Unknown Maneuvers Research Articles

Orbit determination for spacecraft with continuous low-thrust using nonsingular Thrust-Fourier-Coefficients and filtering-through approach

Orbit determination using optical survey measurements for cataloging spacecraft encounters new obstacles from mega-constellations. These challenges arise from the sparse observations, and the frequent occurrences of unknown maneuvers which are difficult to model using traditional methods. By utilizing 14 Fourier coefficients, the Thrust-Fourier-Coefficients (TFC) model can effectively represent the averaged variations of orbital elements caused by arbitrary maneuvers. However, this model contains systematic offsets that will reduce the accuracy of orbit determination, and is unsuitable for spacecraft in nearly circular orbits. This paper first replaces the classical Keplerian elements of the previous TFC model with the nonsingular elements. Then detailed analytical expressions for model offsets have been derived based on Kozai’s orbit-averaging method. A process noise covariance matrix related to the model offsets has been added to the iterated extended Kalman filter to compensate for the unmodeled dynamics and enhance the accuracy. Simulations based on this modified method demonstrate that the accuracy of orbit determination for maneuvering satellites can meet the requirements of catalog maintenance even with sparse observations.

Probabilistic Higher-Order Velocity Obstacle for Dynamic Collision Avoidance in Uncertain Environments

Autonomous systems like unmanned aircraft systems are touted as front-runners in terms of efficiency and agility in challenging operations like emergency response. The ability of autonomous agents in such systems to avoid collisions with dynamic obstacles while navigating through an obstacle-cluttered environment is critical for success in any mission. In addition to that, further challenges are posed by environments with uncertainties in obstacles’ motion, sensing, and occluded regions. To this end, a higher-order velocity obstacle–based novel motion planner is presented in this paper in a probabilistic setup for smooth, collision-free navigation of the agent with acceleration constraints in uncertain, unstructured environments with an element of anticipation for the future environment. The effectiveness of the developed algorithm for safe, collision-free, and smooth navigation of the agent is investigated in simulation studies in two different kinds of environments, one with known trajectories of obstacles and the other with unknown maneuvering trajectories of obstacles. Extensive simulation studies are performed in the presence of dynamic obstacles to elucidate the performance of the proposed algorithm on four crucial parameters—mission time, computational time, minimum obstacle distance, and an overall control effort under varied obstacle densities. With satisfactory performance in all these aspects, the developed algorithm possesses strong potential for real-time implementation.

Detection and estimation of spacecraft maneuvers for catalog maintenance

Building and maintaining a catalog of resident space objects involves several tasks, ranging from observations to data analysis. Once acquired, the knowledge of a space object needs to be updated following a dedicated observing schedule. Dynamics mismodeling and unknown maneuvers can alter the catalog’s accuracy, resulting in uncorrelated observations originating from the same object. Starting from two independent orbits, this work presents a convex-optimization based approach to find admissible maneuvers to correlate the two orbits. In case of a feasible maneuver detection, the time profile of the maneuver is estimated, exploiting the conjugate unscented transform to map the orbits’ covariance into the maneuver uncertainty. It is also shown that a careful choice of the coordinate system is pivotal to obtain the solution in one iteration, without successive convexification.

Multiple maneuvering target tracking based on hierarchical Dirichlet process and hidden Markov model

This paper is concerned with multiple maneuvering target tracking problems. Although the interacting multiple model (IMM) algorithm can be used for maneuvering targets tracking, the performance is limited as the motion mode set of the target is fixed in advance. In this paper, we address the problem of multiple maneuvering targets with unknown maneuvering models in cluttered environments. A finite hidden Markov model (HMM) is developed with truncated Hierarchical Dirichlet process (HDP) to recognize the unknown and changing motion modes. Further, the HDP-HMM is introduced into multiple hypothesis tracking (MHT) and probabilistic multiple hypothesis tracking (PMHT) approaches for multiple maneuvering targets tracking with data association uncertainty. To joint estimate the HDP-HMM parameters and target states, the particle learning and variational inference approaches are used, and the solutions of HDP-HMM-MHT and HDP-HMM-PMHT algorithms are obtained based on Rao-Blackwellized particle filter and variational Bayesian methods, respectively. As the changes of maneuver models can be learned using HDP, the multi-target tracking accuracy of the proposed algorithm is improved. Simulation results show that the proposed algorithms outperform the traditional IMM-MHT method with fixed model sets.

Autonomous Optical-Only Spacecraft-to-Spacecraft Absolute Tracking and Maneuver Classification in Cislunar Space

Traditional concerns regarding spacecraft state estimation are exacerbated in cislunar space due to highly nonlinear dynamics, limited observational information, and increasingly overloaded Earth-based resources. These challenges motivate research into space-based navigation and observation capabilities that provide opportunities for autonomy. This paper demonstrates that relative optical measurements provide full inertial estimates of an agent and target spacecraft, while simultaneously enabling classification of unknown maneuvers in the cislunar environment. To achieve this objective two subtasks are demonstrated. First, the spacecraft-to-spacecraft absolute tracking method, which estimates the absolute state of two vehicles using relative measurements, is tested for observability and shown to produce consistent filter solutions given optical sensors. Second, maneuver classification is performed by labeling an estimated control profile generated from the optimal control based estimator. Collectively, this sequential methodology enables an agent craft to autonomously navigate itself while observing a target craft and classifying its maneuvers.

Detection and characterisation of unknown maneuvers in spacecraft

Space debris detection and characterisation is an important and pressing field, as the amount of space debris is growing due to the increase in spacecraft launches and increasing interests for space uses. Space agencies like NASA and ESA keep track of over 5,000 spacecraft and 20,000 spacecraft-related debris objects currently orbiting the Earth. An active spacecraft may undergo trajectory changes through an impulsive maneuver, or an inactive spacecraft may change its trajectory because of uncontrolled explosions due to residual fuel without warning. These pose risks to operational satellites. In addition, measurement data from tracking and detection consists of uncertainties, causing maneuver detection and characterisation methods to become computationally expensive.Thus, the goal of this work was to develop a quick, reliable, computationally inexpensive method for spacecraft maneuver detection and characterisation to be used by satellite operators and assist in collision avoidance measures. This paper presents such a technique, which is applied to simulated measurement data of an orbiting spacecraft taken from one ground site. With these objectives, a method using a modified Extended Kalman Filter (EKF) with covariance inflation from previous studies was explored and simplified. A new parameter definition is presented for maneuver detection and characterisation, named the Kaderali-parameter, or K, with focus on transverse apogee and perigee maneuvers. A relationship was then found between the parameter and the magnitude of the impulsive artificial maneuver. The method was tested in several different scenarios, varying Δv magnitude and scale, Δv direction, maneuver orbital location, orbit geometry, noise covariance, detection parameter threshold, state covariance inflation threshold, and maneuver duration.In general, it was found that as the Δv magnitude increases, the magnitude of the detection parameter also increases. This relationship was found to be a nonlinear logarithmic relationship through best fit curve testing. Possible extensions of this work in the future include: testing multi-maneuver scenarios, multi-sensor data collection and fusion, break-up or berthing events, rendezvous or mating events, and matlab EKF protocol implementation.

Neural learning control of missile interception against dynamics uncertainty and target evasive maneuver

AbstractThe integrated guidance and control (IGC) design for the advanced interceptors against targets in progress of implementing evasive maneuvers is investigated. During interception, the target's unknown maneuver accelerations, and the extra angle of attack (AOA) caused by wind effects, are considered as disturbances. For the sake of enough hit‐to‐kill accuracy under multisource disturbances, the neural networks (NNs) and disturbance observer (DOB) are applied to solve the model inaccuracy and external disturbance. As a result, a novel DOB‐based neural controller can accomplish high tracking accuracy and hit‐to‐kill interception performance can be accomplished. Simulations studies demonstrate the validity and advantage bring by the DOB‐based neural control.

Fully distributed prescribed performance formation control for UAVs with unknown maneuver of leader

This paper focuses on the formation control for multiple quadrotor unmanned aerial vehicles (UAVs) in a leader-follower structure. Taking account of the unknown maneuver of the leader and external disturbances, a novel fully distributed prescribed performance formation controller is proposed. Firstly, to obtain a quick convergence rate of errors and desired control precision, a performance function is introduced into a time-varying barrier Lyapunov function (TV-BLF). Then, a distributed adaptive extended state observer (AESO) is constructed to estimate the maneuver of the leader and external disturbances simultaneously. A distributed formation controller is established further based on the TV-BLF and estimations of the AESO. It is proved rigorously that by using the proposed formation controller, the desired formation pattern can be formed while the prescribed performance is guaranteed. Moreover, no global topology information is required in the proposed AESO and controller, which means that the formation can be realized in a fully distributed way. Last, simulations are performed to validate the effectiveness and the superiority of the presented scheme.

A LSTM assisted orbit determination algorithm for spacecraft executing continuous maneuver

Orbit determination (OD) for spacecraft with unknown maneuver is always a challenging task. This paper proposes a novel framework for efficiently solving continuously maneuvering spacecraft OD problems by merging the Long Short-Term Memory (LSTM) neural network and the filter algorithms. A polynomial-representation fitted the unknown continuous maneuver is first proposed. Rather than directly output the estimated maneuver, the LSTM is trained to detect the unknown maneuver and then estimate the coefficients of the polynomial-representation. Then a fusion is designed to combine the prediction of the LSTM and the estimation of the filter for a more accurate estimation. The proposed LSTM-based framework is successfully applied to solve a Low-Earth-orbit OD problem and a Middle-Earth-orbit OD problem. The continuously maneuvering target is well tracked and the unknown maneuver is accurately estimated. Numerical simulations show that the LSTM trained based on one training dataset can also be applied to other scenarios that share some common features with the training dataset.

Fast Distributed Multiple-Model Nonlinearity Estimation for Tracking the Non-Cooperative Highly Maneuvering Target

The newly developed near-space vehicle has the characteristics of high speed and strong maneuverability, being able to perform vertical skips and a wide range of lateral maneuvers. Tracking this kind of target with ground-based radars is difficult because of the limited detection range caused by the curvature of the Earth. Compared with ground-based radars, satellite tracking platforms equipped with Synthetic Aperture Radars (SARs) have a wide detection range, and can keep the targets in custody, making them a promising approach to tracking near-space vehicles continuously. However, this approach may not work well, due to the unknown maneuvers of the non-cooperative target, and the limited computing power of the satellites. To enhance tracking stability and accuracy, and to lower the computational burden, we have proposed a Fast Distributed Multiple-Model (FDMM) nonlinearity estimation algorithm for satellites, which adopts a novel distributed multiple-model fusion framework. This approach first requires each satellite to perform local filtering based on its own single model, and the corresponding fusion factor derived by the Wasserstein distance is solved for each local estimate; then, after diffusing the local estimates, each satellite performs multiple-model fusion on the received estimates, based on the minimum weighted Kullback–Leibler divergence; finally, each satellite updates its state estimation according to the consensus protocol. Two simulation experiments revealed that the proposed FDMM algorithm outperformed the other four tracking algorithms: the consensus-based distributed multiple-model UKF; the improved consensus-based distributed multiple-model STUKF; the consensus-based strong-tracking adaptive CKF; and the interactive multiple-model adaptive UKF; the FDMM algorithm had high tracking precision and low computational complexity, showing its effectiveness for satellites tracking the near-space target.

Noise-Adaption Extended Kalman Filter Based on Deep Deterministic Policy Gradient for Maneuvering Targets.

Although there have been numerous studies on maneuvering target tracking, few studies have focused on the distinction between unknown maneuvers and inaccurate measurements, leading to low accuracy, poor robustness, or even divergence. To this end, a noise-adaption extended Kalman filter is proposed to track maneuvering targets with multiple synchronous sensors. This filter avoids the simultaneous adjustment of the process model and measurement model without distinction. Instead, the maneuver detection based on the Dempster-Shafer evidence theory is constructed to achieve the reliable distinction between unknown maneuvers and inaccurate measurements by fusing multi-sensor information, which effectively improves the robustness of the filter. Moreover, the adaptive estimation of the process noise covariance is modeled by a Markovian decision process with a proper reward function. Deep deterministic policy gradient is designed to obtain the optimal process noise covariance by taking the innovation as the state and the compensation factor as the action. Furthermore, the recursive estimation of the measurement noise covariance is applied to modify a priori measurement noise covariance of the corresponding sensor. Finally, the fusion algorithm is developed for the global estimation. Simulation experiments are carried out in two scenarios, and simulation results illustrate the feasibility and superiority of the proposed algorithm.

Near-optimal interception strategy for orbital pursuit-evasion using deep reinforcement learning

Two participants with competing objectives are considered in one-to-one orbital pursuit-evasion problem, one of which attempts to satisfy some certain terminal conditions with a minimum cost through its own control while the other player attempts to maximize the specified payoff and avoids entering this terminal range. This paper treats the problem of minimax time to a given final distance, within which the interception between pursuer and evader is defined to occur. To achieve the successful interception with an evader that adopts any unknown maneuvers, a near-optimal interception strategy for the orbital pursuit-evasion is presented in this paper. The pursuit-evasion problem is formulated as a differential game first, and a closed-form barrier solution is provided next. A near-optimal guidance law using deep learning is proposed to intercept the evader inside the capture zone. For the games that start outside the barrier, a learning algorithm for the capture zone embedding strategy is presented based on deep reinforcement learning to help the game state cross the barrier surfaces. The simulation cases of intercepting the evaders that adopt different maneuvering strategies are provided, and the results demonstrate the effectiveness and onboard feasibility of the proposed strategy in solving the orbital interception problem.

Maneuvering Spacecraft Orbit Determination Using Polynomial Representation

This paper proposed a polynomial representation-based method for orbit determination (OD) of spacecraft with the unknown maneuver. Different from the conventional maneuvering OD approaches that rely on specific orbit dynamic equation, the proposed method needs no priori information of the unknown maneuvering model. The polynomials are used to represent the unknown maneuver. A transformation is made for the polynomials to improve the convergence and robustness. The Extended Kalman Filter (EKF) is used to process incoming observation data by compensating the unknown maneuver using the polynomials. The proposed method is successfully applicated into the OD problem of spacecraft with trigonometric maneuver. Numerical simulations show that the eighth-order polynomials are accurate enough to represent a trigonometric maneuver. Moreover, Monte Carlo simulations show that the position errors are smaller than 1 km, and the maneuver estimated errors are no more than 0.1 mm/s2 using the eighth-order polynomials. The proposed method is accurate and efficient, and has potential applications for tracking maneuvering space target.

Finite-Time Distributed Leaderless Cooperative Guidance Law for Maneuvering Targets under Directed Topology without Numerical Singularities

A new distributed leaderless cooperative guidance algorithm is suggested for multi-directional saturation strikes against maneuvering targets. First, the finite-time disturbance observer (FDO) is used to estimate the target’s unknown maneuvers. After that, the guidance laws along the line-of-sight (LOS) direction and the LOS normal direction are designed separately based on the finite-time consensus theory. The proposed guidance law could satisfy both impact time and LOS angle constraints. Numerical singularities due to feedback linearization are avoided by nonlinear stability analysis. Finally, the effectiveness of the proposed cooperative guidance law is proved by numerical simulation arithmetic.

Recursive Bayesian inference and learning for target tracking with unknown maneuvers

SummaryThis paper addresses the problem of target tracking under completely unknown maneuvering behavior to cope with the complicated target maneuvers. The actual but unknown motion model is formulated as a linear stochastic model with unknown transition matrix and modeling error covariance. Considering the diversity and time‐varying of maneuvers, both the transition matrix and covariance are random. Accordingly, the tracker design amounts to recursively updating the joint posterior of target state and unknown parameters (i.e., the transition matrix and covariance). Since it is difficult to obtain the analytical joint posterior, a Bayesian inference and learning scheme is proposed in the sequential Monte Carlo (SMC) framework to alternatively update the state posterior and the unknown parameters posterior. Particularly, it is revealed that the state prediction density used in the SMC obeys a Student's t‐distribution, thus ensuring the effective sampling of particle trajectories. Finally, a maneuvering benchmark shows that the proposed tracker can significantly reduce the peak tracking error, which is one of the most important performance indices for preventing tracking failure.

Inverse optimal missile guidance law under constraints based on prescribed-time explicit reference governor

In this paper, the utilization of inverse-optimality-based prescribed-time explicit reference governor is investigated for missile intercepting against unknown maneuvering targets under performance and control input constraints. With an arctangent-based disturbance observer equipped for disturbance elimination, incorporating the inverse optimality approach into the missile interception guarantees the minimization of a performance index. In the framework of prescribed-time explicit reference governor, the control constraint is translated into a restriction of time-varying invariant set, and it follows the prescribed-time regulation of the applied reference along with the restriction satisfaction. The combined prescribed-time explicit reference governor approach could be transformed into a linear matrix inequality optimization problem, and its online solution over a receding horizon gives a Lyapunov function value for reference regulation and then control decisions in the continuous time. Simulation studies are performed to illustrate the performance of the proposed guidance control law.

Robust UKF-based filtering for tracking a maneuvering hypersonic glide vehicle

To track a non-cooperative hypersonic glide vehicle (HGV) without any precise information, an approach to the state estimation is presented based on a robust UKF-based filter (RUKFBF) in this paper. The HGV has an uncertain reentry motion because of unknown maneuvers which is a primary factor leading to degradation of tracking accuracy. Aiming at enhancing accuracy, the strong tracking algorithm (STA) is introduced to addressing the model error caused by a bank-reversal maneuver of HGV. Furthermore, the Huber technique is employed to deal with possible measurement model errors. In the RUKFBF, mutual interferences are suppressed between the STA and the Huber technique via two strategies. The one is that the calculation of the fading factor in the STA adopts an unmodified measurement noise covariance, and the other one is that two judgment criteria are proposed to limit large fading factors in the presence of measurement model errors. To simulate real tracking scenarios, the RUKFBF is tested through tracking a HGV trajectory considering a practical guidance strategy. Simulation results demonstrate the effectiveness of the RUKFBF in the presence of model errors and the observability of the estimated state.

Incomplete Information Pursuit-Evasion Game Control for a Space Non-Cooperative Target

Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes.

Tracklet-to-orbit association for maneuvering space objects using optimal control theory

The maintenance of a catalog of space objects is integral for Space Surveillance and Tracking (SST). In order to enable safe space operations, this catalog shall be complete, accurate and traceable. One of the challenges to keep custody of active satellites comes from their unknown maneuvers plan that adds significantly to the uncertainty on their precise dynamics. This fact can imply the failure of conventional measurement-to-orbit association methods leading at the best to an inconsistent traceability in the catalog (a physical object represented by two or more catalog objects) or, at worst, to the loss of the tracking of an object. This paper presents a method to tackle the measurement-to-orbit association in the presence of unknown maneuvers. It is based on optimal control theory coupled with the admissible region. In particular, the orbit-to-orbit association problem is solved with an energy-optimal indirect approach, which is then generalized to the measurement-to-orbit association problem using the admissible regions concept. Measurements are supposed to be a collection of time-close optical measurements or tracklet that can be represented by an attributable vector. A broad bench of simulated tests is presented in the case of a geostationary (GEO) maneuvering satellite, and the method is finally applied to a real case of a longitude-shift GEO satellite using the data provided by the TAROT telescope network.

Discrete-Time Angle Constraint Interception with Model-Assisted Target Maneuver Estimator

This paper investigates the problem of designing angle constraint guidance law against unknown maneuvering targets based on discrete-time sliding mode control theory. Invoking the fact that the future course of action of the target, an independent entity, cannot be predicted beforehand due to its complexity and unpredictability, a model-assisted discrete-time disturbance observer in cooperation with a singularity-free strategy is proposed first to estimate the target maneuver. Based on the reconstructed signal and a fast convergence time-varying sliding surface, a new chattering-mitigated super-twisting-like discrete-time impact angle constraint guidance law is then synthesized. Stability analysis shows that the closed-loop system trajectory can be forced to enter into a small region around the sliding surface. Simulations and comparisons with classical discrete-time sliding mode guidance law validate the effectiveness of the proposed guidance law.