Gaussian-Binary classification for resident space object maneuver detection

doi:10.1016/j.actaastro.2021.06.046

Acta Astronautica

Volume 187, October 2021, Pages 438-446

https://doi.org/10.1016/j.actaastro.2021.06.046 Get rights and content

Highlights

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Propose a data-driven Gaussian Binary resident space objects maneuver detection method.
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The method can detect three types of maneuvers including impulsive and low thrust types.
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The method can detect maneuvers with both high accuracy and high precision.
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The method is robust to data with noise.

Abstract

The capability accurately and timely detect a resident space object (RSO) maneuver is a critical task for monitoring space activities. This paper presents a data-driven Gaussian Binary RSO Maneuver Detection (GaBRSOMD) method to detect whether or not there is a maneuver between two tracks of the same RSO on different orbital paths. Using an in-house simulated space catalog environment, the Gaussian Binary Classification (GBC) method is used to detect three types of maneuvers: the maneuver is due to a small impulsive velocity change; a low thrust, and the maneuver is due to either an impulsive or a low thrust which is unknown a priori. Numerical results demonstrate that the proposed GBC model can achieve high accuracy in detecting all three cases of maneuvers. The paper further demonstrates that the GBC approach is robust to noisy data and has advantages over an AutoEncoder method and the classical Principal Component Analysis (PCA) method. Hence, the proposed GBC has great potential for making quick detection decision with both high accuracy and precision.

Introduction

The Earth’s space environment is getting more and more crowded. More than 34,000 orbital debris larger than 10 cm are known to exist. The estimated population of particles between 1 and 10 cm in diameter is approximately 900,000. The number of particles larger than 1 mm exceeds 128 million. As of May 20, 2021, the amount of material orbiting the Earth exceeded 9,400 metric tons [1]. Among these objects, about 7% of the tracked RSOs are operational satellites [2], implying 93% are space debris which are man-made objects that no longer serve useful purposes but pose risks to astronauts, satellites, and space exploration equipment (e.g., moon robotics).

To detect maneuvers for RSOs accurately and timely is critical to protect the long-term sustainability of space activities, including Space Situational Awareness (SSA) — the knowledge and characterization of space objects and their operational environment to support safe, stable, and sustainable space activities; and Space Traffic Management (STM) — the planning, coordination, and on-orbit synchronization of activities to enhance the safety, stability, and sustainability of operations in the space environment.

Researchers have proposed to detect maneuvers by using the classical estimation methods with different metrics. Kelecy and Jah [3] explored the detection and reconstruction of single low thrust in-track maneuvers by using the orbit determination method based on the batch least squared and Extended Kalman filter (EKF). Song, et al. [4] presented an analysis method called Semi-major Axis Change Method (SACM) by using the relationship between the change of orbit parameters and the change of velocity to detect maneuvers. Ko and Scheeres [5], [6], [7] proposed a method based on Thrust Fourier Coefficients with EKF to detect maneuvers. Jiang, et al. [8] used a residual normalized strong tracking filter (RNSTF) to detect the impulsive maneuvers. These methods are generally established on the standard spacecraft dynamic equations. Compared to the method proposed in this paper, such methods are generally computationally intensive and limited to the various assumptions introduced by the methods.

Rather than building the methods based on dynamic models, approaches based on “data-driven” is another type of the method to detect maneuvers by checking the differences of the observed values from their corresponding historical values [9], [10], [11]. Jia et al. [12] used historical orbit trajectories and asteroid light curves. The criteria for maneuver detection are often defined based on selected statistic measures including the mean and standard deviation of the changes [13]. These methods require different thresholds for different spacecrafts. Furthermore, it is difficult to detect the contextual anomalies when the values are smaller than the threshold limit around the noise level [14]. There are other maneuver detection methods that have been proposed, such as the principal component analysis (PCA) method [15], [16], [17] to reduce the data dimension and select the subspace feature to analyze. However, the traditional PCA method does not work well with nonlinear problems [18].

Recently, more advanced machine learning methods have been proposed. Gao [19] used normal behavior clustering based on the k-nearest neighbors (kNN) algorithm to detect whether an anomaly is presented or not, and also to label the type of anomaly. Gonzalez, et al. [20] proposed a binary classification method with a multi-layer neural network to detect the anomalous data. Shen, et al. have explored a variety of approaches for satellite behavior maneuver detection from tracking data including game theories [21], convolutional neural networks (CNNs) [22], and generative adversarial networks (GANs) [23]. Tariq [24] developed a multivariate convolution long short-term memory (LSTM) with mixtures of probabilistic principal component analysis. Pilastre [25] proposed the method based on sparse representation and dictionary learning. Pang et al. [26] proposed a method which combines Markov chains and a probability prediction method to detect the anomalies. Recent methods include time-delay Neural networks (TDNN) [27], clustering [28], and orbital control theory [29].

In an earlier study, Wang, et al. [30] proved that using AutoEncoder with binary classification can detect whether there is a maneuver or not between two tracks of the same RSO on different orbital paths for a predefined impulsive maneuver. In this paper, we explore a data-driven GBC model to detect maneuvers for three different cases: the maneuver is due to a small impulsive velocity change; the maneuver is due to a low thrust, and the maneuver is due to either an impulsive or a low thrust which is unknown a priori. The orbits and measurements are simulated from an in-house simulation-based space catalog environment. The simulation-based approach supports comparative methods over the sensor, environment, and target (SET) operating conditions such as scenarios of different RSO behaviors. Likewise, with the known “truth” values, performance metrics and bounds can be verified for effectiveness and efficiency. Furthermore, a controlled environment affords testing the robustness of the proposed methods on various scenarios that are presented in this paper.

This paper makes the following contributions. First, to the best of our knowledge, this is the first time that a GBC method is used for RSO maneuver detection. Second, the GaBRSOMD in this paper only needs 5 measurement data from each track to detect a maneuver change, whereas the classical orbit determination can require around 10 measurements due to the measurement errors [31]. Third, the GaBRSOMD can detect whether there are maneuvers between the two tracks of the same RSO on different orbital paths or not with both high accuracy and high reliability. Once trained the GaBRSOMD model can make quick detection decision without solving the orbit estimation problem. Furthermore, the model is robust with data with noise different from what are used in the training data.

The rest of this paper is organized as follows. Section 2 describes the methodology in detail, including the algorithm of GBC and the simulation environment. Sections 3 Impulsive maneuver detection, 4 Low thrust maneuver detection discuss two types of maneuvers, and present the simulation results. Section 5 investigates a hybrid case, compares the results to a principal components analysis (PCA) and an AutoEncoder, and compares the model robustness. Conclusions are presented in the last section.

Section snippets

Gaussian binary classification algorithm

For the space monitoring activity, assume there are $n$ observations: ${X, y} = {x_{i}, y_{i}}$ . $i = 1$ to $n$ , and $y_{i} = f (x_{i})$ . $X$ is an $n \times k$ input matrix with $x_{i} = (x_{i, 1}, x_{i, 2}, \dots, x_{i, k})$ . $k$ is the number of input dimensions. $y = (y_{1}, \dots, y_{n})$ is the corresponding response with value being either 1 or $-$ 1. The goal is to predict the probability of the response being either 1 or $-$ 1 for the test data $x^{*}$ , which is achieved by using a latent function to map the input into the unit interval by a sigmoid function. The general Gaussian Binary

Maneuver definition

To collect enough data to train the model, for a maneuver with a predefined magnitude, we simulate the orbits of a spacecraft for 280 days with the specified maneuver every 28 days, so there are ten orbits and 9 maneuvers in this process. The “DataSet” consists of the 280-day simulation results with the 9 maneuvers. For the DataSet, one orbit is defined as the satellite motion without maneuvers. For simplicity, we refer to these orbits as “orbit 1”, “orbit 2”,…, and “orbit 10” in the DataSet.

Maneuver definition

In this experiment, we keep the initial condition of the satellite orbits as described in the previous section, but change the impulsive maneuver to a low thrust maneuver at the end of every 28 days along the in-track direction and for a finite duration. We explore the low thrust maneuvers by referring to the information in Shafieenejad’s paper [44]: the initial mass of the satellite $m_{0}$ is 1000 kg, and the specific impulse of the engine $I s p$ is 1500 s. In Shafieenejad’s paper, they define the

Maneuver definition

In this section, we test the performance of the GaBRSOMD for a hybrid situation in which the maneuver can be either a small impulsive velocity change or a low thrust maneuver. Both the training data and test data are designed to include both cases. The training database is shown in Table 13, and the test database is shown in Table 14.

To maintain the consistency, the selection of the two databases is the same as the previous sections. The maneuver information contained in test database is

Conclusion

This paper proposes a GaBRSOMD model to detect whether there is a maneuver or not between two tracks of a resident space object on different orbit paths. The experiments includes three maneuvers: (1) small impulse change, (2) low thrust, and (3) impulse or thrust, with sensitivity tests to data noise; and three methods: Gaussian Processes, PCA, and AE.

With a well-trained model, different types maneuvers have been tested. When the maneuvers are impulsive velocity change with different

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was partially supported by the Air Force Research Laboratory, USA contract FA8750-19-C-1000. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the United States Air Force.

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¹: Graduate Student.

²: Associate Professor.

³: Postdoctoral Associate.

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Research paperGaussian-Binary classification for resident space object maneuver detection

Highlights

Abstract

Introduction

Section snippets

Gaussian binary classification algorithm

Maneuver definition

Maneuver definition

Maneuver definition

Conclusion

Declaration of Competing Interest

Acknowledgments

Acta Astronaut.

Adv. Space Res.

Adv. Space Res.

Signal Process.

Acta Astronaut.

Adv. Space Res.

Aerosp. Sci. Technol.

Orbital debris quarterly news

Natl. Aeronaut. Space Adm.

Maneuver detection with event representation using thrust fourier coefficients

J. Guid. Control Dyn.

Tracking maneuvering satellite using thrust-fourier-coefficient event representation

J. Guid. Control Dyn.

Residual-normalized strong tracking filter for tracking a noncooperative maneuvering spacecraft

J. Guid. Control Dyn.

Satellite maneuver detection using two-line element (TLE) data

Space event detection method

J. Spacecr. Rockets

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Adv. Maui Opt. Space Surveill. Technol. (AMOS)

An overview on trajectory outlier detection

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Athmos: Automated telemetry health monitoring system at GSOC using outlier detection and supervised machine learning

Anomaly detection of spacecraft based on least squares support vector machine

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An unsupervised anomaly detection approach for spacecraft based on normal behavior clustering

Combining negative selection and classification techniques for anomaly detection

Research paper
Gaussian-Binary classification for resident space object maneuver detection