Satellite Clustering Framework

• Satellite clustering frameworks are design patterns that partition satellites, observations, or control domains to meet specific objectives such as interference suppression, reduced latency, and enhanced energy efficiency.
• They employ diverse methodologies—including centroidal, spectral, and graph-based algorithms—to adapt to varying requirements in cooperative transmission, federated learning, and control-plane segmentation.
• Empirical evaluations demonstrate significant improvements in speed, energy savings, and communication efficiency while also highlighting challenges like synchronization overhead and dynamic re-clustering.

A satellite clustering framework is a class of models, architectures, and algorithms that partitions satellites, users, beams, controllers, or satellite-derived observations into coordinated groups in order to optimize a target criterion such as interference suppression, aggregation latency, energy consumption, control overhead, coalition value, coverage, capacity, detection performance, or scientific interpretability. In current arXiv literature, the term spans LEO cooperative-transmission clusters, hierarchical clustered federated learning, coalition-formation on inter-satellite graphs, movement-aware control-domain partitioning, dense formation-flying datacenter clusters, and clustering pipelines for satellite imagery and orbital time series (Jung et al., 2023, Liu et al., 18 Feb 2025, Venkatesh et al., 2024, Zhang et al., 10 Dec 2025, Pénot et al., 14 May 2026, Sharma et al., 2016, Marinho et al., 13 Mar 2026).

1. Conceptual scope and cluster semantics

The meaning of “cluster” is not uniform across the literature. In non-terrestrial networking, a cluster may denote a small set $N_c$ of LEO satellites whose relative distances are kept within a few tens–hundreds of kilometers, with one satellite acting as a master and the others as slaves for cooperative transmission. In hierarchical federated learning, it denotes a set of satellites grouped for local aggregation around a selected parameter server before ground-station aggregation. In coalition-formation work, it denotes a partition of a weighted satellite graph. In hierarchical control-plane design, it denotes an FOV-aware control domain. In dense in-orbit computing, it denotes a formation-flying set of compute satellites constrained by $R_{\min}$ and $R_{\max}$. In remote sensing and orbital analytics, it may denote groups of pixels, hotspot detections, or dynamical trajectories rather than network nodes (Jung et al., 2023, Liu et al., 18 Feb 2025, Venkatesh et al., 2024, Zhang et al., 10 Dec 2025, Pénot et al., 14 May 2026, Li et al., 2023, Marinho et al., 13 Mar 2026).

Setting	Clustered entities	Primary objective
Cooperative NTN	LEO satellites with master/slaves	SINR, throughput, coverage
Hierarchical FL	Satellites, PSs, GSs	$T_c$, $E_c$, model accuracy
Coalition/domain partitioning	Satellite graph nodes or domains	coalition value or control overhead
Dense space datacenters	Formation-flying compute satellites	packing, safety, permanent ISLs
Data/observation clustering	images, hotspots, orbital time series	organization, detection, interpretation

This breadth suggests that a satellite clustering framework is better understood as a design pattern than as a single algorithm. The common structure is a partitioning step, a cluster-internal coordination mechanism, and an application-specific objective function.

2. Optimization criteria and formal problem statements

The optimization target depends on the system layer at which clustering is introduced. In hierarchical federated learning, FedHC formulates the cluster aggregation selection problem as a bicriteria minimization of total processing time and energy consumption. With clusters $\{C^1,\dots,C^K\}$, the framework uses

$$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$

with $t_i^{\text{cmp}}=D_iQ/f_i$, $t_i^{\text{com}}=\zeta/r_i$, and $r_i=B_i\ln(1+P_0h_i/N_0)$. The paper writes $R_{\min}$0 under communication and computing constraints (Liu et al., 18 Feb 2025).

In graph-based coalition formation, the objective is combinatorial rather than latency-centric. The constellation is represented as an undirected weighted graph $R_{\min}$1, with edge weights

$R_{\min}$2

and coalition value

$R_{\min}$3

The optimal partition is

$R_{\min}$4

which is explicitly identified as an NP-hard coalition structure generation problem (Venkatesh et al., 2024).

For cooperative-transmission clusters in NTN, the principal metrics are coverage and capacity. The literature defines coverage probability as

$R_{\min}$5

and cluster sum-rate as

$R_{\min}$6

This formalization connects cluster size, spatial spread $R_{\min}$7, synchronization, and ISL performance directly to radio-level outcomes (Jung et al., 2023).

Control-plane partitioning introduces still another objective. Eunomia minimizes

$R_{\min}$8

over domain assignments and controller placements, subject to single-domain membership, single-controller assignment, ISL connectivity, and FOV feasibility (Zhang et al., 10 Dec 2025).

At the user-clustering layer for multicast precoding, the problem is posed as a within-cluster variance minimization. For users in a beam, the Sum-of-Squared-Errors objective is

$R_{\min}$9

where $R_{\max}$0 may be either a 2-D geographic vector or a normalized channel vector (Guidotti et al., 2017).

Taken together, these formulations show that the “framework” is mathematically heterogeneous: some instances are continuous relaxations over cluster statistics, some are graph partitioning problems, and some are hierarchical resource-allocation mechanisms.

3. Architectural patterns in satellite clustering

A dominant architectural motif is hierarchy. FedHC uses a two-tier scheme. At Tier 1, the constellation is partitioned into $R_{\max}$1 disjoint clusters $R_{\max}$2 based on geographical proximity, one satellite $R_{\max}$3 in each cluster is selected as the parameter server, and cluster aggregation is performed as

$R_{\max}$4

At Tier 2, after $R_{\max}$5 local rounds, cluster-PS satellites upload cluster models to a visible ground station $R_{\max}$6, which computes

$R_{\max}$7

The model is then broadcast back through the same hierarchy (Liu et al., 18 Feb 2025).

SFedSat preserves the two-level aggregation pattern but augments it with semi-supervised guidance and compression. Satellite clusters are formed by K-means in a joint feature space

$R_{\max}$8

PS satellites are selected geographically, ground stations provide supervised learning on labeled data, and unlabeled satellites use FixMatch and CutMix under cluster guidance. Sparsification and adaptive weight quantization are integrated into the aggregation path (Liu et al., 30 Jul 2025).

In cooperative NTN architectures, the cluster head is a master satellite with full gNB functions, while slaves carry gNB-DU only or lower-layer functionality depending on the split. Intra-cluster ISLs may be radio-frequency or free-space optical, with data rates up to $R_{\max}$9 Gbps for intra-PHY split and latency $T_c$0 for tight beamforming synchronization. Functional split options range from an intra-PHY split requiring approximately $T_c$1 Gbps and approximately $T_c$2 latency, to PDCP/RLC-like splits with approximately $T_c$3 Gbps and approximately $T_c$4–$T_c$5 ms latency (Jung et al., 2023).

Control-plane clustering introduces a different hierarchy. Eunomia first performs movement-aware FOV segmentation into non-overlap sets and overlap regions, then applies spectral clustering on a Control Overhead Relationship Graph, and finally assigns controllers with the Kuhn-Munkres algorithm. This architecture is explicitly hybrid, combining ground stations and MEO satellites so that domains remain FOV-aware and signaling remains single-hop (Zhang et al., 10 Dec 2025).

Dense in-orbit datacenter frameworks shift the architectural question from aggregation hierarchy to formation geometry. The proposed planar and 3D clusters keep satellites within a cluster radius $T_c$6, enforce minimum spacing $T_c$7, and require collision avoidance, unobstructed sun-vector exposure, and line-of-sight feasibility for ISLs throughout the entire orbit. The same work embeds a VL2-like Clos switching fabric onto feasible ISLs through integer optimization (Pénot et al., 14 May 2026).

4. Algorithmic repertoire

The algorithmic core of satellite clustering frameworks is correspondingly diverse. A large family relies on centroidal clustering. FedHC groups nearby satellites and selects the satellite closest to the cluster centroid with the strongest expected link quality as cluster PS. SFedSat applies K-means in a joint feature space blending geographic and gradient-based similarity. Multicast precoding work uses k-means++ with either Euclidean distance or channel-vector distance. In satellite-image clustering, Scalable K-Means++ MapReduce initialization is followed by simultaneous multi-$T_c$8 K-means and Simplified Silhouette Index validation, while Spark reuses in-memory RDDs across candidate $T_c$9 values (Liu et al., 18 Feb 2025, Liu et al., 30 Jul 2025, Guidotti et al., 2017, Sharma et al., 2016).

Spectral methods are prominent when similarity is non-Euclidean or dynamic. OSC-FSKD computes pairwise cosine similarities between model updates, builds an affinity matrix $E_c$0, forms the normalized Laplacian

$E_c$1

extracts the $E_c$2 smallest eigenvectors, row-normalizes the embedding, and runs k-means to obtain per-round client clusters. Eunomia uses an analogous spectral-clustering pipeline on the Control Overhead Relationship Graph to segment overlap regions by control-overhead affinity rather than by geometric distance alone (Zou et al., 2024, Zhang et al., 10 Dec 2025).

Graph-theoretic and combinatorial approaches depart from centroid-based clustering entirely. GCS-Q reformulates each coalition split as a QUBO with binary variables $E_c$3, standard coefficients $E_c$4 and $E_c$5, and then applies a hybrid quantum-classical top-down recursion: build QUBO, minor-embed, sample low-energy solutions on the D-Wave Advantage annealer, and accept a split only if $E_c$6 (Venkatesh et al., 2024).

Dynamic re-clustering mechanisms are used when topology or task distribution evolves. FedHC introduces a MAML-style re-clustering step in which newly joined satellites adapt the current initialization through an inner-loop update

$E_c$7

followed by a meta-update

$E_c$8

This is intended to avoid cold-start degradation after cluster changes (Liu et al., 18 Feb 2025).

Task-driven clustering can also be markedly lightweight. In collaborative space object detection, a cluster $E_c$9 exchanges only short metadata messages over 1–10 Gbps ISLs, and a distance-aware viewpoint selection rule chooses exactly one satellite per cluster to run inference: $\{C^1,\dots,C^K\}$0 Alternative fusion methods, including bounding-box merging, voting, and early-fusion, were evaluated but discarded because of large registration errors and prohibitive communication costs (Hu et al., 1 Aug 2025).

Beyond networking, satellite-data clustering frameworks employ domain-specific feature pipelines. Bushfire tracking clusters hotspots through sliding windows, geodesic adjacency, connected components, and temporal label inheritance. Orbital synthetic-data clustering applies MiniRocket to 400-timestep resonant-angle series, producing 9,996 features, then uses UMAP $\{C^1,\dots,C^K\}$1 PCA and K-Means to recover dynamical regimes (Li et al., 2023, Marinho et al., 13 Mar 2026).

5. Empirical performance and observed trade-offs

Reported performance gains are substantial but application-specific. On a high-fidelity LEO simulator with altitude $\{C^1,\dots,C^K\}$2 km, inclination $\{C^1,\dots,C^K\}$3, and ground-station elevation $\{C^1,\dots,C^K\}$4, FedHC evaluates LeNet on MNIST and CIFAR-10. For $\{C^1,\dots,C^K\}$5 clusters on MNIST, to reach $\{C^1,\dots,C^K\}$6 accuracy, C-FedAvg requires $\{C^1,\dots,C^K\}$7 s and $\{C^1,\dots,C^K\}$8 J, whereas FedHC requires $\{C^1,\dots,C^K\}$9 s and $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$0 J, corresponding to approximately $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$1 speed-up and approximately $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$2 energy saving. SFedSat reports up to $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$3 faster processing, up to $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$4 lower energy consumption, compression ratios of $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$5–$$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$6 for $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$7 clients and $$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$8–$$T_c=\sum_{k=1}^K\left[\max_{i\in C^k}T_i^{\text{round}}+t^{\text{com}}_{p_k\to G}\right], \qquad E_c=\sum_{k=1}^K\left[\sum_{i\in C^k}P_0\frac{|w_i|}{r_i}+\sum_{i\in C^k}\epsilon_0 f_i t_i^{\text{cmp}}\right],$$9 for $t_i^{\text{cmp}}=D_iQ/f_i$0 clients, and accuracy after $t_i^{\text{cmp}}=D_iQ/f_i$1 rounds of approximately $t_i^{\text{cmp}}=D_iQ/f_i$2 on CIFAR-10 and approximately $t_i^{\text{cmp}}=D_iQ/f_i$3 on SAT-6 (Liu et al., 18 Feb 2025, Liu et al., 30 Jul 2025).

For graph partitioning, GCS-Q is evaluated on both synthetic graphs and real TLEs of approximately $t_i^{\text{cmp}}=D_iQ/f_i$4 Starlink satellites from Celestrak. For dense graphs with sparsity $t_i^{\text{cmp}}=D_iQ/f_i$5 and $t_i^{\text{cmp}}=D_iQ/f_i$6, total remote-annealer time is already below Gurobi’s, on-site QPU calls take $t_i^{\text{cmp}}=D_iQ/f_i$7 s up to the hardware limit, and solution quality is essentially indistinguishable from Gurobi with $t_i^{\text{cmp}}=D_iQ/f_i$8. On the real Starlink graph, clustering reduces the total number of communication links by approximately $t_i^{\text{cmp}}=D_iQ/f_i$9–$t_i^{\text{com}}=\zeta/r_i$0 (Venkatesh et al., 2024).

Control-domain partitioning shows similarly large systems-level effects. Under a Starlink-like constellation with $t_i^{\text{com}}=\zeta/r_i$1 satellites, $t_i^{\text{com}}=\zeta/r_i$2 MEO satellites, and $t_i^{\text{com}}=\zeta/r_i$3 ground stations, Eunomia reduces average request loss by up to $t_i^{\text{com}}=\zeta/r_i$4, control overhead by up to $t_i^{\text{com}}=\zeta/r_i$5, and algorithm execution time by $t_i^{\text{com}}=\zeta/r_i$6 relative to the reported baselines (Zhang et al., 10 Dec 2025).

Performance gains in radio access are more conditional. For clustered NTN, the simulation study shows that when the number of satellites is large, clustered networks outperform unclustered ones, but for small $t_i^{\text{com}}=\zeta/r_i$7 unclustered deployment is better because overhead exceeds cooperation gain. At $t_i^{\text{com}}=\zeta/r_i$8, clustered networks achieve a $t_i^{\text{com}}=\zeta/r_i$9–$r_i=B_i\ln(1+P_0h_i/N_0)$0 dB SINR gain over unclustered ones. The reported optimal cluster size lies in $r_i=B_i\ln(1+P_0h_i/N_0)$1–$r_i=B_i\ln(1+P_0h_i/N_0)$2 satellites, while beyond $r_i=B_i\ln(1+P_0h_i/N_0)$3 synchronization and ISL constraints outweigh the added diversity and beamforming gain. DPS surpasses MRT-JT for $r_i=B_i\ln(1+P_0h_i/N_0)$4 because it reduces interference (Jung et al., 2023).

Task-oriented sensing frameworks show a different trade-off profile. In collaborative object detection with cluster size $r_i=B_i\ln(1+P_0h_i/N_0)$5, the distance-based viewpoint set $r_i=B_i\ln(1+P_0h_i/N_0)$6 yields a $r_i=B_i\ln(1+P_0h_i/N_0)$7 mAP50 gain over the best single view in far clusters. The GELAN-ViT-SE model attains overall mAP50 $r_i=B_i\ln(1+P_0h_i/N_0)$8 versus $r_i=B_i\ln(1+P_0h_i/N_0)$9 for GELAN-t, at $R_{\min}$00 versus $R_{\min}$01 GFLOPs, and both models remain below $R_{\min}$02 ms inference time with peak power around $R_{\min}$03 W on Jetson Orin Nano. For non-IID imagery, OSC-FSKD reports observation accuracy $R_{\min}$04, average accuracy $R_{\min}$05, and Macro F1 $R_{\min}$06 on SAT4, with reported improvements over pFedSD, FedProx, FedAU, and FedALA (Hu et al., 1 Aug 2025, Zou et al., 2024).

6. Limitations, misconceptions, and research directions

A common misconception is that satellite clustering is synonymous with static geographic grouping. The literature does not support that view. Clusters may be formed from orbital proximity, gradient similarity, channel similarity, FOV overlap, control-overhead relations, or task-specific metadata, and may be recomputed every federated round or every topology slot (Zou et al., 2024, Zhang et al., 10 Dec 2025, Liu et al., 30 Jul 2025). A related misconception is that clustering is uniformly beneficial. Cooperative NTN results explicitly show a regime in which unclustered deployment outperforms clustered deployment because clustering overhead dominates, and even within clustered systems there is a reported diminishing-return region beyond $R_{\min}$07 (Jung et al., 2023).

The main technical limitations recur across frameworks. SFedSat states that PS selection and cluster partition are NP-hard and therefore handled by heuristic K-means plus centrality, while rapid orbital movement can break clusters and induce re-clustering overhead. Cooperative-transmission clusters depend on stringent ISL data-rate, latency, and synchronization budgets. Dense datacenter clusters must satisfy collision avoidance, unobstructed sun-vector exposure, and permanent LOS feasibility over the entire orbit. In multicast precoding, high-dimensional channel metrics can cause variable-size k-means++ clusters to become skewed. In collaborative vision, multi-view fusion was rejected because registration errors and communication costs were prohibitive (Liu et al., 30 Jul 2025, Jung et al., 2023, Pénot et al., 14 May 2026, Guidotti et al., 2018, Hu et al., 1 Aug 2025).

Current research directions therefore emphasize adaptive and multi-objective designs rather than fixed clustering recipes. The literature identifies inter-cluster coordination, fault tolerance and master redundancy, secure synchronization, AI-driven cluster management, advanced waveforms and multiple access, and cross-layer optimization as open problems in clustered NTN. Coalition-formation work points to dynamic re-clustering on affected coalitions, heterogeneous satellite capabilities, and multi-objective extensions. Semi-supervised clustered FL points to differential privacy and more adaptive clustering under real orbital dynamics. Satellite-aided communication studies suggest integrated solutions that couple cluster assignment with beam activation and power allocation (Jung et al., 2023, Venkatesh et al., 2024, Liu et al., 30 Jul 2025, Thi-Thanh et al., 17 Sep 2025).

In aggregate, the contemporary satellite clustering framework is best understood as a unifying systems abstraction for structured coordination under orbital dynamics, constrained communications, and heterogeneous objectives. Its enduring technical content lies not in any single clustering rule, but in the explicit coupling between partition structure, inter-satellite or satellite-ground constraints, and end-to-end performance metrics.