Adaptive Spiking Gating Multi-Scale Liquid State Machine for Orbital Maneuver Detection

Abstract

Orbital maneuver detection is a core component of space situational awareness. The multi-scale characteristics of satellite orbital behavior and sample imbalance issues lead to challenges in existing methods, including insufficient feature adaptation and limited detection accuracy. This paper proposes an Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) for orbital maneuver detection based on variations in satellite orbital parameters. The method integrates multi-scale reservoir pools with different scale-dependent decay factors and Leaky Integrate-and-Fire (LIF) neurons to enhance multi-scale temporal feature extraction capability. A spiking gating network is designed to adaptively learn fusion weights for multi-scale features, replacing traditional fixed equal-weight fusion strategies. During training, weighted binary cross-entropy loss is employed to address class imbalance. Experimental results based on real satellite data demonstrate that the proposed method significantly outperforms baseline models in maneuver detection metrics, achieving higher recall, improving feature separability, and reducing both missed detections and false alarms. These results indicate that the proposed method provides a robust solution for orbital maneuver detection.

1. Introduction

The rapid development of Low Earth Orbit (LEO) satellites has made the detection of orbital maneuvers a fundamental task in the field of Space Situational Awareness (SSA). Reliable identification of maneuver events is a critical prerequisite for collision avoidance, orbital resource allocation, and space behavior analysis. Consequently, satellite orbital maneuver detection technology has garnered widespread attention in both the aerospace and computational intelligence communities.

Existing orbital maneuver detection methods can be broadly divided into physics-driven and data-driven approaches. Physics-driven methods usually infer maneuvers by analyzing orbital dynamics, prediction residuals, or anomalies derived from two-line element (TLE) data and observational measurements [1,2,3,4]. These methods are generally interpretable and consistent with orbital mechanics, but their performance may degrade when maneuver patterns become increasingly complex or when satellite populations grow rapidly. In parallel, data-driven methods, including conventional machine learning and deep learning models, have been introduced for maneuver detection and orbit behavior analysis [5,6,7,8]. Although these methods have shown promising performance, they still face several limitations. In particular, many existing approaches do not explicitly model the multi-scale temporal characteristics of orbital evolution, exhibit limited robustness under class-imbalanced conditions, and lack an adaptive mechanism for cross-scale feature fusion.

Spiking neural networks (SNNs), as a biologically inspired neural computing paradigm, are particularly well suited for temporal information processing, owing to their event-driven dynamics and high energy efficiency [9]. Among them, Liquid State Machines (LSMs) [10] provide a reservoir computing framework that realizes nonlinear temporal mapping through a randomly connected spiking reservoir, thereby avoiding the computational burden of backpropagation through time. This makes LSMs especially attractive for time-series analysis tasks. However, conventional LSMs typically employ homogeneous neuronal time constants within a single reservoir, which limits their ability to simultaneously capture fast transient responses and slow temporal dependencies. This limitation is particularly pronounced in satellite maneuver detection, where variations in orbital parameters exhibit multiple time scales, ranging from rapid thrust-induced changes to gradual orbital drift.

To address these limitations, this paper proposes an Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) for satellite orbital maneuver detection. The main contributions of this study are as follows:

• Unlike conventional Liquid State Machines (LSMs) that rely on homogeneous reservoir dynamics, we design a multi-scale reservoir architecture with different scale-dependent decay factors. Parallel LSM modules explicitly capture temporal features at different scales—fast-scale reservoirs respond sensitively to abrupt orbital changes, while slow-scale reservoirs model long-term trends—thereby achieving more comprehensive multi-rate temporal dynamics modeling for satellite maneuver detection.
• A learnable spiking gating mechanism based on Leaky Integrate-and-Fire (LIF) neurons is implemented as a multi-layer LIF network that learns scale-specific fusion weights for multi-scale reservoir states through spike-driven computation. It replaces fixed equal-weight fusion and incorporates per-scale feature transformations with a projection-based residual pathway to enhance feature discrimination, achieving class-discriminative feature aggregation that emphasizes scale-specific patterns for maneuver and non-maneuver samples.
• To address the severe class imbalance in satellite maneuver detection, we employ a weighted binary cross-entropy loss, which ensures balanced optimization between the minority maneuver class and the majority non-maneuver class during training.

2. Related Work

2.1. Orbital Maneuver Detection Based on Two-Line Element and Observational Data

Traditional maneuver detection methods often rely on two-line element (TLE) data for maneuver identification. Lemmens [11] analyzed the maneuver events of low Earth orbit (LEO) satellites based on TLE data through consistency checks and time-series analysis. Cui [12] proposed a spacecraft orbit-transfer maneuver detection method based on TLE data, in which in-plane orbital maneuvers of on-orbit spacecraft were identified by detecting variations in the semi-major axis and the minimum relative distance. Kelecy [13] designed and implemented a maneuver detection algorithm using TLE data, which identifies abnormally large discrepancies between adjacent data segments by analyzing smoothed differences in TLE time-history data and uses these discrepancies as indicators of maneuver events. Shorten [14] proposed a particle filter (PF)-based TLE anomaly detection method, in which the proposal distribution was optimized to improve filtering efficiency and anomaly detection accuracy. Liu [15] developed a TLE outlier detection filter based on the Expectation-Maximization (EM) algorithm, where variance was estimated through polynomial regression and prediction to determine outlier thresholds. Zhong [16] proposed an orbital maneuver inversion model and a situation assessment value calculation model, using discrete orbital data to analyze satellite maneuver epochs and situational states. However, when confronted with increasingly complex maneuver patterns and the growing number of satellites, these methods still face challenges in terms of detection efficiency and accuracy.

2.2. Orbital Maneuver Detection Based on Data-Driven Methods

Conventional maneuver detection methods often struggle to meet practical requirements in terms of both efficiency and accuracy when confronted with increasingly complex maneuver patterns and the growing number of satellites. As a result, data-driven orbital maneuver detection has become an important research area. Early studies primarily employed machine learning methods. Perovich [17] adopted a Random Forest approach and combined it with deep neural networks to train and validate the model using simulated data, achieving a significantly lower false alarm rate than that of traditional statistical methods. Bai [18] proposed a multi-scale maneuver detection method based on K-means, hierarchical clustering, and fuzzy C-means clustering algorithms, while employing silhouette analysis for feature selection and determination of the number of clusters, thereby enabling automatic maneuver threshold selection and yielding lower false alarm and missed detection rates than conventional threshold-based methods. More recent studies have increasingly leveraged deep learning techniques, particularly convolutional neural networks (CNNs) and long short-term memory (LSTM) networks, for orbital maneuver detection and prediction. Ying [19] employed an LSTM network to analyze residuals in observational data in order to determine whether a satellite had performed a maneuver. Long [20] addressed the problem of identifying future maneuver states of GEO satellites by integrating LSTM, CNN, transfer entropy, and attention mechanisms, and further optimized the network parameters using intelligent algorithms, thereby achieving accurate prediction of future satellite longitude variations and maneuver identification. Wu [21] utilized an LSTM model to capture long-term dependencies in satellite orbital data, significantly improving orbit prediction accuracy. Despite the considerable potential of data-driven methods for orbital maneuver detection, existing studies still exhibit several limitations. Mainstream deep learning approaches rely heavily on large-scale labeled datasets and show limited generalization capability under class-imbalanced conditions. In addition, their ability to characterize the multi-scale temporal features and complex spatiotemporal correlations inherent in orbital maneuver processes remains insufficient.

3. Proposed Method

3.1. Overview

The proposed satellite maneuver detection method is built upon an Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) architecture, as illustrated in Figure 1, with the objective of effectively characterizing the multi-scale temporal dynamics embedded in orbital parameter sequences. Specifically, the method first constructs a parallel multi-scale liquid-state reservoir with different scale-dependent decay factors, enabling the extraction of rapid variation information and slow-varying trend features during orbital evolution, and thereby achieving collaborative modeling of temporal dynamics across multiple time scales. Subsequently, a learnable spiking-gating mechanism based on spiking neurons is introduced to adaptively fuse the outputs of reservoirs at different scales, so as to emphasize the key scale-specific information that contributes most to maneuver discrimination. On this basis, final classification is performed by combining feature enhancement and projection-based representation, thereby improving the model’s capability to distinguish maneuvering from non-maneuvering states. By integrating multi-scale spiking reservoir computation with an adaptive gating-based fusion mechanism, the proposed method is able to more fully exploit the multi-resolution temporal dependencies inherent in complex orbital dynamics, thus enabling robust and efficient detection of satellite maneuver events.

3.2. Multi-Scale Liquid State Machine

The Liquid State Machine (LSM) is a biologically inspired reservoir computing paradigm that projects input temporal signals into a high-dimensional dynamical system, as illustrated in Figure 2. Unlike conventional recurrent neural networks, which require training of all network weights, the LSM maintains randomly initialized reservoir connections and trains only a lightweight readout layer, thereby offering significant computational advantages for temporal processing. The fundamental principle of the LSM lies in the separation between temporal dynamics, handled by the reservoir, and pattern recognition, performed by the readout layer, which enables efficient learning while preserving rich temporal representations. Given an input time series $\mathbf{x}\left(t\right)$ and the corresponding target output $y\left(t\right)$, the LSM can be formulated as two sequential mappings [22]:

$${\mathbf{x}}^M\left(t\right)=L^M\left(\mathbf{x}\left(t\right)\right)$$

$$y\left(t\right)=f^M\left({\mathbf{x}}^M\right(t\left)\right)$$

where ${\mathbf{x}}^M\left(t\right)$ represents the reservoir state vector, $L^M$ denotes the liquid transformation implemented by the reservoir, and $f^M$ represents the memoryless readout function.

However, conventional single-scale LSMs exhibit inherent limitations when handling multi-resolution spatiotemporal data, particularly in capturing temporal dependencies that evolve over different time horizons. To address this issue, a Multiscale Liquid State Machine (M-LSM) architecture [23] is adopted to capture such multi-scale temporal structures. Specifically, the reservoir is divided into $K$ parallel sub-reservoirs, each operating at a distinct temporal scale. For the $k$-th sub-reservoir, all neurons share the same decay factor ${\beta }_k$, which controls the temporal memory of the reservoir dynamics. The membrane potential dynamics of neuron $i$ in sub-reservoir $k$ are updated in discrete time as

$${\mathit{u}}_i^{\left(k\right)}\left(t+1\right)={{\beta }_k\mathit{u}}_i^{\left(k\right)}\left(t\right)\left({\mathbf{1}-\mathit{s}}_i^{\left(k\right)}\left(t\right)\right)+{\sum }_j{\mathit{W}}_{res,ij}^{\left(k\right)}{\mathit{s}}_j^{\left(k\right)}\left(t\right)+{\sum }_j{\mathit{W}}_{in,ij}^{\left(k\right)}{\mathit{x}}_j\left(\mathrm{t}\right)$$

where ${\mathit{u}}_i^{\left(k\right)}\left(t\right)$ denotes the membrane potential of neuron $i$ in the $k$-th sub-reservoir at time $t$, ${\mathit{s}}_j^{\left(k\right)}\left(t\right)$ denotes the spike output of presynaptic neuron $j$ at time $t$, and ${\mathit{x}}_j\left(t\right)$ denotes the $j$-th component of the input signal at time $t$. ${\mathit{W}}_{res}^{\left(k\right)}$ and ${\mathit{W}}_{in}^{\left(k\right)}$ represent the recurrent reservoir weight matrix and input projection matrix, respectively. In accordance with the standard reservoir computing paradigm, both ${\mathit{W}}_{res}^{\left(k\right)}$ and ${\mathit{W}}_{in}^{\left(k\right)}$ are randomly initialized before training and then kept fixed, while only the downstream trainable modules are optimized. When the membrane potential exceeds a predefined threshold, the neuron emits a spike and is subsequently reset. Each sub-reservoir processes the input sequence independently and produces a scale-specific state representation. The resulting multi-scale representations capture temporal dynamics ranging from rapid transient variations to slowly evolving trends.

3.3. Feature Enhancement and Adaptive Gating Fusion

Although the multi-scale reservoir can capture temporal dynamics at different time scales, the original reservoir states may still contain redundant information and may not provide sufficient discriminative capability for complex orbital maneuver detection. To improve the quality of multi-scale representations, a feature refinement mechanism is introduced on top of the multi-scale liquid state outputs, including scale-specific feature enhancement, adaptive gating fusion, and joint representation construction.

For the output of the $k$-th sub-reservoir, denoted by ${\mathbf{h}}^{\left(k\right)}$, the state vector is first obtained by temporal integration of the spike responses over the input window:

$${\mathbf{h}}^{\left(k\right)}=IntegrateSpikes\left({\mathit{s}}^{\left(k\right)}\right)={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}{\mathit{s}}_t^{\left(k\right)}$$

where ${\mathbf{s}}_t^{\left(k\right)}$ denotes the spike output of the $k$-th sub-reservoir at time step $t$, and $T$ is the window length. Thus, ${\mathbf{h}}^{\left(k\right)}$ represents the time-averaged spike response of the $k$-th sub-reservoir over the observation window. Although ${\mathbf{h}}^{\left(k\right)}$ is a temporally aggregated representation, the sequential information has already been encoded through the recurrent membrane dynamics and spike evolution across the full time window.

A scale-specific enhancement module is then applied to ${\mathbf{h}}^{\left(k\right)}$ to obtain

$${\mathbf{e}}^{\left(k\right)}=E_k\left({\mathbf{h}}^{\left(k\right)}\right)$$

where $E_k(\cdot )$ denotes the feature enhancement network at the $k$-th scale. This module maps the original $H$-dimensional reservoir state into an enhanced feature space of dimension $H/2$. Since different temporal scales correspond to different dynamic patterns, independent enhancement modules are used for different scales so that scale-adaptive transformations can be learned before feature fusion.

After feature enhancement, an adaptive spiking gating mechanism is introduced to model the relative importance of different temporal scales. First, the original multi-scale joint representation is constructed as

$${\mathbf{h}}_{\mathrm{r}\mathrm{a}\mathrm{w}}=\left[{\mathbf{h}}^{\left(1\right)}; {\mathbf{h}}^{\left(2\right)};\cdots ; {\mathbf{h}}^{\left(K\right)}\right]$$

It is then fed into the spiking gating network

$$\mathbf{g}=G_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{k}\mathrm{e}}\left({\mathbf{h}}_{\mathrm{r}\mathrm{a}\mathrm{w}}\right)$$

where $G_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{k}\mathrm{e}}(\cdot )$ consists of linear transformations, batch normalization, LIF neurons, and dropout layers. It should be noted that the inputs to the gating network are time-aggregated reservoir representations rather than raw spike trains. For each sub-reservoir, the temporal state is first summarized over the input window by averaging the spike responses across time steps. Therefore, ${\mathbf{h}}_{\mathrm{r}\mathrm{a}\mathrm{w}}$ is a static sample-level feature vector constructed from multi-scale temporal summaries.

Although LIF neurons are used in the intermediate layers of the gating network, the final pre-softmax output $\mathbf{g}$ is generated by a last linear layer, so that $\mathbf{g}$ is a continuous logit vector rather than a binary spike vector. The adaptive scale weights are then obtained by

$$\mathit{\alpha }=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}\left(\mathbf{g}\right)$$

where $\mathit{\alpha }=\left[{\alpha }_1,{\alpha }_2,\cdots ,{\alpha }_K\right]$, and ${\displaystyle {\sum }_{k=1}^K}{\alpha }_k=1$. In this way, the contribution of each temporal scale is determined adaptively for each input sample rather than being fixed in advance. Based on these weights, the enhanced scale-specific features are fused as

$${\mathbf{h}}_{\mathrm{f}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d}}={\displaystyle \sum _{k=1}^K}{\alpha }_k{\mathbf{e}}^{\left(k\right)}$$

To further improve the discriminability of the learned representation, a projection head is introduced on the concatenated enhanced features. Let

$${\mathbf{e}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{t}}=\left[{\mathbf{e}}^{\left(1\right)}; {\mathbf{e}}^{\left(2\right)};\cdots ; {\mathbf{e}}^{\left(K\right)}\right]$$

then the projected representation is defined as

$$\mathbf{z}=P\left({\mathbf{e}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{t}}\right)$$

where $P(\cdot )$ denotes the projection head network. The projected feature $\mathbf{z}$ is not used as an independent classification branch. Instead, it is introduced as a complementary representation to the fused feature ${\mathbf{h}}_{\mathrm{f}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d}}$, so that additional discriminative information can be incorporated into the final feature space.

3.4. Classification Layer and Loss Function

After adaptive fusion, the fused representation ${\mathbf{h}}_{\mathrm{f}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d}}$ and the projected representation $\mathbf{z}$ are concatenated to form the classification input:

$${\mathit{h}}_{final}=\left[{\mathbf{h}}_{\mathrm{f}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d}};\mathbf{z}\right]$$

This joint representation combines the multi-scale dynamic information selected by the adaptive gating mechanism with the complementary discriminative information provided by the projection head. The final prediction is produced by the readout network:

$$o=F_{\mathrm{c}\mathrm{l}\mathrm{s}}\left({\mathit{h}}_{final}\right)$$

where $F_{\mathrm{c}\mathrm{l}\mathrm{s}}(\cdot )$ denotes the classification readout network and $o$ is the scalar output logit.

Because maneuver samples are usually much fewer than non-maneuver samples, the class distribution is imbalanced. To address this issue, a weighted binary cross-entropy loss is adopted. Let $y_i\in \left\{\mathrm{0,1}\right\}$ denote the ground-truth label and $o_i$ denote the output logit of the $i$-th sample. The classification loss is defined as

$${\mathcal{L}}_{\mathrm{c}\mathrm{l}\mathrm{s}}=-\sum _i\left[{\omega }_{\mathrm{p}\mathrm{o}\mathrm{s}} y_i\log \sigma \left(o_i\right)+\left(1-y_i\right)\log \left(1-\sigma \left(o_i\right)\right)\right]$$

where $\sigma (\cdot )$ denotes the sigmoid function and ${\omega }_{\mathrm{p}\mathrm{o}\mathrm{s}}$ is the positive-class weight. Let $N_{\mathrm{p}\mathrm{o}\mathrm{s}}$ and $N_{\mathrm{n}\mathrm{e}\mathrm{g}}$ denote the numbers of positive and negative samples in the training set, respectively. The positive-class weight is defined as

$${\omega }_{\mathrm{p}\mathrm{o}\mathrm{s}}={\displaystyle \frac{N_{\mathrm{n}\mathrm{e}\mathrm{g}}}{N_{\mathrm{p}\mathrm{o}\mathrm{s}}+\epsilon }}$$

where $\epsilon$ is a small constant introduced to avoid division by zero. This weighting increases the contribution of maneuver samples during optimization and alleviates the bias toward the majority class.

It should be noted that the above expression is written in an explicit form using the sigmoid function for clarity, while in implementation, the loss is computed directly from logits using the mathematically equivalent weighted binary cross-entropy with logits formulation for improved numerical stability. Accordingly, the sigmoid function is not applied before loss computation during training, but is used only to convert logits into probabilities for inference and evaluation:

$$\widehat{y}=\sigma \left(o\right)$$

where $\widehat{y}\in \left(\mathrm{0,1}\right)$ denotes the predicted probability.

The overall training procedure of the proposed Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) for satellite orbital maneuver detection is summarized in Algorithm 1.

Algorithm 1 ASG-MSLSM Satellite Maneuver Detection
Input: Orbital time-series dataset: $\mathit{X}\in {\mathbb{R}}^{N\times T\times d},$ Maneuver labels: $\mathit{y}\in \{\mathrm{0,1}{\}}^N,$ Number of scales: $K,$ Epochs: $E,$ Batch size: $B$ Output: Trained model parameters: ${\mathsf{\Theta }}^{*},$ Prediction results: $\widehat{\mathit{y}}$
1: Preprocess satellite data:
2: ${\mathit{X}}_{feat}$←CreateFeatures($\mathit{X}$)	▷ Feature construction
3: ${\mathit{X}}_{scaled}$←StandardScaler(${\mathit{X}}_{feat}$) 4: Split (${\mathit{X}}_{scaled},$ $\mathit{y}$) into (${\mathit{X}}_{train},$ ${\mathit{X}}_{val},$ ${\mathit{X}}_{test},$ ${\mathit{y}}_{train},$ ${\mathit{y}}_{val},$ ${\mathit{y}}_{test}$)
5: Define multi-scale decay factors $\left\{{\beta }_1,\dots ,{\beta }_K\right\}$ 6: Initialize $K$ spiking reservoirs ${\left\{{\mathit{W}}_{res}^{\left(k\right)},{\mathit{W}}_{in}^{\left(k\right)} \right\}}_{k=1}^K$ 7: Initialize feature enhancement networks $\left\{E_k{\}}_{k=1}^K\right.$ 8: Initialize spiking gating network $G_{spike}$ 9: Initialize projection head $P$ 10: Initialize readout network $F_{cls}$ 11: for epoch = 1 to E do 12:     for each mini-batch $\left({\mathit{X}}_b, {\mathit{y}}_b\right)$ from $\left({\mathit{X}}_{train}, {\mathit{y}}_{train}\right)$ do 13:         Encode input sequence ${\mathit{X}}_{enc}\leftarrow \mathrm{RepeatEncoding}\left({\mathit{X}}_b\right)$ 14:         for $k=1$ to $K$ do 15:             for $t=1$ to $T$ do 16:                ${\mathit{u}}^{\left(k\right)}\left(t+1\right)={\beta }_k{\mathit{u}}^{\left(k\right)}\left(t\right)\left(1-{\mathit{s}}^{\left(k\right)}\left(t\right)\right)+{\mathit{W}}_{res}^{\left(k\right)}{\mathit{s}}^{\left(k\right)}\left(t\right)+{\mathit{W}}_{in}^{\left(k\right)}{\mathit{X}}_{enc}\left(t\right)$
▷Update membrane potential
17:                ${\mathit{s}}^{\left(k\right)}\left(t+1\right)=H\left({\mathit{u}}^{\left(k\right)}\left(t+1\right)-\theta \right)$	▷Generate spike
18:             end for
19:             ${\mathit{h}}^{\left(k\right)}\leftarrow \mathrm{IntegrateSpikes}\left({\mathit{s}}^{\left(k\right)}\right)$	▷Reservoir state
20:             ${\mathit{e}}^{\left(k\right)}\leftarrow E_k\left({\mathit{h}}^{\left(k\right)}\right)$	▷Feature enhancement
21:         end for
22:         ${\mathit{h}}_{raw}=[{\mathit{h}}^{\left(1\right)};{\mathit{h}}^{\left(2\right)};\dots ;{\mathit{h}}^{\left(K\right)}]$	▷Construct raw multi-scale representation
23:         $\mathit{\alpha }=softmax\left(G_{spike}\right({\mathit{h}}_{raw}\left)\right)$	▷Compute gating weights
24:         ${\mathit{h}}_{fused}={\displaystyle {\sum }_{k=1}^K}{\alpha }_k{\mathit{e}}^{\left(k\right)}$	▷Fuse enhanced features
25:         ${\mathit{e}}_{concat}=[{\mathit{e}}^{\left(1\right)};{\mathit{e}}^{\left(2\right)};\dots ;{\mathit{e}}^{\left(K\right)}]$	▷Concatenate enhanced features
26:         $\mathit{z}\leftarrow P\left({\mathit{e}}_{concat}\right)$	▷Projection feature
27:         ${\mathit{h}}_{final}=[{\mathit{h}}_{fused};\mathit{z}]$	▷Joint representation
28:         $o\leftarrow F_{cls}\left({\mathit{h}}_{final}\right)$ 29:         ${\mathcal{L}}_{\mathrm{c}\mathrm{l}\mathrm{s}}\leftarrow$ WBCEWithLogits $\left(o,{\mathit{y}}_b\right)$ 30:         $\widehat{ \mathit{y}}\leftarrow \sigma \left(o\right)$ 31:         Backpropagate with surrogate gradients 32:         Update parameters: $\mathsf{\Theta }\leftarrow \mathsf{\Theta }-\eta {\nabla }_{\mathsf{\Theta }}\mathcal{L}$ 33:     end for 34:     Evaluate model on $\left({\mathit{X}}_{val}{,\mathit{y}}_{val}\right)$: 35:     Adjust learning rate or apply early stopping 36: end for

4. Experiments

4.1. Dataset

The dataset used in this study was adopted from the benchmark dataset reported by Chen et al. [24], which was constructed from publicly available Two-Line Element (TLE) sets released on Space-Track.org. According to the source paper, the dataset covers orbital elements published between November and December 2021 and is organized into two subsets, namely OC.mat for maneuver samples and NC.mat for non-maneuver samples. Such a temporal span may provide only limited coverage of seasonal variability in low Earth orbit (LEO) conditions. It should be noted that raw TLE data do not contain native maneuver annotations. Therefore, in this benchmark, the labels were generated using a rule-based criterion based on the variation in semi-major axis: samples with semi-major-axis changes exceeding a statistically derived threshold of ±0.1 km were categorized as maneuver samples, whereas samples with variations within the corresponding natural range were categorized as non-maneuver samples.

Each data instance comprises a 24-dimensional feature vector that captures the orbital parameters of a given satellite object at adjacent observation moments. The features are organized into three categories: orbital elements at the previous observation, orbital elements at the subsequent observation, and derived features. Specifically, the feature vector includes the following components:

• Orbital elements at the previous observation:

  1.

  Target orbital elements number (previous observation)

  2.

  Satellite ID (previous observation)

  3.

  Epoch time (previous observation)

  4.

  Orbital inclination (previous observation)

  5.

  Right ascension of the ascending node—RAAN (previous observation)

  6.

  Eccentricity (previous observation)

  7.

  Argument of perigee (previous observation)

  8.

  Mean anomaly (previous observation)

  9.

  Mean motion (revolutions per day, previous observation)

  10.

  Revolution number at epoch (previous observation)

  11.

  Semi-major axis (previous observation)

• Orbital elements at the subsequent observation:

  12.

  Target orbital elements number (subsequent observation)

  13.

  Satellite ID (subsequent observation)

  14.

  Epoch time (subsequent observation)

  15.

  Orbital inclination (subsequent observation)

  16.

  RAAN (subsequent observation)

  17.

  Eccentricity (subsequent observation)

  18.

  Argument of perigee (subsequent observation)

  19.

  Mean anomaly (subsequent observation)

  20.

  Mean motion (revolutions per day, subsequent observation)

  21.

  Revolution number at epoch (subsequent observation)

  22.

  Semi-major axis (subsequent observation)

• Derived features:

  23.

  Change in semi-major axis (subsequent observation minus previous observation)

  24.

  maneuver label (0 for non-maneuver, 1 for maneuver)

This data organization supports sequence-based detection and analysis of satellite maneuvers. The training, validation, and test sets were partitioned by non-overlapping satellite IDs, while the chronological order of observations was preserved within each satellite sequence, thereby reducing the risk of temporal information leakage. Since the adopted labels are derived from a threshold-based rule rather than externally validated maneuver logs, potential label noise or bias may still exist, especially for subtle maneuvers and borderline cases.

4.2. Parameter Configuration

The main hyperparameters of the proposed Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) are summarized in

Table 1. Model Hyperparameter Configuration.

Parameter Category	Parameter Name	Value	Functional Description
Input	input_dims	6	Dimensionality of orbital element features for model input
Multi-Scale Reservoir	num_scales	3	Number of temporal scales (sub-reservoirs)
	reservoir_size	256	Total number of neurons in multi-scale reservoir
	decay_factors	[2.0, 5.0, 10.0]	Scale-dependent decay factors used to characterize different temporal scales in the multi-scale reservoirs.
	sparsity	0.1	Sparsity ratio of recurrent reservoir connections
Gating Network	gating_dims	[768, 256, 128, 3]	Network structure for generating adaptive gating weights
Feature Enhancement	enhancement_dim	128	Output dimension per scale for feature enhancement
Projection Head	projection_dims	[384, 256, 128]	Feature projection dimensions for discriminative representation
	projection_head_activation	LIF	Activation function: LIF (ATan surrogate gradient) for hidden layers, linear (no activation) for output layer
Readout Network	readout_dims	[192, 128, 64, 1]	Network structure concatenating fusion and projection features
	readout_network_activation	LIF	Activation function: LIF (ATan surrogate gradient) for hidden layers, linear (no activation) for output layer
	dropout	0.3	Dropout rate for regularization
Training Configuration	batch_size	256	Batch size for model training
	epochs	100	Total number of training epochs
	optimizer	AdamW	Optimizer with weight decay regularization
	learning_rate	0.001	Initial learning rate
	weight_decay	1 × 10−4	Weight decay coefficient

. The input dimension is set to 6 according to the selected orbital element features. Specifically, the six input channels are not formed by directly using paired pre- and post-maneuver orbital states. Instead, they are defined as time-ordered orbital-change variables computed between two consecutive observations for each satellite, including semi-major-axis change, inclination change, eccentricity change, RAAN change, argument-of-periapsis change, and mean-anomaly change. These six sequentially computed variables constitute the original input feature set of the model. The maneuver indicator is not used as an input feature; it is treated only as the supervision label for the target time step. The multi-scale reservoir contains 3 temporal scales with 256 neurons, and the membrane time constants are set to $\left(2.0, 5.0, 10.0\right)$ to capture temporal dynamics at different response rates. The reservoir adopts sparse recurrent connections with a sparsity ratio of 0.1. The spiking gating network uses a three-layer architecture of $768\to 256\to 128\to 3$, while the projection head is configured as $384\to 512\to 256\to 128$. The readout network uses a hidden dimension of 128 with a dropout rate of 0.3. During training, the batch size and epoch number are set to 256 and 100, respectively. Weighted binary cross-entropy loss is adopted to address class imbalance, and model parameters are optimized using AdamW with an initial learning rate of 0.001, a weight decay of $1\times {10}^{-4}$, and a ReduceLROnPlateau scheduler.

4.3. Comparative Results

To evaluate the effectiveness of the proposed ASG-MSLSM, comparative experiments were conducted against CNN, MLP, Basic-SNN, and MLF-SNN [24], as shown in Figure 3 and

Table 2. Satellite Maneuver Detection Results Comparison.

Method	Accuracy (%)	Precision (%)	Recall (%)	F1 (%)	Sparsity (%)
ASG-MSLSM (Ours)	95.41	90.29	98.68	94.30	89.43
CNN	95.41	99.43	88.57	93.68	-
MLP	93.00	92.41	89.12	90.74	-
Basic-SNN	83.95	91.07	64.62	75.60	85.46
MLF-SNN	94.36	98.74	86.37	92.14	84.38

. Overall, the proposed method achieved the best comprehensive performance among all compared models, particularly in terms of recall and F1-score, indicating a more favorable balance between detection sensitivity and overall reliability.

As shown in Table 2 and Figure 3, ASG-MSLSM achieved an accuracy of 95.41%, a precision of 90.29%, a recall of 98.68%, and an F1-score of 94.30%. Although CNN obtained a higher precision (99.43%), its recall dropped to 88.57%, indicating a higher risk of missed detections in maneuver samples. MLP further showed inferior results across all major metrics, suggesting that static nonlinear models are insufficient for effectively characterizing the temporal dynamics of satellite maneuvers. These results indicate that high precision alone is not sufficient for this task, since reliable maneuver detection also requires strong sensitivity to anomalous temporal variations.

Compared with the spiking-based baselines, the advantage of the proposed method becomes more evident. Basic-SNN yielded the weakest performance, with a recall of 64.62% and an F1-score of 75.60%, demonstrating limited capability in modeling complex maneuver dynamics. MLF-SNN improved the overall results and achieved an F1-score of 92.14%, but it still remained below ASG-MSLSM, especially in recall. This comparison suggests that performance gains cannot be achieved merely by increasing spiking depth or network complexity. Instead, compared with MLF-SNN, the proposed ASG-MSLSM explicitly combines multi-timescale liquid-state encoding with an adaptive spiking gating mechanism, enabling more effective modeling and adaptive integration of temporal dynamics across different scales. In addition, ASG-MSLSM achieves a spike sparsity of 89.43%, higher than Basic-SNN (85.46%) and MLF-SNN (84.38%). Here, higher spike sparsity indicates that fewer spikes are emitted overall. This suggests that ASG-MSLSM maintains a sparser activation pattern while achieving superior detection performance, providing indirect evidence of its theoretical energy-efficiency potential.

Overall, the superior performance of ASG-MSLSM can be attributed to its ability to capture complementary multi-scale temporal representations and to adaptively fuse them according to the characteristics of input samples. More importantly, its novelty lies not simply in using a more complex spiking architecture, but in providing a more explicit and task-oriented framework for multi-scale temporal representation and adaptive integration in satellite maneuver detection. As a result, the proposed model achieves a better trade-off between precision and recall, leading to the most competitive overall performance for satellite maneuver detection.

4.4. Ablation Study

To evaluate the contribution of each key component, a progressive ablation study was conducted with three configurations: Single-Scale, Multi-Scale, and the full Adaptive Spiking Gating model. Specifically, Single-Scale uses only one temporal scale, Multi-Scale introduces fixed multi-scale feature fusion, and the full model further incorporates adaptive spiking gating to dynamically weight multi-scale representations.

As shown in

Table 3. Ablation study results.

Variant	Accuracy (%)	Precision (%)	Recall (%)	F1 (%)	ΔF1 (%)	Sparsity (%)	ΔSparsity (%)
Single-Scale	75.72	62.19	94.11	74.89	-	93.79
Multi-Scale	84.79	72.50	97.41	83.13	+8.24	94.17	+0.38
Adaptive Spiking Gating Multi-Scale	95.41	90.29	98.68	94.30	+11.17	89.43	−4.74

and Figure 4, the overall performance improves consistently as the model becomes more complete. The Single-Scale model achieves 75.72% accuracy, 62.19% precision, 94.11% recall, and 74.89% F1-score. After introducing Multi-Scale modeling, these values increase to 84.79%, 72.50%, 97.41%, and 83.13%, respectively. With the addition of Adaptive Spiking Gating, the model further improves to 95.41% accuracy, 90.29% precision, 98.68% recall, and 94.30% F1-score. In terms of performance gain, multi-scale modeling improves the F1-score by 8.24 percentage points over the Single-Scale baseline, while adding Adaptive Spiking Gating on top of Multi-Scale brings a further 11.17-point improvement. Overall, the full model outperforms the baseline by 19.41 percentage points in F1-score. These results indicate that both multi-scale modeling and adaptive gating contribute substantially to the final performance, with the latter providing the larger marginal gain. In terms of sparsity, the Multi-Scale variant shows a slightly higher sparsity (94.17%) than the Single-Scale model (93.79%), suggesting that the introduction of multi-scale modeling allows the network to maintain or even enhance feature extraction while preserving a relatively sparse activation pattern. By contrast, the proposed Adaptive Spiking Gating Multi-Scale model exhibits a lower sparsity (89.43%) than the Multi-Scale variant, indicating that adaptive gating activates relatively richer neural responses when needed. This change is consistent with the observed gains in detection performance and suggests that the gating mechanism improves representational flexibility beyond the sparse multi-scale baseline.

The confusion matrices provide further evidence for this observation. As shown in Figure 5, Single-Scale exhibits evident class confusion, particularly a relatively high false-positive rate on normal samples. The introduction of Multi-Scale reduces both false positives and false negatives, while the full model further suppresses both types of errors. This suggests that adaptive spiking gating not only enhances anomaly sensitivity but also improves the discrimination of normal patterns.

The t-SNE visualization in Figure 6 shows a consistent trend. Compared with the evident class overlap in Single-Scale, Multi-Scale improves the feature distribution to some extent, whereas Adaptive Spiking Gating produces clearer inter-class separation and more compact intra-class clustering. To provide quantitative support for the visual analysis, a customized separation metric is defined within the two-dimensional t-SNE embedding space. This index is calculated as the ratio of the Euclidean distance between two class centroids to the average within-class dispersion. A higher score indicates superior feature discriminability and clearer boundary between maneuver and non-maneuver samples. Notably, this metric only acts as an auxiliary indicator for supplementary visualization analysis, rather than a universal standard evaluation metric for model performance. These results indicate that multi-scale modeling enhances the representation of complex temporal dynamics, while adaptive spiking gating further improves the discriminability of feature selection and fusion. Overall, the superiority of the full model can be attributed to the synergistic effect of multi-scale temporal modeling and adaptive spiking-gated fusion.

4.5. Analysis of Adaptive Scale Gating Mechanism

To gain deeper insights into the working principles of the adaptive scale gating mechanism, we analyze the feature transformation process and the learned gating weights. This analysis demonstrates the effectiveness of the mechanism in adaptively selecting and integrating multi-scale features for different sample types.

4.5.1. Feature Transformation Visualization

To investigate the effect of adaptive scale gating on feature representation, we further compare the distributions of raw multi-scale features, gated fused features, and projection features. As shown in Figure 7, the raw multi-scale features still exhibit evident class overlap, with a separation score of 1.86. After gated fusion, the separation score increases to 3.66, and the class boundary becomes much clearer. After projection, the separation score further reaches 3.81, together with more compact intra-class clustering. These results indicate that adaptive scale gating effectively enhances the discriminability of multi-scale features and provides a better representation basis for downstream classification.

4.5.2. Gating Weight Analysis

To further reveal the internal behavior of the gating mechanism, we analyze the distribution of scale weights across different sample categories. As shown in Figure 8, the gate weights of normal samples are relatively dispersed, mainly shared by $\beta =2$ and $\beta =10$, whereas the weights of anomalous samples are strongly concentrated on $\beta =2$, with limited contribution from the other scales. The heatmap further confirms this pattern: the branch associated with β = 2 consistently dominates in the anomalous region, while normal samples exhibit a more balanced multi-scale combination. These results suggest that the adaptive scale gating mechanism is clearly sample-dependent and can dynamically select more suitable temporal-scale representations according to class-specific dynamics, thereby improving the model’s representational and discriminative capability.

5. Conclusions

This study proposes an Adaptive Spiking Gating Multi-Scale Liquid State Machine (ASG-MSLSM) for satellite orbital maneuver detection. By combining multi-scale reservoirs with different scale-dependent decay factors and an adaptive spiking gating mechanism, the proposed method achieves a more favorable balance between precision and recall than conventional approaches. The adaptive gating mechanism enhances the learning of fine-grained features that are crucial for maneuver detection, while simultaneously integrating multi-scale information to characterize normal operational states, thereby substantially reducing missed detections. Both the ablation study and the visualization analysis demonstrate that the gating mechanism can adaptively allocate scale weights according to sample characteristics, offering interpretable insights into the model’s decision-making process. Nevertheless, the present study was conducted under a specific experimental setting, and further validation is required for broader application scenarios. In particular, because the adopted dataset covers only a limited temporal span, the robustness of the proposed model against seasonal atmospheric-drag variations and solar-activity-related perturbations has not yet been rigorously evaluated. This issue will be investigated in future work through cross-season evaluation on datasets with broader temporal and environmental coverage. In addition, the current study mainly focuses on detection performance, and the computational efficiency of the proposed method has not been directly evaluated. Future research could explore extending the model to more diverse maneuver patterns and orbital conditions, as well as examining its computational efficiency under practical deployment scenarios, contingent on the availability of broader datasets and further experimental validation.