground resources. These optimizations explicitly consider constraints in terms of time, energy, as well as computation and communication resources. Our proposed scenario integrating observation and computation scheduling is illustrated in Fig. 1: A set of EO satellites capture images subject to atmospheric turbulence, and may belong to, or operate independently from, the LEO constellation providing edge computing capabilities. Although the theoretical framework is general and task-agnostic to accommodate a broad class of semantic and goal-oriented inference problems, we focus on the EO task of observing a set of vessels (the targets) on the Earth’s surface. The resource orchestrator at the ground station (GS) translates this query into an observation scheduling, to decide what to be observed and the corresponding observation parameters, and a processing scheduling, to decide how image processing is distributed between satellite edge nodes and, if necessary, ground resources. The scheduled satellites run an object detection and localization algorithm on the acquired images and encode the result. The processed information is then transmitted to the ground for final aggregation, interpretation, and delivery to the end user. Extensive research has addressed the data acquisition process, including agile satellites, as reviewed in Section 2. However, despite being a mature technology, several aspects remain unexplored for realtime, quality-aware optimization, with a few exceptions [13]. The second component of interest, edge computing in space, has only recently begun to receive attention. Relevant use cases include mobile edge computing, Internet of Things (IoT), EO and federated learning [11, 12, 14–17]. An example of a joint observation and communication optimization is found in [18]. However, the observation model does not 2 Draft
capture image quality or atmospheric turbulence, and the processing model also includes simplifications that moves it away from the optimal allocation. The rest of the paper is organized as follows. In Section 2 we describe the fundamentals of EO, including the key elements of the considered optimizations: the data acquisition and observation scheduling, the meteorological and atmospheric turbulences, and the data processing techniques. Then, the system model is introduced in Section 3. In Section 4, the optimization problems for the observation scheduling and the edge computing are formulated, and Section 5 includes the evaluation results that demonstrate the achieved gains. Section 6 concludes the paper.
2
Fundamentals of Earth Observation
EO satellites generate large amounts of data about the Earth’s surface, water bodies, and atmosphere. For example, the ESA Sentinel missions acquire approximately 12 TB of images daily, while NASA missions collectively provide 20-30 TB per day. These volumes are rapidly increasing as new missions are planned and launched. EO images are used for different purposes requiring computer vision processing and inference, e.g., object localization and detection, semantic labeling of image regions, change detection, or time series analysis. Table 1 provides a representative list of EO missions and State-of-the-Art (SoA) processing algorithms.
2.1
Data acquisition and scheduling
The EO satellite payload includes various remote sensing instruments, such as cameras, radar, spectrometers, or thermal sensors. Optical cameras are often multi-spectral, ranging from the near infrared (NIR) to the ultraviolet (UV) wavelengths. A full frame is typically obtained by superimposing frames captured at different wavelengths. For example, a color image is produced by combining red, green, and blue (RGB) channels, whereas a panchromatic image is obtained from a wide-band capture that provides higher spatial resolution. The area covered and the quality of the resulting images are primarily affected by (i) the altitude of the orbit; (ii) the Field of View (FOV), which is the angular width that determines the extent of the observable area captured by the camera sensor; (iii) the Ground Sample Distance (GSD), which represents the actual distance on the ground between the centers of adjacent pixels, determining the spatial resolution of the imagery [7]. Typically, lower altitudes correspond to lower GSD and FOV values. Since high-resolution imagery requires low GSD values, LEO satellites are the prevalent choice for EO. As the captured frame extends further off-nadir (away from the point directly below the satellite), the GSD increases, degrading image spatial resolution [19]. Therefore, accurate control of the observed surface footprint is essential for high-resolution EO. Modern attitude control subsystems enable dynamic adjustment of pointing to meet such observation requirements. Additionally, pansharpening, where a multispectral frame is combined with a panchromatic frame, can be used to reduce the GSD and enhance image quality. The new generation of agile EO satellites (AEOSs), equipped with full three-axis attitude control (roll, pitch, and yaw) [20], significantly enhances data acquisition capabilities, extending the duration of visible time windows (VTWs), while enabling multiple observation time windows (OTWs) for a given observation target within a single orbital pass. We refer to VTW as the time interval during which a satellite has visibility of a target, whereas OTWs denote the specific subintervals during which the actual imaging takes place. Although this improved flexibility expands the range of feasible observation schedules, it also complicates the OTW selection when multiple targets are involved in the same scheduling time horizon (STH). This challenge is known as AEOS scheduling problem (AEOSSP), which consists of determining the target observation sequence, the corresponding OTW, and, in multi-satellite scenarios, the satellite responsible for executing such actions [21]. The objective is to maximize the observation profit while satisfying a set of operational and resource constraints. The observation profit is a metric that quantifies the value of an observation and depends on the purpose of the mission; common definitions include image quality [22], target priority [23], or the influence of atmospheric conditions [24]. Given the NP-hard nature of the AEOSSP [25], where computational complexity grows rapidly with the number of satellites and targets, exact optimization approaches become impractical for large problem instances. Consequently, a large volume of literature has focused on heuristic and learning-based methods [13, 26], especially when resources are limited and real-time scheduling is required. Recent research integrates the AEOSSP into the operation of the entire satellite system to jointly optimize observation, computation, and communication tasks [18, 27, 28]. 3 Draft
Table 1: Earth Observation (EO) missions and SoA image processing algorithms. EO missions Name
Agency/Company Constellation
Imaging capabilities
Sentinel-2
ESA
2 satellites at 786 km.
GOES
NOAA and NASA
3 geostationary satellites.
PlanetScope [29] WorldView Series [30]
PlanetLabs
> 430 3U CubeSats Doves and SuperDoves at 475-525 km. 3 satellites at 496 km (WorldView-1), 770 km (WorldView-2) and 617 km (WorldView-3).
13 spectral bands from Visible and Near Infra-Red (VNIR) to Short Wave Infra-Red (SWIR). 16 spectral bands: VNIR, Mid Wave Infra-Red (MWIR), and Long Wave Infra-Red (LWIR). 8-band multispectral images.
Maxar
WorldView-1: panchromatic images. WorldView-2 and 3: 8-band multispectral images.
Image processing algorithms Name
Application
Architecture and characteristics
Performance
JPEG2000
Compression
–
Single Shot Detector (SSD)
Object detection and localization
YOLO (v8) [31]
Classification, segmentation, object detection, and tracking Time series analysis
Scalable lossy and lossless compression. Single CNN to predict multiple bounding boxes and their class probabilities from multiple feature maps. Multiple CNN and fully connected layers to predict the bounding boxes of the objects CaffeNet architecture to predict the bounding box coordinates of an object in the frame from a previous one. Encoder-decoder NN
Accuracy = 61%, Robustness = 90%.
GOTURN [32]
EndNet [33]
2.2
Multimodal fusion
data
Mean Average Precision (mAP) @0.5 ≥ 68% on PASCAL VOC2007 dataset. mAP @0.5 = 76.8%.
Averaged accuracy = 93.88%.
Meteorological effects
Meteorological factors play a key role in selecting the most suitable image acquisition and processing techniques, directly impacting their effectiveness and accuracy. The atmosphere acts as a massive thermodynamic system with slow, periodic oscillations caused by atmospheric tides, and small fluctuations in the atmospheric refractive index due to slight temperature variations. The thermal micro-variations are explained by the appearance of convective air currents. These are caused, horizontally, by the progressive warming of the ground by the Sun and, vertically, by velocity gradients between different atmospheric layers. The latter modifies the uniform characteristics of medium’s viscosity due to dynamic mixing and random subflows, called turbulent vortices or eddies [34], which induce characteristic image aberrations, compromising the achievable angular camera resolution. Atmospheric turbulence can be modelled through phase screens, which contain the phase fluctuation related to the refractive index fluctuation spectrum. To realistically simulate the way lightwave aberrations are captured by a camera, a thin phase screen technique is employed, based on the Kolmogorov power spectrum density of the refractive index [34]. This phase screen is then superimposed on the wavefront of the light as it propagates through the simulated atmospheric layer. Figure 2 shows an example of the impact of the atmospheric turbulence in the performance of the state-of-the-art object detection
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Figure 2: Impact of the atmospheric turbulence in ship detection and localization using YOLOv8. The severity of the atmospheric turbulence is parametrized in the structure parameter Cn2 (0) [34]. The input images and mission parameters are from [35]. The output of the algorithm are the blue bounding boxes that include coordinates and confidence about the detection.
Figure 3: CDF for Cn2 (0) based on experimental ground-level measurements. Measures taken from [36]. and localization algorithm, YOLOv8, applied to a pre-trained EO database of images collected from a 500 m eye altitude level [35]. As the turbulence becomes more severe, parameterized in larger refractive index fluctuations and structure parameter Cn2 [34], the algorithm struggles to detect vessels. However, this effect is often overlooked in system optimization. Fig. 3 shows an empirical CDF of this parameter as derived from experimental ground-level measurements [36]. 2.2.1
Atmospheric channel estimation
Accurate estimation of the refractive index structure constant, Cn2 , is essential for modeling optical propagation, outage probability, scintillation, and beam-wander effects in satellite-to-ground optical links. Unlike ground-based astronomy or terrestrial FSO, where Cn2 can be measured directly using SCIDAR (Scintillation Detection and Ranging), MASS (Multi Aperture Scintillation Sensor), DIMM (Differential Image Motion Monitor), or scintillometers, LEO platforms impose strict constraints on payload mass, power, pointing, and telemetry budget. Consequently, a rigorous assessment of all estimation methodologies is required to identify those suitable for spaceborne implementation. In Table 2 we summarize the most robust and practical methods for estimating Cn2 in LEO missions based on physical arguments, algorithmic feasibility, and published empirical evidence. Passive optical approaches, including speckle-based, image-gradient, and hybrid CNN–physics methods, are fundamentally unsuitable for spaceborne implementation, as they are primarily sensitive to turbulence local to the receiver, which is negligible at satellite altitude, while the dominant contribution to optical degradation arises in the lower atmosphere; moreover, their assumptions of quasi-stationary, long-path geometries are incompatible with rapid orbital motion and impose significant on-board computational and calibration burdens. Instrumental profilers such as scintillometers, SCIDAR, MASS, and radiosondes are likewise infeasible for LEO platforms and remain limited to ground-based validation. In contrast, meteorological estimation methods based on Numerical Weather Prediction (NWP) models and satellite sounders provide a physically consistent and operationally viable solution, offering global, continuous, and fore5 Draft
Table 2: Overview of C2n estimation techniques . Comparison of C2n Estimation Techniques and Associated References Category
Passive Optical
Technique
Method Basis
Key Limitation / Challenge
Speckle-based Observation (ML) [37]
ML reconstruction of the Cn2 profile from single-shot star/beacon speckle patterns.
Image Gradient Method [38, 39]
Calculates Cn2 from the statistics of image shifts (tilt variance) in long-range video, simplifying physics-based assumptions. Integrates convolutional layers with a differentiable gradient approach, explicitly incorporating optical parameters like aperture (D) and distance (L). Calculates Cn2 using the vertical gradient of potential temperature derived from satellite (AIRS) or Numerical Weather Prediction (NWP) data. Estimates Cn2 from horizontal spatial statistics from NWP, applying corrections for inherent model smoothing. Predictive approach solving prognostic equations for scalar variances within NWP turbulence closure schemes. Turbulent mixing effects. Double-ended optical measurement of irradiance scintillation and angle-of-arrival fluctuations. Measures path-averaged Cn2 . Balloon-borne fine-wire probes measuring temperature turbulence (CT2 ) directly over a wide range of elevations.
Lack of a clear analytical theory connecting speckle observations to the turbulence profile. For GSs only. Influenced by turbulence near the camera, gradient implementation and ROI choice. Critical for implementing and processing on-board a satellite. Suffer from poor generalization across unseen datasets or changes in optical parameters.
Physics-based CNN (Hybrid) [37, 38]
Tatarskii Gradient (NWP/Satellite) [40–44]
Meteorological Horizontal Structure Functions [43, 44] Second-Order Turbulence Closure [43]
Instrumental
Scintillometers [38, 39, 41]
Thermosondes [37, 39, 42, 44]
Requires empirical estimation of the outer length scale. Suffers from zero-gradient problem in neutrally-buoyant boundary layer. Produces area-averaged estimates that fail to capture local, highly intermittent turbulence variability. Largest errors near the top of the boundary layer. Requires accurate determination of Convective Boundary Layer (CBL) height (zi ). Bulky, costly, and requires precise alignment over long distances. Systematic errors due to poor focal alignment. For communications with GSs. Estimation error is dominated by the intrinsic intermittency of turbulence (RMS error ≈ 50%). Intrusive deployment.
castable Cn2 profiles with full four-dimensional coverage and inherent sensitivity to the atmospheric layers that dominate optical propagation. These characteristics enable seamless integration with link-budget analyses and end-to-end simulators without imposing additional payload, power, or calibration requirements on the spacecraft. While existing SemCom frameworks increasingly account for physical and semantic noise, atmospheric noise that originates at the observation stage remains largely unexplored. Incorporating atmospheric effects into a unified system optimization of observation, communication, and semantic processing constitutes a key open research challenge.
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2.3
Data processing
There is a plethora of image processing and compression techniques that can be applied to the acquired images, ranging from traditional methods like JPEG to advanced AI semantic extraction algorithms designed for specific tasks. This also includes popular object detection and localization algorithms, such as the YOLOv8 algorithm mentioned earlier and, more recently, the use of generative AI [45]. The selection of the specific algorithm depends on multiple factors, including the compression factor, the complexity of the algorithm, and the accuracy of the task. The compression factor indicates the reduction of the data size, which is critical for efficient data storage and transmission. The algorithm complexity affects the time elapsed from data capture until the information is ready for transmission, as well as the energy consumed during processing. More complex algorithms require additional resources but may provide better performance. Finally, task accuracy is measured by specific performance parameters that ensure the desired outcomes are met. AI algorithms can be trained on EO image datasets that often include images captured under varying conditions and featuring a small GSD to achieve a high accuracy [35]. Regarding object detection and localization algorithms, several performance metrics are used to evaluate their effectiveness, with the supported frames per second (FPS) being crucial for real-time applications. Precision and recall refer to the proportion of correctly detected objects among all detected objects and among all actual objects, respectively. In addition, the mAP, ranging between 0 and 1, is derived from the precision and recall values. Another metric is the Intersection over Union (IoU), which measures the overlap between the predicted boundary and the real object boundary (i.e., the ground truth). An IoU threshold is predefined (typical values being 0.5 and 0.95) to determine whether a detection is correct.
3
System description
In the considered network, the space segment is responsible for sensing (image capturing), preliminary data handling, and on-board processing, and is organized into two logically distinct but tightly coupled functional layers: the Observation Layer, for Earth data acquisition, and the Edge Layer, for distributed computing, storage, and communication. These layers define functional roles rather than physically distinct satellite platforms. Typically, EO satellites have limited on-board computing and storage, being optimized for sensing performance, including spatial resolution, coverage, and revisit time, rather than onboard processing and long-term storage. They transmit raw or minimally processed data (the images) to the edge layer for processing and delivery to the ground segment, where the GS and end-users are located. However, other missions may adopt more integrated designs, with sensing and processing capabilities coexisting on the same spacecraft. This layered abstraction enables a general and technologyagnostic system analysis based on a logical separation between sensing and processing functionalities, while still allowing flexible cooperation between satellites. The end-to-end workflow of the system (Fig. 4) can be described as a sequence of interconnected functional blocks across the different layers. An end-user issues a query, which specifies an observation task that can be either semi-static (“Map area X for Y months”) or dynamic (“Track vessel with ID X” or “Map the area around volcano Y in eruption”). In our scenario, the task is dynamic, involving the observation of multiple targets over a specified time horizon. The query is translated into a technical request to the network in the form of an orchestration of sensing, energy, computation, and communication resources, typically performed at the GS. This orchestration is divided into observation scheduling and processing scheduling, both representing complex optimization problems [1], as they must account for resource availability, network conditions, and environmental factors such as metheorological effects. Following the observation schedule decision, which includes the attitude parameters to be applied, the EO satellites acquire raw observational data. These measurements are affected by atmospheric noise, which impacts the quality of the acquired information, while the observation strategy aims at maximizing observation profit. The acquired data, consisting of images containing the observed targets, is then transmitted from the observation layer to the edge layer through inter-satellite links. At the edge layer, semantic-aware processing is performed in parallel by cooperating edge nodes according to the processing schedule. The images are processed and compressed using either classical algorithms, such as JPEG, or more advanced semantic-empowered processing techniques (see Table 1), enabling task-oriented data reduction prior to transmission of the processed information to the GS. The workload associated with semantic processing and compression is distributed across multiple edge nodes, each characterized by heterogeneous computing, energy, and connectivity capabilities. The allocation of processing tasks to
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Figure 4: E2E procedure of the proposed framework: (1) Upon receiving a task, the ground station orchestrates sensing, computation, and communication resources; (2) EO satellites acquire images according to the observation schedule; (3) the acquire data is transmitted to the edge layer; (4) based on the processing schedule, the edge layer performs semantic processing and delivers the processed data to ground; (5) any data not processed on-board is further computed at the ground layer; (6) the ground layer performs data gathering, producing the final result for the end user. edge nodes is a key system decision that must account for the available computational resources at each node, the current network conditions, and the timing constraints imposed by the end-user query. The processed outputs generated by the edge nodes are forwarded to the GS through the downlink, where they are gathered. If complete processing at the edge is not feasible due to timing constraints, the remaining data is processed at the cloud-enabled GS. The final result is then delivered to the end-user. For this workflow, satellites in the Observation and the Edge layer are connected to the ground segment through feeder links, in the downlink and uplink directions, while intra-space communications are enabled via intra- and cross-layer ISLs. We next describe the models and notation for the elements of Fig. 4.
3.1
Topology
Observation Layer: The AEOS satellites in the Observation Layer, indexed by s ∈ S, perform data acquisition over a set of targets T distributed across the visible surface. The satellites are deployed at an altitude ho with an inclination io . The quality of observations is affected by atmospheric turbulence, as detailed in Section 2. Each target t ∈ T can be observed by a satellite s ∈ S across multiple orbital passes; we denote by Os,t the set of orbits during which satellite s can observe target t. As representative cases, our evaluations in Section 5 consider two configurations for this layer: a single AEOS and a four-satellite Walker Star constellation, with one satellite per orbital plane. Edge Layer: The Edge Layer consists of a LEO satellite constellation of N cooperative satellites, indexed by e ∈ E. These satellites process raw or partially processed data close to the source, supporting timely and efficient delivery of results to the GS. Without loss of generality, we consider a single orbital plane deployed at an altitude he with an inclination ie , noting that the extension to multiple planes follows
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directly. The slant range between these satellites is defined as dISL = 2(RE + he ) sin (π/N ), where RE denotes the Earth’s radius. Each satellite in this layer is equipped with computational resources to perform onboard processing, as detailed later, and communicates with both the Observation and the Ground Layer. Ground Layer: The ground segment comprises a set of GSs, denoted by g ∈ G, which connect to end-users and the space segment via feeder links, in the downlink and uplink directions. Without loss of generality, we assume a single GS receives user requests, which are translated into a resource orchestration plan that includes the observation scheduling and processing allocation, and all GSs can potentially receive processed images from the Edge Layer. Ground stations are equipped with substantial cloud computing resources to handle non-time-critical tasks and to augment edge capacity. The downlink feeder links connecting the GSs to the Edge Layer are typically the main communication bottleneck. In the evaluations of Section5, the 26 GSs are located at ground positions accordingly to the KSAT ground station service [46].
3.2
Acquisition model
For each orbit o ∈ Os,t of the Observation Layer satellites, VTWs,t,o represents the VTW for satellite s over target t, defined as the interval [sws,t,o , ews,t,o ], with sws,t,o and ews,t,o representing its start and end times. Exploiting the enhanced maneuverability of AEOSs, each VTWs,t,o is discretized into a set of OTWs with a fixed time step of prc seconds. Accordingly, OTWs,t,o,w denotes the OTW for satellite s and target t in orbit o, and w ∈ Ws,t,o refers to the indexes of OTWs contained within such VTWs,t,o . We assume that the actual observation duration is significantly shorter than the required attitude maneuvering and onboard processing times, which is typically the case; hence, the operation is constrained by these tasks rather than by acquisition time. Accordingly, each OTWs,t,o,w is characterized solely by its observation timestamp τs,t,o,w and an associated profit σs,t,o,w . For the sake of simplicity, this profit is defined in terms of image quality, specifically the GSD, although the formulation can be extended to incorporate additional Key Performance Indicators (KPIs) such as image freshness. [13]. Observing OTWs,t,o,w requires a given attitude defined by its roll (θs,t,o,w ), pitch (ϕs,t,o,w ), and yaw (ψs,t,o,w ) angles. Each satellite’s maneuvering capabilities are restricted by its maximum roll, pitch, and yaw angles (θmax , ϕmax , and ψmax , respectively), as well as by the slewing velocity of the sensor. The attitude transition time function is typically modeled as a piecewise linear function. Specifically, the attitude transition time between two consecutive observations is computed as [47]: αt,w−t′ ,w′ ≤ 10◦ 11.66, 5 + αt,w−t′ ,w′ /1.5, 10◦ < αt,w−t′ ,w′ ≤ 30◦ (1) ∆τt,w−t′ ,w′ = 10 + αt,w−t′ ,w′ /2, 30◦ < αt,w−t′ ,w′ ≤ 60◦ , ◦ ◦ 16 + αt,w−t′ ,w′ /2.5, 60 < αt,w−t′ ,w′ ≤ 90 22 + α αt,w−t′ ,w′ > 90◦ t,w−t′ ,w′ /3, αt,w−t′ ,w′ = |θs,t,o,w − θs,t′ ,o,w′ | + |ϕs,t,o,w − ϕs,t′ ,o,w′ | + |ψs,t,o,w − ψs,t′ ,o,w′ |,
(2)
where αt,w−t′ ,w′ is the total attitude transition angle between OTWs,t,o,w and OTWs,t′ ,o,w′ . The power required for attitude maneuver transitions is denoted by Pman . While existing literature on the AEOSSP frequently discusses the energy consumption rate (energy per unit of time), we explicitly formulate this in terms of power to maintain consistency throughout this work. For each satellite s, the total maneuvering energy is limited by Emax , which defines the maximum allowable energy budget for attitude transitions. The sequence of selected OTWs,t,o,w by the AEOSSP is denoted by OTW⋆ , and it defines the sequence of times τsk ,tk ,ok ,wk at which the Observation Layer will deliver a new image to be processed by the Edge Layer: OTW⋆ = OTWs1 ,t1 ,o1 ,w1 , OTWs2 ,t2 ,o2 ,w2 , . . . , OTWsK ,tK ,oK ,wK , τs1 ,t1 ,o1 ,w1 ≤ τs2 ,t2 ,o2 ,w2 ≤ · · · ≤ τsK ,tK ,oK ,wK ,
(3)
ysi ,ti ,oi ,wi = 1, ∀i = 1, . . . , K, where ysi ,ti ,oi ,wi is the binary decision variable that denote if OTWsi ,ti ,oi ,wi is scheduled or not. Each element in OTW⋆ corresponds to an observation, i.e., a frame composed of Nimg images of size Dimg with a total size Ds to be processed by the Edge Layer. The images containing the targets have a resolution wimg × himg bits, where wimg and himg are the width and height in pixels.
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As described in Section 2, atmospheric turbulence significantly affects the quality of this acquired data and is quantified by the Cn2 value during the OTW, which in our evaluations is sampled from 2 the distribution in Fig. 3. To ensure high-quality observations, we establish a threshold, Cn,max (0), measured at ground-level, which represents the maximum allowable turbulence for a high-quality frame. Any observation performed under conditions exceeding this threshold is discarded.
3.3
Computation model
We next introduce the computational and energy consumption models used to characterize the processing capabilities of the Edge and Ground Layers nodes, providing an abstract representation of execution time and energy consumption. The space and ground processing nodes, indexed by p ∈ P = E ∪ G, are equipped with a multi-core parallel processing architecture, characterized by the number of available (p) (p) (p) processing cores Ncores , the maximum operating frequency fmax , and the power consumption Pmax when operating at maximum frequency. In the evaluations of Section 5, both Central Processing Unit (CPU) and Graphics Processing Unit (GPU) architectures are considered, resulting in heterogeneous parameter settings. (p) When processing node p operates at a clock frequency fp ≤ fmax , its processing power consumption is modeled as !3 fp (p) . (4) P (fp ) = Pmax (p) fmax Let W denote the work of the algorithm of interest, defined as the number of floating-point operations (FLOPs) required to process a single unit of data (i.e., an image). The value of W is assumed to be known and depends on the algorithmic characteristics, such as the stopping criteria or the architecture of a neural network in a machine learning model. To account for non-ideal execution, we introduce a random variable (RV) C (p) that captures the computational inefficiency at processing node p when executing a computing task. This factor models the overhead due to imperfect task allocation, memory access, and data management, and depends on both the node architecture and the algorithm. Finally, let (p) NFLOPs denote the number of FLOPs that each processing core at node p can perform per clock cycle. According to the Bulk-Synchronous Parallel (BSP) model [48], the execution time of an algorithm that is executed in parallel in processing node p operating at frequency fp can be modeled as (p) (p) (p) Tproc (fp ) = Twork fp ; C (p) + Tsync , (5) (p)
where RV Tsync is the delay due to communication and synchronization among processing cores in the architecture, and the RV of the time needed to execute the work of the algorithm is (p) Twork fp ; C (p) =
C (p) W (p) (p) Ncores NFLOPs fp
.
(6)
(p)
Consequently, the mean execution time µT is modeled as (p)
µC W
(p)
µT (fp ) = (p)
(p)
(p)
Ncores NFLOPs fp
(p)
+ µ(p) sync ,
(p)
(7) (p)
where µC and µsync are the mean values of C (p) and Tsync , respectively. Tproc (fp ) is experimentally characterized in Section 5 for representative computing platforms. If the processing power for a given clock frequency P (fp ) is constant, the mean energy consumption for processing an image at node p using an algorithm requiring W FLOPs can be calculated as (p)
(p)
Pmax fp3 µT (fp ) 3 (p) fmax ! (p) fp2 µC W + fp3 µ(p) sync . (p) (p) Ncores NFLOPs
(p)
(p) Eproc (fp ; W )= P (fp ) · µT (fp ) =
(p)
=
Pmax 3 (p) fmax
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(8)
3.4
Communication model
The satellites are interconnected both with the ground segment and with each other through the feeder link and the ISLs, respectively. Free-space optical (FSO) technology is considered the primary ISL solution, as it has become the de facto standard for high-data-rate LEO inter-satellite communications. Due to the controlled relative positioning and stable distances among satellites within the constellation, pointing errors can be effectively minimized. Consequently, ISLs are assumed to be fixed during network operation, with a constant data rate RISL and consuming a fixed transmission power PISL . In contrast, satellite-to-ground Radio Frequency (RF) feeder links are more robust to atmospheric impairments and less sensitive to pointing errors than FSO, which makes them suitable for DL transmissions where channel conditions vary due to satellite mobility and atmospheric effects. Hence, the feeder links are assumed to rely on conventional RF technology, characterized by bandwidth B, transmission power PDL , and total antenna gain GDL . The system operation is divided into time slots of equal duration Tslot , which are indexed by k ∈ {0, 1, 2, . . . }. Let Nimg (k) be the number of images captured at time slot k by the Observation layer, with a total data size Ds . Moreover, for notation simplicity,let g(k) denote the ground station defined for transmitting the images captured at slot k in the downlink and ℓg (k) = (e, g(k)) be the (edge) satelliteto-ground link established to download the data captured at time slot k, such that e ∈ E is the satellite that communicates with ground station g(k). We define the time-varying data rate for ℓg (k) from its signal-to-noise ratio (SNR) on an interference-free additive-white Gaussian noise (AWGN) channel with free-space path loss and with noise power σ as 2 c , (9) γk = GDL PDL 4π de,g (k) fc σ where fc is the carrier frequency, and de,g (k) is the distance between satellite e and GS g(k). Then, the communication rate is selected using the set of achievable spectral efficiencies defined in the DVB-S2X system [49], which constitute the set RDVB = {r} in b/s/Hz. Next, let γmin (r) ≥ 2r − 1 be the minimum required SNR to achieve a block error rate < 10−5 with spectral efficiency r. The modulation and coding scheme for downlink communication is selected to achieve the data rate Rk = B max {r ∈ RDVB-S2 : γk ≥ γmin (r)} .
(10)
Scattering refers to the transmission of uncompressed data from a source EO satellite s ∈ S to a processing node p ∈ P = E ∪ G, i.e., either to an edge-layer satellite or directly to a ground station for processing. Gathering, on the other hand, is the operation of collecting the compressed data from all the servers at the ground station. In the following, the apex (u) will be the label associated to the scatter phase where the data is uncompressed, while the apex (c) the label associated to the gather phase where the data has been compressed. Immediately after capturing a frame of Nimg images at satellite s with a total data size Ds , these are scattered to the edge satellites for processing, leading to a distributed computing problem. The goal is to deliver the data in a timely manner while reducing the end-to-end (E2E) energy consumption, which involves the joint optimization of communications and computing. To maintain the stability of the system, the scatter phase for an observation performed at time slot k ∈ {0, 1, . . . } is scheduled in the same time slot k. Then, the processing of the Nimg captured images is scheduled in time slot k + 1, and the gather phase is scheduled in time slot k + 2. Note that this allows for implementing pipelining, where the scatter phase of the images captured at time slot k occurs in parallel with the processing and gathering phases for images captured at time slots k − 1 and k − 2, respectively. The overall path from satellite s to ground station g is time-varying. During scattering and gathering, data may need to traverse multiple ISLs before reaching a satellite that is currently connected to the ground segment. While the ISLs are assumed to be stable and fixed during network operation, the ground-to-satellite feeder link may change over time. In particular, both the satellite e ∈ E connected to the GS via the feeder link eg (k) and the corresponding transmission rate Rk may vary with time index k. Hence, time dependence is explicitly captured in the notation through the time-slot index k. Accordingly, the path for sending uncompressed data from s to p and compressed data from p to g in time slot k is denoted as [ Ls,p,g (k) = L(u) L(c) p ∈ P. (11) s,p (k) p,g (k), (u)
where Ls,p (k) is the set of links where uncompressed bits are routed to satellite p (scatter phase) and (c) Lp,g (k) is the set of links over which the compressed bits are routed from satellite p to the ground station (gather phase) in time slot k. 11 Draft
During the scatter phase, the observation satellite transmits data packets – each containing entire images of average size Dimg or segments of them – to the edge satellites. Let D ∈ (0, Dimg ] bits be the size of a data packet to be transmitted. Since the intra-plane ISL data rate, RISL , is fixed, the mean time needed to deliver and image from the source satellite s to a processing satellite p ∈ E is the sum of the transmission time and the propagation time, i.e., X D dISL (u) + (12) Tcomm (s, p, D) = RISL c (u) ℓ∈Ls,p (k)
Conversely, the time needed to deliver the semantic information extracted from an image in satellite p to the GS g in time slot k is (c) (c) (c) Tcomm (p, g, D) = Tcomm (p, e, D) + Tcomm (e, g, D) X D dISL D de,g (k) + + + , = ρR c ρR c ISL k (c)
(13) (14)
ℓ∈Lp,e (k)
where ρ ≥ 1 is the summarization capacity (i.e., compression ratio) of the compression algorithm. Next, we define the energy consumption models for communication. Since the ISLs operate at a fixed transmission power and we assume an ideal power amplifier efficiency, the energy required to transmit D bits of data over the ℓ-th FSO ISL is given by the product of the effective transmit power and the transmission duration PISL,ℓ D tx . (15) EISL,ℓ (D) = RISL Similarly, the energy required to transmit D bits of data over the feeder link during time slot k is tx EDL (D, k) =
4
PDL D . Rk
(16)
Optimization
Fulfilling an EO task in a constrained environment involves a delicate balance between accuracy, delay, and energy consumption. The conflicting objectives must all be considered in the resource allocation optimization, which can be conceptually formulated as follows: Identify the best set of EO and edge satellites for image capturing, semantic information extraction and encoding, and routing to the ground, with the aim of minimizing energy consumption while meeting accuracy and timing constraints. Energy consumption is influenced mainly by the data acquisition, on-board algorithm execution, and data transmission. Image capturing is mainly impacted by the amount and frequency of the targets to be observed, which can exceed the Observation Layer capacity. On the Edge Layer, semantic extraction introduces a fundamental trade-off: it increases onboard processing energy, yet significantly reduces transmission energy by shrinking the data volume, since semantically processed information is much smaller than raw imagery. Additionally, the system optimization must take into account the hard constraint that each frame must be captured, processed, and completed before the subsequent frame arrives. If this is not achieved, images may need to be discarded or not captured to avoid congestion in the system. If only a portion of the data can be processed, the remaining data will be transmitted in its raw form to the GS, thereby increasing the load on the communication network and prolonging transmission time. These considerations form the basis for formulating the two optimization problems underlying observation scheduling (Pobs ) and processing scheduling (Psch ), as discussed next.
4.1
Observation scheduling and attitude control for observation profit maximization
The main difficulty when addressing the AEOSSP, denoted Pobs , is that the volume of requests exceeds the observation capacity of the AEOS and therefore only a selection of targets can be observed in each time slot. In this case, the aim is to maximize the collected observation profit while meeting all time, energy, and storage constraints. Data from the Observation Layer is dynamically processed as it is acquired, and therefore storage constraints are neglected in this problem. As introduced in (3), for each observation time window OTWs,t,o,w , let ys,t,o,w ∈ {0, 1} denote whether the window is scheduled (ys,t,o,w = 1) or not (ys,t,o,w = 0). Furthermore, let zt,w,t′ ,w′ ∈ {0, 1} 12 Draft
indicate whether OTWs,t,o,w is scheduled immediately before OTWs,t′ ,o,w′ . The goal is to optimize the profit associated with observation OTWs,t,o,w , which we define in terms of image quality. Without loss of generality, we assume that all targets have the same priority and define the profit in terms of the GSD during the observation as GSDnadir , (17) σs,t,o,w = GSDs,t,o,w where GSDnadir and GSDs,t,o,w are the GSD at nadir and during OTWs,t,o,w , respectively. The observation scheduling problem is then formulated as Pobs :
maximize
ys,t,o,w , zt,w,t′ ,w′ ∈{0,1}
subject to
XX X
X
σs,t,o,w · ys,t,o,w
(18)
s∈S t∈T o∈Os,t w∈Ws,t,o
sws,t,o ≤ τs,t,o,w ≤ ews,t,o
(18a)
zt,w,t′ ,w′ · (τs,t,o,w + ∆τt,w−t′ ,w′ ) ≤ τs,t′ ,o,w′ X X zt,w,t′ ,w′ · (Pman · ∆τt,w−t′ ,w′ ) ≤ Emax
(18b) (18c)
t,t′ ∈T w,w′ ∈Ws,t,o
X X
X
ys,t,o,w ≤ 1
(18d)
s∈S o∈Os,t w∈Ws,t,o
where the optimization objective function (18) is designed to maximize the sum of collected profits; constraint (18a) ensures that the observation of target t occurs within one of its VTW; constraint (18b) models the attitude transition requirement, ensuring that OTWs,t′ ,o,w′ can only be scheduled after OTWs,t,o,w if the attitude maneuver is feasible; constraint (18c) guarantees that the total energy consumption does not exceed the maximum allowed energy and constraint (18d) guarantees that each target can be observed at most once in the schedule. In Pobs , the integer optimization variables take values in {0, 1}, and both the objective function and the constraints are linear; therefore, this is a binary integer linear programming (0–1 ILP) problem. Such formulations, which are commonly used to model resource-constrained scheduling tasks, do not admit closed-form solutions and can exhibit high computational complexity, especially at scale. Therefore, sub-optimal or heuristic approaches are typically adopted in practice, as exhaustive search becomes computationally prohibitive for large-scale instances. In this work, we solve Pobs using the SCIP solver [50, 51], a state-of-the-art framework for mixed-integer optimization.
4.2
Edge computing for energy minimization
The scheduling of edge computing and downlink tasks is organized according to the available downlink times at the ground segment and the observation scheduling for image acquisition at the EO satellites. The pipeline model establishes that Nimg captured and scattered in time slot k are processed in k + 1 and gathered in time slot k + 2. This imposes a constraint for the optimization that the scattering and processing of the images in a frame captured at time slot k must complete in time to reach the downlink satellite before the end of time slot k + 2. Otherwise, downlink is considered a failure and the system must proceed to capture, process, and deliver the frames captured in the upcoming time slots. The optimization variables are the P -dimensional vector of the processing frequencies f = [f1 , f2 , . . . , fP ] of each satellite and GS in P and the SP -dimensional vector of the load distribution x = [x1,1 , x1,2 , . . . , xS,P ]. The variable xs,p indicates the fraction of the computation load generated in s ∈ S that is processed in p ∈ P. Accordingly, a value of xs,p ̸= 0 means that xs,p Ds uncompressed bits are scattered from the source satellite s to the processing node p and then xs,p Ds /ρ compressed bits are gathered from satellite p to ground station g. Both the computing load and data scale linearly with the value of xs,p , so that if source s generates the load Cs and data Ds , the load processed at the satellite p is xs,p Cs addressing xs,p Ds data. The mean energy consumption for a batch of images captured at time slot k is modeled as the sum of the transmission energy and the processing energy, i.e., X Ds xs,p (u) (c) E (p) (fp ; W ) . (19) Ek (x, f ; W, Ds , ρ) = Ek (s, g, x, Ds ) + Ek (s, g, x, Ds , ρ) + Dimg proc p∈P
Given the workload allocation vector x, the total energy consumed during the scattering phase, which occurs during the observation time slot k, corresponds to the energy required to transmit the 13 Draft
n o (u) uncompressed data to the processing nodes through the routing paths Ls,p (k) , including the downlink to the GS g(k) as X (u) Ek (s, g, x, Ds ) = p∈E
X
X
tx EISL,ℓ (xs,p Ds ) +
tx tx xs,g(k) Ds + EDL xs,g(k) Ds , k , EISL,ℓ
(u)
(u)
ℓ∈Ls,e (k)
ℓ∈Ls,p (k)
(20) Similarly, the energy consumed during the gathering phase corresponds to the energy required to transmit the compressed data to the ground station. X X Ds Ds (c) tx tx EISL,ℓ xs,p Ek (s, g, x, Ds , ρ) = + EDL xs,p (21) ρ ρ (c) p∈E
ℓ∈Lp,g (k)
Accordingly, the scheduling optimization Problem Psch , which determines the optimal task allocation vector x and processor frequency vector f , is formulated based on the BSP model as Psch : minimize Ek (x, f ; W, Ds , ρ)
(22)
x,f
(p)
subject to
Ds xs,p µT (fp ) ≤ Tslot D img X 1 Ds xs,g + xs,p ≤ (Tslot − Tdelay (k))Rk ρ p∈E 1 X (c) I ℓ, L (k) Dxs,p I ℓ, L(u) ≤ Tslot RISL,ℓ (k) + p,g s,p ρ
∀p ∈ P
(22a) (22b)
ℓ ∈ Ls,g,p (k) (22c)
p∈P
fp ≤ fpmax ,
∀p ∈ P
(22d)
0 ≤ xs,p ≤ 1, X xs,g + xs,p = 1.
∀p ∈ P
(22e) (22f)
p∈E
Constraint (22a) represents the processing latency constraint, ensuring the computation assigned to processing node p in ∈ P can be completed, on average, within one time slot. Specifically, the mean processing time required to handle the fraction xs,p of the workload generated at source s must not exceed the slot duration Tslot . Constraint (22b) ensures that the total data sent to the ground station during time slot k + 2, including both compressed and uncompressed portions, remains within the available downlink capacity, where n o (c) (p) Tdelay (k) = max Tcomm (p, e, Ds xs,p ) + max Tproc (fp ; Ds xs,p /Dimg ) − Tslot , 0 (23) p∈E
is the maximum delay experienced by the data from an observation at slot k to begin the downlink in the scheduled time slot k + 2. Constraint (22c) enforces the inter-satellite link (ISL) capacity limit. For each ISL ℓ involved in the routing path Ls,g,p (k) during time slot k, the total traffic — either compressed or not — must not exceed the available ISL transmission capacity. The indicator function I(ℓ, L) equals 1 if the routing path L contains link ℓ and 0 otherwise. It is therefore used to account only for the portion of traffic that traverses link ℓ. Constraint (22d) imposes bounds on the processor frequencies, ensuring that each processing node operates within its feasible frequency range. Constraint (22e) enforces that the workload allocation variables are fractional and bounded between zero and one. Finally, constraint (22f) guarantees workload conservation, i.e., the total computation load generated at source s is fully allocated across the ground station and the edge satellites. Problem Psch is non-convex: a local-optimal solution can be obtained through partial dual decomposition, block coordinate descent, or successive convex approximation. However, we observed that the processor frequency fp∗ for all p ∈ P that minimizes the energy consumption under stability constraints (22a) and (22d) is (p)
fp∗ =
µ W C Tslot Dimg (p) (p) (p) Ncores NFLOPs − µTsync D xs,p 14 Draft
(24)
(p)
which makes µT
fp∗ = Tslot for all p ∈ P. Thus, for a given xs,p , the optimal processing energy is 3 (p) (p) P T µ W max slot C Dxs,g (p) E f ∗; W = 3 Dimg proc p Tslot Dimg (p) (p) (p) (p) Ncores NFLOPs − µTsync fmax D xs,p
By substituting (25) into (22) and replacing the constraints (22a) and (22d) with ! (p) µC W Ds xs,p (p) + µTsync ≤ Tslot , ∀p ∈ P, (p) (p) (p) Dimg Ncores N fmax
(25)
(26)
FLOPs
problem Psch becomes convex and can be readily solved using standard optimization libraries.
5
Performance evaluation
We present exemplary results for the two optimization problems in a system comprising a satellite constellation with 23 satellites that provide edge computing resources to one EO satellite. Parameters from the satellite WorldView-3 [30] are used for the image acquisition model and orbital parameters. Without loss of generality, we assume that the observation satellites also serve as edge node, i.e., they perform dual functions, so that he = ho = 617 km and ie = io = 98.6◦ . The task of interest is vessel detection within a defined area of interest. The Observation Layer captures images of regions where vessels are present, which are then semantically processed using YOLOv8 to perform vessel localization and detection. Attitude maneuvers are constrained by slew limits θmax = 45◦ , ϕmax = 45◦ , and ψmax = 90◦ , and by a total energy budget of Emax = 1000 J. The power consumption for attitude transitions is set to Pman = 2 W. Additionally, aligning with WorldView-3 specifications, we assume GSDnadir = 0.31 m/pixel. We consider scenarios both with and without the effect of atmospheric turbulence. When turbulence is accounted for, we perform a Monte Carlo simulation by sampling Cn2 (0) values from the CDF shown in 2 Fig. 3, generating 1000 realizations for each acquisition. A threshold of Cn,max (0) = 2 × 10−14 , m−2/3 is applied to evaluate these cases. The EO satellite captures a given number of FPS with a resolution of 600 × 600 pixels and an average GSD of 0.5 m, which might be affected by atmospheric turbulence. On average, the size of the semantic data for ship detection (i.e., ships and bounding boxes) is 336 bits per image. Executing YOLOv8 for this task requires WYOLO = 79.1 GFLOPs per image. We consider both CPU and GPU architectures for the edge satellites. Specifically, three different configurations are considered, where each satellite has either an 8-core CPU running at up to 1.8 GHz with a power consumption of 6 W, or an NVIDIA Jetson Orin GPU, which can be either a Nano Super or AGX, with a maximum power consumption of 15 and 60 W, respectively. The GS has a 64-core CPU operating at a maximum frequency of 2.6 GHz with a maximum power consumption of 280 W. For the considered constellation, average image size Dimg = 788.513 kbits and compression ratio ρ = 2346. Under these conditions, the communication latency due to the transmission of both uncom(u) (c) pressed Tcomm (s, p, Dimg ) and compressed data Tcomm (p, e, Dimg ) can be closely approximated through the propagation latency per intra-plane ISL for an orbital plane with N satellites in the Edge Layer deployed at an altitude he : Tprop (N, he ) =
2(RE + he ) sin (π/N ) dISL (N, he ) = , c c
(27)
where RE is the radius of the Earth. The later gives 3.1 ms for the selected N = 23 and he = 617 km, which is much larger than the time to transmit one image per ISL Dimg /RISL ≤ 0.1 ms. Building on this, the upper bound in propagation delay for a path between satellites in the Edge Layer following a shortest-path routing algorithm is ⌊N/2⌋ Tprop (N, he ), which gives 34.1 ms for N = 23. Therefore, (c) during optimization, we approximate Tcomm (p, e, D), defined in (14), with the latter upper bound of the propagation latency. Note that the upper bound of propagation latency for any value of N is achieved as N → ∞ and is 2(RE + he )/c, which gives 36 ms for the selected he . The summary of main parameters and values can be found in Table 3.
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Table 3: Parameters and settings. Parameter
Processing architectures
Settings Cloud CPU AMD EPYC 7H12
Satellite CPU Snapdragon 855
64 280 2.6 32 1.079 0 62.377
8 6 1.8 32 1.079 0 5.398
Number of cores Ncores Max. power consumption Pmax [W] Max. clock frequency fmax [GHz] Number of FLOPs per Hz NFLOPs Processing inefficiency µC Mean synchronization time µTsync [ms] (p) (p) Max. processing speed 1/µT (fmax ) [FPS]
Satellite GPU Nano AGX 1024 25 1.02 2 1.071 17.48 17.231
2048 60 1.3 2 1.122 14.14 32.45
Data acquisition train eval No. of images in a frame, for training, for evaluation (Nimg , Nimg , Nimg ) Image resolution wimg × himg Average frame, image, ship (Dframe , Dimg , Dship )
GSD, GSDnadir STH Time slot Tslot Power for camera maneuvering Pman Total energy budget for image acquisition Emax
2601, 1668, 50 images 600×600 pixels 2.05·106 , 788.513, 6.913 kbits 0.43, 0.31 m 1600 s 10 s 2W 1000 J
Communication network Number of orbital planes Np Edge satellites per plane N Altitude ho , he Inclination io , ie Edge Layer ISL data rate RISL Edge Layer ISL transmit power PISL Satellite-to-ground transmit power PDL Downlink bandwidth B 2 Noise power σdB Total downlink antenna gain GDL
5.1
1 23 617, 617 km 98.6, 98.6◦ 10 Gbps 60 W 10 W 500 MHz –119.32 dBW 66.33 dBi
Observation scheduling
To evaluate observation scheduling performance, we present two sets of results. The first demonstrates how an effective optimization of the AEOSSP leads to high-quality data acquisition. The second assesses the impact of atmospheric turbulence. First, we evaluate the scheduling performance in an idealized environment, disregarding atmospheric turbulence effects. The AEOSSP is solved for a single AEOS, problem instances of {80, 100, 120, 140} targets (i.e., areas with vessels), and a STH ≈ 1600 s. Our proposed solution is compared against schedules generated by two conventional benchmark algorithms: first-in first-out (FIFO) and genetic algorithm (GA). For the GA, we utilize the implementation provided by the pymoo library [52], extended with custom crossover and mutation operators to ensure schedule feasibility. Specifically, the population size is set to 20, the number of generations to 100, and both crossover and mutation probabilities are fixed at 0.2. As shown in Fig. 5, a higher observation profit correlates with a larger number of observed targets, and
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(a)
(b)
Figure 5: Performance results for the turbulence-free scenario. (a) Observation profit (left) and number of observed targets (right). (b) GSD distribution of the acquired data.
2 Figure 6: Impact of atmospheric turbulence (Cn,max (0) = 2 × 10−14 , m−2/3 ) on the actual collected observation profit (left) and average schedule precision defined as the ratio of observations meeting quality requirements (right).
acquisitions with lower GSD, i.e., better image spatial resolution. In turn, improved spatial resolution enhances the accuracy of the semantic extraction algorithm, YOLOv8 in this study. To quantify this impact, evaluating the algorithm’s performance in terms of recall (the ratio of correctly detected objects to total actual objects) reveals a drop from 87% to 73% when images are downsampled to simulate a GSD twice the original. Thus, effective observation scheduling, achieved through a precise solution of the AEOSSP, significantly boosts overall system performance. Specifically, the exact solution given by SCIP yields an average observation profit improvement of 77.86% and 6.25% compared to FIFO and GA, respectively. Furthermore, as illustrated in Fig. 5b, the proposed schedule attains an average GSD of approximately 0.43 m/pixel. This matches the characteristics of one of the reference datasets [53]; consequently, this value will be assumed for the subsequent processing scheduling section. The output of this scheduling is the set of OTWs,t,o,w , OTW⋆ , and corresponding times τsk ,tk ,ok ,wk at which the edge nodes will receive new frames to be processed. 2 When the atmospheric turbulence is considered, with a threshold Cn,max (0) = 2 × 10−14 , m−2/3 , Fig. 6 illustrates the divergence between the expected and actual average collected profit. .Additionally, the figure displays the average schedule precision, defined as the portion of observations meeting quality requirements. Two key conclusions emerge: (1) the actual profit is significantly lower than expected; and (2) the proportion of acquisitions failing to meet quality standards is substantial. It should be noted that, although the volume of data declines in a similar way to observation profit, it does not do so in exactly the same way, as the value of each individual acquisition is different. This difference would probably be accentuated in conventional scenarios where each observation target is associated with a different priority. Therefore, accounting for atmospheric turbulence is essential for optimal resource allocation. It avoids wasted energy during image acquisition and attitude maneuvers, while also reducing the load on data processing and transmission, ultimately leading to more efficient satellite resource management. Without prior knowledge of the Cn2 value during the schedule generation, we next evaluate the impact of targets observed under unfavorable conditions that are deemed invalid and re-queued for subsequent scheduling processes. For this simulation, we consider a constellation of four AEOSs arranged in a Walker Star topology, with each satellite in its own orbital plane. The AEOSs are tasked with observing target sets of sizes {150, 200, 250, 300} over 10 consecutive STHs, where each STH corresponds to one orbital
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Table 4: Observation performance. Number of targets
Total profit
Successfully observed targets [%]
Average observations per target
Rescheduled targets [%]
150
109.16
90
1.49
36.5
200
148.06
84.5
1.46
38.4
250
177.18
86.8
1.5
36.3
300
205.15
86
1.5
33.6
2 period (≈ 97 minutes). If a target is observed satisfying Cn2 (0) ≤ Cn,max (0), it is considered successfully acquired, and its corresponding candidate OTWs are removed from subsequent STHs. Conversely, if such condition is not met, the target is retained in the problem instance for future scheduling. Consequently, certain targets may undergo multiple observation attempts before a high-quality image is obtained. Table 4 summarizes the results of the simulation, specifically: the actual collected profit (accounting for turbulence), the percentage of successfully observed targets, the average number of observations per target, and the percentage of rescheduled targets. It is observed that each target undergoes an average of 1.5 observation attempts, with 33.6% to 38.6% of targets requiring at least two attempts due to turbulence effects. Despite these rescheduling efforts, full coverage is not attained in every instance, with success rates ranging from 84.5% to 90%. Finally, as with the single-satellite experiment, instances with a larger number of targets yield a higher total profit.
5.2
Processing scheduling
To optimize the processing of the collected data at the Edge Layer, we first characterize the execution time of the task of interest, i.e. semantic extraction using YOLOv8, on the considered computing architectures. Then, we illustrate the performance of distributed edge processing for the different computing architectures in an isolated and controlled snapshot, where the task parameters and network topology have been fixed. Finally, we showcase the performance of the optimization in a realistic scenario with scheduled observations throughout the satellite orbit. As a starting point, we perform a statistical analysis of the execution time for single images and for the available clock frequencies. We then employ a BSP model to extend the mean execution time to other frequencies and the Central Limit Theorem (CLT) to derive a statistical model for the execution time of an arbitrary number of images. (p) Specifically, we first obtained the mean execution time µT (fp ) of YOLOv8 on individual images executed on the GPU NVIDIA Jetson Orin platforms. For this, the mean execution times were estimated for each available operating frequency fp using all the images in the dataset. Then, to estimate the mean (p) execution time for all f (p) ∈ (0, fmax ), we performed a least-squares regression for the parameters of the (p) (p) BSP model µC and µTsync . Table 3 lists the operational parameters for the GPUs and the estimated parameters for the BSP model. Recall that the complexity of YOLOv8 is WYOLO = 79.1 GFLOPs. The results of the estimated mean execution times are shown in Fig. 7, where the mean execution times obtained empirically are shown with markers and the solid lines show the estimation using the BSP model with least-squares regression. Fig. 7 also shows the estimated mean execution time using the BSP models for the CPUs at the satellite and GS, which were adapted following same procedure on (p) similar CPU architectures and scaled to the number of cores Ncores and CPU clock frequencies of the models considered in Table 3. Clearly, the BSP model provides a nearly perfect fit to the mean execution times obtained in our experiments, which validates its suitability for the numerical optimization of the processing at the Edge Layer. Next, we aim to characterize the randomness of the execution time on the GPU architectures. Fig. 8 (p) shows the results obtained for three clock frequencies fp available at both Nano Super and AGX models, where we observe that the execution time of YOLOv8 individual images executed on the GPU (p) NVIDIA Jetson Orin platforms Tproc (fp ) at the selected clock frequencies follows a Gamma (α(fp ), θ(fp )) (p) (p) distribution with mean µT (fp ) = α(fp )θ(fp ) and variance varT = α(fp )θ(fp )2 . Interestingly, we observed that the execution time of YOLOv8 on images with a high object density can exhibit a bimodal distribution, primarily due to Non-Maximum Suppression (NMS) post-processing. For simplicity, our
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Mean execution time [ms]
103
Empirical BSP model Satellites’ CPU
102 NVIDIA Jetson Orin Nano Super Cloud CPU
NVIDIA Jetson Orin AGX 101
0
500
1000 1500 2000 Clock frequency [MHz]
2500
3000
Figure 7: Estimated mean execution time of YOLOv8 on individual images with the considered computing architectures obtained empirically for all the operating clock frequencies fp (markers) and using the least-squares regression for the BSP model parameters (solid lines).
(a) Jetson Nano
(b) Jetson AGX Orin
0.8
Probability Density
Probability Density
0.8 0.6 0.4 Fitted Distribution 306 MHz 714 MHz 1020 MHz
0.2 0.0
60
80
100
120
Execution Time (ms)
140
0.6 0.4 Fitted Distribution 306 MHz 816 MHz 1300 MHz
0.2 0.0
160
30
40
50
60
70
Execution Time (ms)
80
90
Figure 8: Probability density of YOLOv8 execution time on the NVIDIA Jetson Orin (a) Nano Super and (b) AGX platforms at selected GPU clock frequencies. Solid lines represent fitted Gamma distributions, (p) indicating the execution time distribution follows Tproc (fp ) ∼ Gamma(α(fp ), θ(fp )). Total Computing Time Quantiles Normal Distribution Adjusted