Robust range-parameterized cubature Kalman filter for bearings-only tracking

In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.

Consecutive tracking for ballistic missile based on bearings-only during boost phase

This paper proposes a modified centralized shifted Rayleigh filter（MCSRF） algorithm for tracking boost phase of ballistic missile（BM） trajectory with a highly nonlinear dynamical model based on bearings-only.This paper contributes three folds.Firstly,the mathematical model of an MCSRF for multiple passive sensors is derived.Then,minimum entropy based onedimensional optimization search to adaptively adjust the probability of the different filters for real time state estimation is deployed.Finally,the unscented transform（UT） is introduced to resolve the asymmetric state estimation problem.Simulation results show that the proposed algorithm can consecutively track the BM precisely during the boost phase.In comparison with the unscented Kalman filter（UKF） algorithm,the proposed algorithm effectively reduces the tracking position and velocity root mean square（RMS） errors,which will make more sense for early precision interception.

Constrained auxiliary particle filtering for bearings-only maneuvering target tracking

To track the nonlinear,non-Gaussian bearings-only maneuvering target accurately online,the constrained auxiliary particle filtering(CAPF)algorithm is presented.To restrict the samples into the feasible area,the soft measurement constraints are implemented into the update routine via the1 regularization.Meanwhile,to enhance the sampling diversity and efficiency,the target kinetic features and the latest observations are involved into the evolution.To take advantage of the past and the current measurement information simultaneously,the sub-optimal importance distribution is constructed as a Gaussian mixture consisting of the original and modified priors with the fuzzy weighted factors.As a result,the corresponding weights are more evenly distributed,and the posterior distribution of interest is approximated well with a heavier tailor.Simulation results demonstrate the validity and superiority of the CAPF algorithm in terms of efficiency and robustness.

A new algorithm of bearings-only multi-target tracking of bistatic system

Much research mainly focuses on the batch processing method （e.g. maximum likelihood method） when bearings-only multiple targets tracking of bistatic sonar system is considered. In this paper, the idea of recursive processing method is presented and employed, and corresponding data association algorithms, i.e. a multi-objective ant-colony-based optimization algorithm and an easy fast assignment algorithm are developed to solve the measurements-to-measurements and measurements-to-tracks data association problems of bistatic sonar system, respectively. Monte-Carlo simulations are induced to evaluate the effectiveness of the proposed methods.

Adaptive Extended Kalman Filtering for Bearings-Only Targets Tracking Problem

An adaptive extended Kalman filtering (AEKF) is proposed for nonlinear control systems. For bearingsonly targets tracking problem, we present an adaptive extended Kalman filter which suits a nonlinear observation model and a linear dynamical model. Simulation results have shown that the adaptive extended Kalman filter for the passivetracking problem performs better than the original extended Kalman filter (EKF).

Posterior Cramer-Rao lower bounds for multitarget bearings-only tracking

Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.

Bearings-only fusion tracking for maneuvering target with wavelettransform in three dimensional space

A new fusion tracking algorithm is presented to track maneuvering target in three-dimensional (3D) space with bearings-only measurements. With the introduction of passive location and interacting multiple model (IMM) algorithm based on multirate model, the high-rate sequence measurements of two sensors are utilized. Simulation results show that the performance of tracking has been improved. The new algorithm removes the barrier of processing high-rate bearings-only measurements.

Ant colony optimization for bearings-only maneuvering target tracking in sensors network

In this paper, the problem of bearings-only maneuvering target tracking in sensors network is investigated. Two objectives are proposed and optimized by the ant colony optimization （ACO）, then two kinds of node searching strategies of the ACO algorithm are presented. On the basis of the nodes determined by the ACO algorithm, the interacting multiple models extended Kalman filter （IMMEKF） for the multi-sensor bearings-only maneuvering target tracking is introduced. Simulation results indicate that the proposed ACO algorithm performs better than the Closest Nodes method. Furthermore, the Strategy 2 of the two given strategies is preferred in terms of the requirement of real time.

Cramér-Rao lower bound analysis for guidance systems with bearings-only measurements

Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.

BIASED BEARINGS-ONLY PARAMETER ESTIMATION FOR BISTATIC SYSTEM

According to the biased angles provided by the bistatic sensors, the necessary condition of observability and Cramer-Rao low bounds for the bistatic system are derived and analyzed, respectively. Additionally, a dual Kalman filter method is presented with the purpose of eliminating the effect of biased angles on the state variable estimation. Finally, Monte-Carlo simulations are conducted in the observable scenario. Simulation results show that the proposed theory holds true, and the dual Kalman filter method can estimate state variable and biased angles simultaneously. Furthermore, the estimated results can achieve their Cramer-Rao tow bounds.

Maximum correntropy-based pseudolinear Kalman filter for passive bearings-only target tracking

This paper proposes a new approach for solving the bearings-only target tracking (BoT) problem by introducing a maximum correntropy criterion to the pseudolinear Kalman filter (PLKF). PLKF has been a popular choice for solving BoT problems owing to the reduced computational complexity. However, the coupling between the measurement vector and pseudolinear noise causes bias in PLKF. To address this issue, a bias-compensated PLKF (BC-PLKF) under the assumption of Gaussian noise was formulated. However, this assumption may not be valid in most practical cases. Therefore, a bias-compensated PLKF with maximum correntropy criterion is introduced, resulting in two new filters: maximum correntropy pseudolinear Kalman filter (MC-PLKF) and maximum correntropy bias-compensated pseudolinear Kalman filter (MC-BC-PLKF). To demonstrate the performance of the proposed estimators, a comparative analysis assuming large outliers in the process and measurement model of 2D BoT is conducted. These large outliers are modeled as non-Gaussian noises with diverse noise distributions that combine Gaussian and Laplacian noises. The simulation results are validated using root mean square error (RMSE), average RMSE (ARMSE), percentage of track loss and bias norm. Compared to PLKF and BC-PLKF, all the proposed maximum correntropy-based filters (MC-PLKF and MC-BC-PLKF) performed with superior estimation accuracy.

On distributed Kalman filter based state estimation algorithm over a bearings-only sensor network

This paper studies the distributed state estimation problem for a class of discrete-time linear time-varying systems over a bearingsonly sensor network.A novel fusion estimation algorithm of the distance between the target and each sensor is constructed with the mean square error matrix of corresponding estimation being timely provided.Then,the refined estimation of distance is presented by minimizing the mean square error matrix.Furthermore,the distributed Kalman filter based state estimation algorithm is proposed based on the refined distance estimation.It is rigorously proven that the proposed method has the consistency and stability.Finally,numerical simulation results show the effectiveness of our methods.

Q-Learning-Based Target Selection for Bearings-Only Autonomous Navigation

This paper presents a Q-learning-based target selection algorithm for spacecraft autonomous navigation using bearing observations of known visible targets.For the considered navigation system,the position and velocity of the spacecraft are estimated using an extended Kalman filter(EKF)with the measurements of inter-satellite line-of-sight(LOS)vectors obtained via an onboard star camera.This paper focuses on the selection of the appropriate target at each observation period for the star camera adaptively,such that the performance of the EKF is enhanced.To derive an effective algorithm,a Q-function is designed to select a proper observation region,while a U-function is introduced to rank the targets in the selected region.Both the Q-function and the U-function are constructed based on the sequence of innovations obtained from the EKF.The efficiency of the Q-learning-based target selection algorithm is illustrated via numerical simulations,which show that the presented algorithm outperforms the traditional target selection strategy based on a Cramer-Rao bound(CRB)in the case that the prior knowledge about the target location is inaccurate.

Methods for bearings-only underwater target motion analysis

The problem of estimation of underwater target motion parameters via bearings only is the most of ten encountered and most difficult to solve in the underwater target motion analysis.As the bearings-only target motion analysis is a nonlinear and multiextremal global optimization problem, so most classical estimation methods often lead the solution to convergence to one of the local extremes other than the global extreme, especially, when the noise of target bearing observation is added. In this paper we propose to use the Generalized Least Square method on the rough estimation of target motion parameters, and then use the Sequential Uniform Design method to gain a more precise estimation on the bases of rough estimation.The latter ensures that the result convergences to the global extreme. The algorithm based on the above two methods is profitable for the bearings-only target motion analysis even under conditions of large bearing observation error.

Passive bearings-only target motion analysis based on association of multiple arrays

The method for Bearings-Only Target Motion Analysis (BO-TMA) based on bearing measurements fusion of two arrays is studied. The algorithms of pseudolinear processing, extended Kalman filter and maximum likelihood estimation are presented. The results of simulation experiments show that the BO-TMA method based on association of multiple arrays not only makes contributions towards eliminating maneuvers needed by bearings-only TMA based on single array,but also improves the stabilization and global convergence for varied estimation algorithms.

Improved Particle Filter for Target Tracking

A new improved particle filter algorithm with the simplified UT （unscented transformation） and the modified unscented Kalman filter （UKF） proposal distribution is presented. The scaling factor is added to adaptively estimate on line and to improve the filtering performance. An adaptive algorithm is developed. In the bearings-only tracking experiments, the results confirm the improved particle filter algorithm outperforms others.

Multiple Model Filtering in the Presence of Gaussian Mixture Measurement Noises

A simplified multiple model filter is developed for discrete-time systems inthe presence of Gaussian mixture measurement noises. Theoretical analysis proves that the proposedfilter has the same estimation performance as the interacting multiple model filter at the price ofless computational cost. Numerically robust implementation of the filter is presented to meetpractical applications. An example on bearings-only guidance demonstrates the effect of the proposedalgorithm.