Unknown Maneuvers Research Articles

Tracking the maneuvering spacecraft propelled by swing propulsion of constant magnitude

This paper proposes partially norm-preserving filtering for a class of spacecraft in the presence of time-varying, but constant-magnitude maneuver. The augmented state Kalman filter (ASKF) is commonly used to track the maneuvering spacecraft with unknown constant propulsion; however, if the maneuver varies via time, the estimation performance will be degraded. To promote the tracking performance of the ASKF in case of time-invariant, constant-magnitude disturbance, the partially norm-preserving ASKF is developed by applying the norm constraint on the unknown maneuver. The proposed estimator, which is decomposed into two partial estimators and iteratively propagated in turns, projects the unconstrained maneuver estimation onto the Euclidian surface spanned by the norm constraint. The illustrative numerical example is provided to show the efficiency of the proposed method.

An Algebraic Closed-Form Solution for Bearings-Only Maneuvering Target Motion Analysis From a Nonmaneuvering Platform

In bearings-only target motion analysis (TMA), the observer is often required to outmaneuver the target. However, under specific conditions, an observer moving with constant velocity is sufficient to compute the state of a target that changes its course. A maximum likelihood estimator (MLE) has been developed for this problem in the literature. Unfortunately, the MLE is not only computationally expensive but also prone to divergence problems when poorly initialised. To overcome these shortcomings, this paper proposes a novel quadratically constrained weighted instrumental variable (QC-WIV) estimator. Being a closed-form algorithm, the proposed QC-WIV is inherently more stable than the MLE while at the same time being computationally much more efficient. Moreover, it is shown analytically to be asymptotically unbiased. Numerical simulation studies are presented to corroborate the performance advantage of the proposed QC-WIV, where it is observed to be asymptotically efficient as well. In addition, the QC-WIV performance is on par with the MLE in small noise scenarios for both cases of known and unknown maneuver time. More importantly, the QC-WIV is observed to produce stable estimation performance in large noise levels at which the MLE suffers from divergence.

Trajectory Estimation of Hypersonic Glide Vehicle Based on Analysis of Aerodynamic Performance

Due to high speed and high maneuverability of hypersonic glide vehicles (HGVs), the state estimation of such targets has always been a research hotspot. In order to improve accuracy of the trajectory estimation, a nonlinear aerodynamic parameter model for target estimation based on aerodynamic performance analysis is proposed. Firstly, the dynamic characteristics of the hypersonic glide vehicle during the hypersonic gliding stage was analyzed. Then, aiming at HTV-2-liked vehicle, the engineering calculation method was used to form the reference aerodynamic model for the target estimation. Secondly, a deviation model described by first-order Markov process was introduced to compensate the uncertainties of the unknown maneuver information from the target. Finally, extended Kalman filter was utilized to estimate the state of the target. The simulation results show that the proposed model is able to improve the accuracy of acceleration estimation for the HTV-2-liked hypersonic gliding vehicles.

Distributed cooperative encirclement hunting guidance for multiple flight vehicles system

Distributed cooperative encirclement hunting guidance strategy design and analysis issues for multiple flight vehicles system against a maneuvering target are considered in this paper. Distinct from the former results, the cooperative encirclement hunting guidance laws are based on the leader-follower coordination structure, and are divided into two parts. Firstly, for the leader flight vehicle, a full-head-on interception guidance law is proposed against the maneuvering target, where the uncertain dynamics and the target's unknown maneuver are estimated and compensated by using an extended state observer. For the follower flight vehicles, the distributed time-varying encirclement hunting line of sight angle formation tracking laws with overload saturation are designed where distributed extended state observers are introduced to approximate the complicated uncertain items and the leader vehicle's input signals. Then, the design processes of cooperative encirclement hunting guidance laws are summarized within five steps as an algorithm. Thirdly, the stability and the properties of the proposed cooperative encirclement hunting guidance algorithm are analyzed by employing Lyapunov theories. Finally, numerical simulation results illustrate the effectiveness of achieved cooperative encirclement hunting guidance strategies.

Flight Control for UAV Loitering Over a Ground Target With Unknown Maneuver

This paper proposes a flight controller for an unmanned aerial vehicle (UAV) to loiter over a ground moving target (GMT). We are concerned with the scenario that the stochastically time-varying maneuver of the GMT is unknown to the UAV, which renders it challenging to estimate the GMT's motion state. Assuming that the state of the GMT is available, we first design a discrete-time Lyapunov vector field for the loitering guidance and then design a discrete-time integral sliding mode control (ISMC) to track the guidance commands. By modeling the maneuver process as a finite-state Markov chain, we propose a Rao-Blackwellised particle filter (RBPF), which only requires a few number of particles, to simultaneously estimate the motion state and the maneuver of the GMT with a camera or radar sensor. Then, we apply the principle of certainty equivalence to the ISMC and obtain the flight controller for completing the loitering task. Finally, the effectiveness and advantages of our controller are validated via simulations.

Relative motion and thrust estimation of a non-cooperative maneuvering target with adaptive filter

With the rapid increase in the number of spacecraft in outer space, the unknown maneuvers of a spacecraft significantly increase the probability of a collision between neighborhoods. In order to guarantee the safety of an operational spacecraft, we need to estimate and predict the relative trajectories of a non-cooperative target in real time. Traditional filter routines are ineffective when the target spacecraft performs unknown continuous maneuvers. In this work, we focus on the development of relative estimators with enhanced robustness against unknown maneuvers. First, a variable state dimension estimator based on filter switching and covariance inflation is proposed to adaptively cope with a constant unknown maneuver. To strengthen the robustness in response to the time-varying maneuvers, a novel observer-enhanced Kalman filter is subsequently proposed by incorporating an observer into the filtering routines. Finally, the performance of the proposed estimators is evaluated with a series of numerical simulations, both the advantages and the disadvantages are analyzed using the simulation results.

Tracking a Maneuvering Target by Multiple Sensors Using Extended Kalman Filter With Nested Probabilistic-Numerical Linguistic Information

Tracking a maneuvering target is an important technology. Due to complex environment and diversity of sensors, errors need to be optimized with respect to various motion states during the tracking process. In this paper, we first propose how to unify the coordinate system and data preprocessing in case of tracking using multiple sensors. We then combine fuzzy sets with a novel trace optimization method based on extended Kalman filter (EKF) with nested probabilistic-numerical linguistic information (NPN-EKFTO). We present a case study of trace optimization of an unknown maneuvering target in Sichuan province in China. We solve the case by using both the proposed method and the traditional EKF and offer comparative analysis to validate the proposed approach.

Optimal Cooperative Guidance Laws in a Multiagent Target–Missile–Defender Engagement

A cooperative interception scenario between a target, its defenders, and missiles attacking said target is considered. Optimal cooperative guidance laws are developed for two distinct scenarios: 1) a scenario with a missile using a known maneuver, yielding an optimal strategy for the target and its defenders; and 2) a scenario with a missile using an unknown maneuver, which is treated as a zero-sum differential game, between the team consisting of a target and its defenders and a team of the attacking missiles. From the general solutions of the two scenarios, analytical solutions are synthesized and analyzed for two cases: 1) a single target with a single defender, as well as a single attacking missile; and 2) a single target with two defenders, as well as two attacking missiles.

Nonsingular Continuous Finite-Time Convergent Guidance Law with Impact Angle Constraints

This paper documents a novel nonsingular continuous guidance which can drive the line-of-sight (LOS) angular rate to converge to zero in finite time in the presence of impact angle constraints. More specifically, based on the second-order sliding mode control (SMC) theory, a second-order observer (2-OB) is presented to estimate the unknown target maneuvers, while a super twisting algorithm- (STA-) based guidance law is presented to restrict the LOS angle and angular rate. Compared with other terminal sliding mode guidance laws, the proposed guidance law absorbs the merits of the conventional linear sliding mode (LSM) and terminal sliding mode (TSM) and uses switching technique to avoid singularity. In order to verify the stability of the proposed guidance law, a finite-time bounded (FTB) function is invited to prove the boundedness of the proposed observer-controller system and a Lyapunov approach is presented to prove the finite-time convergence (FTC) of the proposed sliding system. Rigorous theoretical analysis and numerical simulations demonstrate the mentioned properties.

Augmented unbiased minimum-variance input and state estimation for tracking a maneuvering satellite

The technique of tracking a maneuvering satellite is significantly important for Space Situation Awareness (SSA). Traditional Kalman filters (KF) cannot robustly track unknown maneuvers. Motivated by the problem of tracking a non-cooperative maneuvering satellite, an augmented unbiased minimum-variance input and state estimation (AUMVISE) method is developed for estimating the state and the maneuver acceleration in this study. The maneuver acceleration estimate of the proposed method is proven to be more accurate than the original unbiased minimum-variance input and state estimation (UMVISE) method. Approaches based on the measurement residuals and the acceleration estimates are developed for maneuver start and end detection. The filter is switched between the AUMVISE method and the classical extended Kalman filter (EKF) to obtain an accurate tracking result during both the maneuver period and the non-maneuver period. Simulation results show that the proposed method has a suitable maneuver detection delay and outperforms the UMVISE method in estimating the state and maneuver acceleration.

Robust extended Kalman filter with input estimation for maneuver tracking

This study investigates the problem of tracking a satellite performing unknown continuous maneuvers. A new method is proposed for estimating both the state and maneuver acceleration of the satellite. The estimation of the maneuver acceleration is obtained by the combination of an unbiased minimum-variance input and state estimation method and a low-pass filter. Then a threshold-based maneuver detection approach is developed to determinate the start and end time of the unknown maneuvers. During the maneuvering period, the estimation error of the maneuver acceleration is modeled as the sum of a fluctuation error and a sudden change error. A robust extended Kalman filter is developed for dealing with the acceleration estimate error and providing state estimation. Simulation results show that, compared with the Unbiased Minimum-variance Input and State Estimation (UMISE) method, the proposed method has the same position estimation accuracy, and the velocity estimation error is reduced by about 5 times during the maneuver period. Besides, the acceleration detection and estimation accuracy of the proposed method is much higher than that of the UMISE method.

Non-cooperative maneuvering spacecraft tracking via a variable structure estimator

A spacecraft performing unknown maneuvers significantly increases the probability of a collision between spacecraft with neighboring orbits. Traditional orbit determination filters cannot robustly cope with unknown maneuvers. To track non-cooperative, unknowingly maneuvering spacecraft, a novel variable structure estimator is proposed based on the input compensation to a normal filter. We develop an observer to estimate the unknown maneuver and then analyze the estimated maneuver performance based on error propagation. Once the maneuver detector declares the occurrence of an unknown maneuver, the estimated maneuver is fed to an extended Kalman filter as compensation, which enables the estimator to work adaptively. Finally, a series of numerical simulations are carried out to demonstrate the effectiveness of the proposed variable structure estimator, and the estimation performances in the cases of constant and time-varying maneuvers are analyzed based on the simulation results.

Discrete‐Time Super‐Twisting Guidance Law with Actuator Faults Consideration

AbstractThis paper proposes a robust fault‐tolerant guidance law against unknown maneuvering targets based on discrete‐time sliding mode control theory. To address this problem, a time‐delay observer is designed to estimate the lumped disturbance, which includes target maneuver as well as actuator faults. A robust discrete‐time guidance law is then synthesized based on the discrete‐time super‐twisting algorithm. Due to the principle of the super‐twisting algorithm, the presented guidance law is a naturally chattering‐free formulation. Detailed stability analysis shows that the line‐of‐sight angular rate under the proposed guidance law can be stabilized in a small region around zero. Simulation results are also provided to verify the effectiveness of the proposed approach.

Three-Dimensional Impact Angle Guidance Laws Based on Model Predictive Control and Sliding Mode Disturbance Observer

This paper presents a suboptimal three-dimensional guidance law to intercept unknown maneuvering targets with terminal angle constraint using multivariable control design. The presented guidance law is essentially a composite control method, which is constructed through a combination of standard continuous model predictive control (MPC) and adaptive multivariable sliding mode disturbance observer (SMDO). More specifically, the MPC method is utilized to obtain optimal line-of-sight (LOS) angle tracking performance for nonmaneuvering targets, while the SMDO technique is used to estimate and compensate for the unknown target maneuver online. By virtue of the adaptive nature, the proposed guidance law does not require any information on the bounds of target maneuver and its gradient except for their existence. The stability of the closed-loop guidance system is also analyzed by using Lyapunov function method. Simulation results clearly confirm the effectiveness of the proposed formulation against a maneuvering target.

Adaptive parameter particle CBMeMBer tracker for multiple maneuvering target tracking

Cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter has been demonstrated as a promising algorithm for multi-target tracking, and the multi-model (MM) method has been incorporated into the CBMeMBer filter to solve the problem of multiple maneuvering target tracking. However, it is difficult to construct a proper set of models due to the unknown maneuvering parameters of the targets. Moreover, the number of models may increase exponentially if more unknown parameters have to be taken into account to match the target motion modes, which may lead to prohibitive computational complexity. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the framework of CBMeMBer filters, so that the model with unknown maneuvering parameter can be modified adaptively by using the selected parameter particles. Moreover, a particle labeling technique is introduced in the proposed algorithm in order to obtain the individual target track, which results in the adaptive parameter particle filter CBMeMBer (APPF-CBMeMBer) tracker. Simulation results show that the proposed algorithm can effectively track multiple maneuvering targets with abruptly changing parameters and exhibit better robustness than those of the well-known MM-based approaches.

Maneuver Detection with Event Representation Using Thrust Fourier Coefficients

A systematic way of detecting unknown maneuvers is developed by representing an unknown acceleration tied to an event with thrust Fourier coefficients. Event representation using thrust Fourier coefficients can rigorously represent an unknown maneuver by generating an equivalent maneuver with the same secular behavior. By appending 14 thrust Fourier coefficients as solve-for states, the modified sequential filter processes observation data both forward and backward in time to detect maneuver onset and termination time, respectively. Along with the represented perturbing acceleration, the detection algorithm provides more accurate postmaneuver orbit solutions. A case study of detecting unknown maneuvers with different types of simulated measurement data verifies the presented approach.

Orbit determination across unknown maneuvers using the essential Thrust-Fourier-Coefficients

Any maneuver performed by a satellite transitioning between two arbitrary orbital states can be represented as an equivalent maneuver involving Thrust-Fourier-Coefficients (TFCs). With a selected TFC set as a basis, a thrust acceleration can be constructed to interpolate two unconnected states across an unknown maneuver. This representation technique with TFCs enables us to facilitate the analytical propagation of uncertainties of the satellite state. This approach allows for the usage of existing pre-maneuver orbit estimation to compute the orbit solution after the unknown maneuver. In this paper, we applied this approach to orbit determination (OD) problems across unknown maneuvers by appending different combinations of TFCs to the state vector in the batch filter. The aim is to investigate how different maneuver representations with different TFC sets affect the OD solution across unknown maneuvers. Simulation results show that each TFC set provides different representations of the unknown perturbing acceleration, which yields varying magnitudes of delta velocity for a given maneuver. However, OD solutions across unknown maneuvers using different TFC sets display equivalent performance over the post-maneuver arc as long as those TFC sets are capable of generating the apparent secular motion caused by a given unknown maneuver.

Tracking maneuvering spacecraft with filter-through approaches using interacting multiple models

When spacecraft maneuver unknowingly, traditional orbit determination filters diverge. This paper postulates using Interacting Multiple Models and covariance inflation methods to filter-through unknown maneuvers. This work proposes accurate methods for real-time tracking of a non-cooperative, maneuvering spacecraft and compares the performance to traditional techniques. Results show that a filter-through Interacting Multiple Model orbit determination filter can converge on a post-maneuver orbit in real-time with similar performance to off-line Initial Orbit Determination approaches.

Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO

This paper proposes a novel composite integrated guidance and control (IGC) law for missile intercepting against unknown maneuvering target with multiple uncertainties and control constraint. First, by using back-stepping technique, the proposed IGC law design is separated into guidance loop and control loop. The unknown target maneuvers and variations of aerodynamics parameters in guidance and control loop are viewed as uncertainties, which are estimated and compensated by designed model-assisted reduced-order extended state observer (ESO). Second, based on the principle of active disturbance rejection control (ADRC), enhanced feedback linearization (FL) based control law is implemented for the IGC model using the estimates generated by reduced-order ESO. In addition, performance analysis and comparisons between ESO and reduced-order ESO are examined. Nonlinear tracking differentiator is employed to construct the derivative of virtual control command in the control loop. Third, the closed-loop stability for the considered system is established. Finally, the effectiveness of the proposed IGC law in enhanced interception performance such as smooth interception course, improved robustness against multiple uncertainties as well as reduced control consumption during initial phase are demonstrated through simulations.

ML estimation of transition probabilities for an unknown maneuvering emitter tracking

We consider the problem of an unknown maneuvering emitter tracking by a wireless sensor network with time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. Interacting multiple models combined with square-root cubature Kalman filter with correlated noises (IMM-SCKF-CN) is proposed to update the parameters in the maneuvering emitter tracking. Essential to this tracking framework is the Markov transition probability matrix (TPM) which governs the jumps between multiple dynamic motion models for the maneuvering target. However, in practice, the TPM is unknown and has to be estimated. In this paper, we consider the maximum likelihood (ML) estimation of the TPM and propose a recursive algorithm based on the improved weighted analytical center cutting plane method (ACCPM). Compared with some batch ML methods, the resulting recursive ML estimation method has a much lower per sample complexity. Simulation results show the efficacy of the proposed method with greatly improved tracking performance.