Target State Vector Research Articles

An Hybrid Integration Method-Based Track-before-Detect for High-Speed and High-Maneuvering Targets in Ubiquitous Radar

Due to the limited transmission gain of ubiquitous radar systems, it has become necessary to use a long-time coherent integration method for range-Doppler (RD) analysis. However, when the target exhibits high-speed and high-maneuver capabilities, it introduces challenges, such as range migration (RM), Doppler frequency migration (DFM), and velocity ambiguity (VA) in the RD domain, thus posing significant difficulties in target detection and tracking. Moreover, the presence of VA further complicates the problem. To address these complexities while maintaining integration efficiency, this study proposes a hybrid integration approach. First, methods called Keystone-transform (KT) and matched filtering processing (MFP) are proposed for compensating for range migration (RM) and velocity ambiguity (VA) in Radar Detection (RD) images. The KT approach is employed to compensate for RM, followed by the generation of matched filters with varying ambiguity numbers. Subsequently, MFP enables the production of multiple RD images covering different but contiguous Doppler frequency ranges. These RD images can be compiled into an extended RD (ERD) image that exhibits an expanded Doppler frequency range. Second, an improved particle-filter (IPF) algorithm is raised to perform incoherent integration among ERD images and to achieve track-before-detect (TBD) for a target. In the IPF, the target state vector is augmented with ambiguous numbers, which are estimated via maximum posterior probability estimation. Then, to compensate for the DFM, a line spread model (LSM) is proposed instead of the point spread model (PSM) used in traditional PF. To evaluate the efficacy of the proposed method, a radar simulator is devised, encompassing comprehensive radar signal processing. The findings demonstrate that the proposed approach achieves a harmonious equilibrium between integration efficiency and computational complexity when it comes to detecting and tracking high-speed and high-maneuvering targets with intricate maneuvers. Furthermore, the algorithm’s effectiveness is authenticated by exploiting ubiquitous radar data.

Vardiational Bayesian Hybrid Multi-Bernoulli and CPHD Filters for Superpositional Sensors

This paper addresses the problem of multi-target tracking with superpositional sensors, while the covariance matrices of measurement noise are not known. The proposed method is based on the hybrid multi-Bernoulli cardinalized probability hypothesis density (HMB-CPHD) filter, which has been developed for superpositional sensors-based multi-target tracking with known measurement noises. Specifically, we firstly propose the Gaussian mixture (GM) implementation of the HMB-CPHD filter, and then the covariance matrices of measurement noises are augmented into the target state vector, resulting in the Gaussian and inverse Wishart mixture (GIWM) representation of the augmented state. Then the variational Bayesian (VB) method is exploited to approximate the posterior distribution so that it maintains the same form as the prior distribution. A remarkable feature of the proposed method is that it can jointly perform multi-target tracking and measurement noise covariance estimation. The performance of the proposed algorithm is demonstrated via simulations.

Linear sequential filtering based on the debiased measurement matrix of the converted pseudo measurement for radar target tracking

For radar target tracking with nonlinear position and range rate measurements, a linear sequential filtering method based on the debiased measurement matrix of the converted pseudo measurement (DMM-LSF) is proposed. A novel and simple linear measurement matrix is constructed based on the relationship between the pseudo measurement and target's state vector. To estimate the involved unknown parameters in the measurement matrix, the filtering results from the linear position filter are utilized in the sequential linear filter, where a totally linear sequential filtering framework is formed. The measurement matrix estimation error is fully considered, which is incorporated into original converted pseudo measurement error and a new synthetical measurement error is formed. The statistic characteristics of the synthetical measurement error are deduced, resulting a debiased measurement matrix. Simulation results demonstrate the effectiveness of the proposed DMM-LSF algorithm. Compared with existing algorithms, the proposed one can achieve the best tracking performance for non-maneuvering and maneuvering target tracking in different scenes.

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Shenvi et al. have proposed a quantum algorithm based on quantum walking called Shenvi–Kempe–Whaley (SKW) algorithm, but this search algorithm can only search one target state and use a specific search target state vector. Therefore, when there are more than two target nodes in the search space, the algorithm has certain limitations. Even though a multi-objective SKW search algorithm was proposed later, when the number of target nodes is more than two, the SKW search algorithm cannot be mapped to the same quotient graph. In addition, the calculation of the optimal target state depends on the number of target states m. In previous studies, quantum computing and testing algorithms were used to solve this problem. But these solutions require more Oracle calls and cannot get a high accuracy rate. Therefore, to solve the above problems, we improve the multi-target quantum walk search algorithm, and construct a controllable quantum walk search algorithm under the condition of unknown number of target states. By dividing the Hilbert space into multiple subspaces, the accuracy of the search algorithm is improved from p c = (1/2) – O(1/n) to p c = 1 – O(1/n). And by adding detection gate phase, the algorithm can stop when the amplitude of the target state becomes the maximum for the first time, and the algorithm can always maintain the optimal number of iterations, so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach .

Prevalence of shifted Rayleigh filter for passive surveillance in underwater

PurposeFrom many decades, bearings-only tracking (BOT) is the interested problem for researchers. This utilises nonlinear filtering methods for state estimation as there is only information about the target, i.e. bearing is a nonlinear measurement. The measurement bearing is tangentially related to the target state vector. There are many nonlinear filtering algorithms developed so far in the literature.Design/methodology/approachIn this research work, the recently developed nonlinear filtering algorithm, i.e. shifted Rayleigh filter (SRF), is applied to BOT.FindingsThe SRF is tested for two-dimensional BOT against various scenarios. The simulation results emphasise that the SRF performs well when compared to the standard nonlinear filtering algorithm, unscented Kalman filter (UKF).Originality/valueSRF utilises the nonlinearities present in the bearing measurement through the use of moment matching. The SRF is able to produce the solution in highly noisy environment, long ranges and high dimension tracking.

Sensor selection for target tracking based on single dimension information gain

In sensor management for target tracking, the existing sensor selection methods based on information entropy generally select the sensor that brings the most information gain for target; however, for multi-dimension state vector of target, information gain for target in the specified dimension cannot be guaranteed. For the ambiguity problem in the measure for multi-dimension state vector using information entropy, this study proposes a sensor selection method based on single dimension information gain of the target, which uses particle filter to compute the marginal probability density of target state in the specified dimension and exploits the Kullback–Leibler divergence to measure the information gain of target in the specified dimension, in such a way, by selecting the sensor that brings the most information gain for target in the specified dimension. The proposed method can guarantee higher tracking accuracy gain of target in the specified dimension and obtain more reliable tracking results. Experiment results illustrate that the proposed method has a higher track accuracy of position and velocity in the specified dimension than sensor selection method based on target state entropy.

Extended K alman Filter for Bearings Only T racking

Target tracking using bearings-only measurements in passive mode operation of sonar is a crucial issue of underwater tracking. Target motion in underwater scenario is analyzed using bearings-only measurements and calculating parameters like range, course and speed of the target. This is called Target Motion Analysis (TMA). TMA process is highly non-linear as the measurements chosen are nonlinearly related to the selected target state vector and the traditional, optimal linear Kalman filter will not be appropriate to use. It is presumed that the target is moving in straight line path with constant velocity, so Extended Kalman Filter (EKF) is proposed in this paper. The algorithm is simulated for several scenarios using MATLAB. Monte-Carlo runs are performed to evaluate the capability of the algorithm.

Autonomous relative navigation for noncooperative target using stereo vision measurements

An autonomous relative navigation method based on stereo vision measurements is proposed for noncooperative targets without any prior information. Firstly, a target identification model using only stereo vision measurements is established. Based on the relative position vector computed from the stereo image sequence, the initial state vector of the noncooperative target and navigation filter covariance matrix are initialized by taken spacecraft attitude and camera installation information into account. Then, an extended Kalman filter considering state noise compensation as well as observation variance matrix and state noise matrix adaptive correction is formulated to solve the noncooperative relative navigation problem. Finally, a low Earth orbit, noncooperative target approaching navigation scenario is considered. The simulation results demonstrate the effectiveness of the proposed method for noncooperative autonomous relative navigation.

Observability of a Thrusting/Ballistic Trajectory in 3-D From a Single Fixed Passive Sensor

In previous works, it has been shown that the motion of a thrusting/ballistic object in a three-dimensional (3-D) space is observable with 2-D measurements from a stationary passive sensor. The measurements can either start from the launch point or can be delayed. The observability was investigated by testing the invertibility of the Fisher Information Matrix (FIM). This paper discusses the observability via the uniqueness of the target state vector for a certain sequence of 2-d angle-only measurements from a single fixed passive sensor. The discussion starts with polynomial motion from which the results are extended to nonlinear thrusting/ballistic motion. To illustrate the observability of a thrusting/ballistic target, the estimation problem of such a target with delayed acquisition after burn-out time is solved with a 7-d parameter vector (velocity vector azimuth angle and elevation angle, drag coefficient, 3-d acquisition position, and target speed at the acquisition time). A maximum likelihood (ML) estimator is used for the motion parameter estimation at acquisition time. The impact point prediction is then carried out with the ML estimates. The FIM is investigated via simulations to prove the observability numerically and the maximum likelihood estimator is shown to be efficient.

Modified UBB-based input estimation method for nonlinear manoeuvring target tracking problem

ABSTRACTThe input detection and estimation methods in the manoeuvring target tracking (MTT) application need algorithms for manoeuvring detection and covariance resetting. This algorithm causes an improper delay in target states tracking. In this paper, for solving this problem, unknown but bounded approach for uncertainties modelling is used and a different state space model is developed. In this model, target acceleration is treated as an augmented state in the corresponding state equation. By using interval mathematics, the linearisation error is bounded by an ellipsoidal set and considered in the model development. In augmented state equations, the MTT problem converted to non-manoeuvring target tracking problem. Therefore, the set membership filter is rearranged and used for simultaneous target state and manoeuvre estimation. Furthermore, estimated convex set boundedness is analysed and an upper bound for the estimation error is calculated. The theoretical development of the proposed method is verified with numerical simulations, which contain examples of tracking various manoeuvring targets. The simulation result of the proposed method is compared with traditional input estimation methods. The comparison shows the acceptable performance of the proposed method in the simultaneous estimation of the target acceleration and state vector for the manoeuvring and non-manoeuvring scenarios.

Guidance and Control of a Robot Capturing an Uncooperative Space Target

This paper presented a new method to guide and control a space robot for capturing an uncooperative target. The dynamic model of a target is unknown and estimated with the help of vision system. This methodology has three different steps. First, the feature points of a space target were extracted using the vision system, then the pose of the target (position and orientation) relative to the space robot was determined based on Homography method. Second, because of an unknown model of the target, the location of the center of mass is calculated using kinematic equations and Iterative Closest Point (ICP) algorithm. This would help tracking moving target. Third, a new Adaptive Unscented Kalman Filter (AUKF) was introduced to estimate the dynamic state vector (position, orientation, linear and angular velocities) of an arbitrary space target. The error in AUKF estimation was prevented from divergence by using Fuzzy Logic Adaptive System (FLAS). Finally, a new trajectory method for planning the end-effector velocities of the space robot arm was implemented based on the measurement information from the vision system and estimation a target state using AUKF. The results from simulation experiments were presented and discussed.

Spatiotemporal Registration for Multi-sensor Fusion Systems

A method of online sensor fusion with spatially and temporally misaligned sensors is considered in this paper. A spatiotemporal registration mode is developed for sensor alignment, and augment the target state vector with spatiotemporal bias. An unscented Kalman filter (UKF) is used to fuse and register these sensors, then the target state estimation as well as the spatial and temporal bias estimation can be obtained simultaneously. Simulations show that the proposed algorithm not only can align these sensors properly with both spatial and temporal bias, but can also obtain accurate fused tracks.

Radar network topology optimization for joint target position and velocity estimation

In this paper, we tackle the problem of selecting the radar node positions to provide an estimate of the target state vector with a prescribed accuracy. The topology optimization problem is formulated as selection of a fixed number of radar node positions from a set of available ones, where the radar observations are modeled by a general non-linear model. We further propose a topology optimization framework for the simultaneous estimation of the multi-modal parameter vector. In particular, the task of joint position and velocity estimation is considered. The feasibility of the proposed approach is demonstrated for several cost functions, namely the frame potential as well as the log-determinant and maximum eigenvalue of the error covariance matrix.

Unscented Kalman Filter with Application to Bearings-only Passive Target Tracking

Background/Objectives: Target tracking is an age old problem which demands robust statistical estimators which can effectively track the target within the acceptable limits of errors in target motion parameters. The objective of this paper is to develop a novel estimation algorithm based target tracking simulator for underwater target tracking applications. Methods/Statistical Analysis: The unscented transformation developed by Julier, et al., is applied to the body of Kalman filter to synthesize Unscented Kalman filter. The modeling of target state and measurement vectors is carried out. Unscented Kalman filter is integrated into the model to result in evolution of simulator. Extensive performance evaluation of UKF with respect to bearings-only target tracking problem in Monte-Carlo simulation is carried out and the results are presented. Findings: UKF algorithms effectively track the target with encouraging convergence time which is proved from the results obtained in single run and Monte-Carlo simulation. It is observed that UKF is suitable algorithm for bearings-only target tracking problem. Application/Improvements: The results obtained are satisfactory and UKF can be used in futuristic submarines in Indian Navy owing to its advantages as envisaged in this paper.

Application of Cubature Kalman Filter for Bearingsonly Target Tracking

Background/Objectives: The objective of this paper is to develop a novel estimation algorithm based target tracking simulator for underwater target tracking applications. Methods/Statistical Analysis: An own ship observes corrupted sonar bearings from a radiating target and finds out Target Motion Parameters (TMP) - viz., range, course, bearing and speed of the target. The issue is inherently nonlinear as the bearing measurement is non-linearly related to the target state. CKF is a new nonlinear filter for state estimation. The modeling of target state and measurement vectors is carried out. CKF is integrated into the model to result in evolution of simulator. Extensive performance evaluation of CKF with respect to bearings-only target tracking problem in Monte-Carlo simulation is carried out and the results are presented. Findings: CKF depends on spherical-radial cubature rule that makes it potential to numerically figure variable moment integrals encountered within the nonlinear filter. The underwater passive target tracking following Cubature Kalman filter is explored in this paper. Application/Improvements: The results obtained are satisfactory and UKF can be used in futuristic submarines in Indian Navy owing to its advantages as envisaged in this paper.

Application of Pseudo Linear Estimator for Target Tracking

Background/Objectives: Pseudo Linear Estimator (PLE) is developed for active sonar applications. Methods/Statistical analysis: The PLE offers features of Extended Kalman Filter (EKF). Findings: The results of PLE are compared with that of EKF. The results of MC simulation are presented for typical scenarios. Application/Improvements: In PLE, there is no need to initialize target state vector and its covariance matrix with prior (approximate) knowledge and hence its performance is found to be better than that of EKF.

Multi-Sensor Submarine Surveillance System using MGBEKF

Background/Objectives: The modern submarines use mutlitple sensors for tracking multiple targets in sea environment. In general, multiple sensor data can be handled in two ways: measurement fusion and state vector fusion. Methods/ Statistical Analysis: Measurement fusion is not practical for implementation due to various reasons and hence state vector fusion is proposed. Target trackingusing Modified Gain Bearings only Extended Kalman Filter in generic two-dimensional platform is carried out in each channel. Findings: In this approach, a state vector and its corresponding covariance matrix are extracted from the sensor measurements by an estimator equipped on each sensor. The output of each channel is transported via a data link in to order to be reach the fusion center. Applications/Improvements: A composite target state vector is obtained by performing track-to-track correlation and fusion at the fusion center.Monte-Carlo simulation is carried outand the results are presented for a typical scenario.

Analysis of Effect of Ballistic Coefficient in the Formulations and Performance of EKF with Emphasis on Air Drag

In one dimensional vertical motion in the case of tracking a target, many types of filters included Kalman varieties have been used so far. This paper is presenting a new approach of inverse ballistic coefficient included in the target state vector for reducing the convergence time. For analysis, estimation of object’s altitude and velocity is done by simulation based on noisy error environment measurements. The important of beta (ballistic coefficient) for non linear studies on extended Kalman filter has been established with proper evidence. This work can be further extended to consider the effect of hang off errors and air drag.

Joint range ambiguity resolving and multiple maneuvering targets tracking in clutter via MMPHDF-DA

It is difficult to track multiple maneuvering targets of which the number is unknown and time-varying, especially when there is range ambiguity. The random finite sets (RFS) based probability hypothesis density filter (PHDF) is an effective solution to the problem of multiple targets tracking. However, when tracking multiple targets via the range ambiguous radar, the problem of range ambiguity has to be solved. In this paper, a multiple model PHDF and data association (MMPHDF-DA) based method is proposed to address multiple maneuvering targets tracking with range ambiguous radar in clutter. Firstly, by introducing the turn rate of target and the discrete pulse interval number (PIN) as components of target state vector, and modeling the incremental variable of the PIN as a three-state Markov chain, the problem of multiple maneuvering targets tracking with range ambiguity is converted into a hybrid state filtering problem. Then, by implementing a novel “track-estimate” oriented association with the filtering results of the hybrid filter, target tracks are provided at each time step. Simulation results demonstrate that the MMPHDF-DA can estimate target state as well as the PIN simultaneously, and succeeds in multiple maneuvering target tracking with range ambiguity in clutter. Simulation results also demonstrate that the MMPHDF-DA can overcome the limitation of the Chinese Remainder Theorem for range ambiguity resolving.

Multiple model particle filter track-before-detect for range ambiguous radar

The middle pulse repetition frequency (MPRF) and high pulse repetition frequency (HPRF) modes are widely adopted in airborne pulse Doppler (PD) radar systems, which results in the problem that the range measurement of targets is ambiguous. The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio (SNR) is high enough. In this paper, a multiple model particle filter (MMPF) based track-before-detect (TBD) method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment. By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number (PIN) as components of the target state vector, and modeling the incremental variable of the PIN as a three-state Markov chain, the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state filtering problem. At last, the hybrid filtering problem is implemented by a MMPF-based TBD method in the Bayesian framework. Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously, and succeeds in detecting and tracking weak targets with the range ambiguous radar. Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis (MH) method in low-SNR environment.