Performance Analysis of Bayesian Filtering and Smoothing Algorithms for Underwater Passive Target Tracking

A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets’ numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets’ intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.

In this paper, according to the characteristics of underwater target tracking, extended Kalman filter (EKF) algorithm was applied to address underwater bearing-only non-maneuverable target tracking problem. To ensure the observability in bearing-only passive target tracking, we use two sensor arrays in uniform rectilinear motion to track the single target. EKF is recursive Bayesian filter algorithm based on the linearization of the nonlinearities in the state and the measurement system. And the simulation experiment shows that, to the constant velocity single target, the bearings-only EKF algorithm with dual-array has good results, also the EKF has lower computation complexity than unscented Kalman filter and particle filter. It confirms the effectiveness of the EKF algorithm in solving the underwater bearing-only target tracking problem.

A new approach to the optimal formation problem is proposed in the sense of the passive target tracking using time difference of arrival (TDOA) data obtained by cooperative UAVs. In most existing methods, under the assumption that arbitrary unbiased and efficient estimator could be designed for target tracking, the objective function for the information maximizing formation is defined without particular consideration of the filter structure used for passive target tracking. However, this approach might be restrictive because the overall performance of passive target tracking depend on the UAV formation and the filter structure as well. To overcome this limitation, the proposed technique takes account of the practical tracking filter structure and its properties in the problem. To do this, it is firstly shown that the amount of moving target information is expressed in terms of the variance of UAVs' angular positions. In order to guarantee the satisfactory target tracking performance even when the UAVs-target relative geometry is time-varying, the optimal formation problem is formulated as finding the maximizing solution of the objective function in worst-case. Through the simulations, the effectiveness of the proposed scheme is demonstrated.

Object-Oriented Environment for Assessing Tracking Algorithms

There are many target tracking applications where measurements are nonlinearly related to target state. Typical examples of this include active sonar tracking with range-bearing measurements and passive sonar tracking with bearings-only measurements, where target state is position and velocity in Cartesian coordinates. In this paper, ellipsoidal set based estimators are derived for both of these nonlinear measurement scenarios. The premise of an estimate that provides a guaranteed bound on target state is maintained throughout the paper. Monte Carlo simulation results are presented for each type of nonlinear measurement, including a comparison with the extended Kalman filter in the case of bearings-only measurements.

When tracking maneuvering targets, the sudden changes of target states and nonlinear problems in passive tracking cause serious decline and even divergence in the performance of some conventional algorithms. Taking this into account, a novel adaptive tracking algorithm for maneuvering targets is proposed in this paper. First, a new weighed factor could adaptively adjust the filter gain is introduced in Modified Input Estimation (MIE) algorithm to improve its tracking performance. Then, the least squares technique is combined for tracking passive multi-sensor maneuvering targets in high accuracy without any priori information of maneuver. Simulation results show the effectiveness of the proposed algorithm. Compared with the traditional MIE and fuzzy MIE algorithm, this algorithm has a better tracking performance.

Data fusion algorithms are inevitable in improving the accuracy and reliability of radar target tracking. Considering the shortcomings of target tracking in Cartesian coordinates, all the fusion process are carried out in spherical coordinate system. To fuse data from bidimensional radar and Infrared Search and Track (IRST), five data fusion methods, Bayesian fusion, Signal variance based fusion, Optimal fusion, Error variance based fusion and Extended Kalman Filter (EKF) based fusion are proposed and analyzed. The performances of the methods are analyzed in terms of Root Mean Square Error in Position (RMSPE) and Mean Absolute Error in Position (MAPE) for a wide range of measurement noise variances. It is concluded that EKF based fusion has the best error performance. Kalman Filter State-Vector Fusion (KF-SVF) which is a hierarchical fusion architecture, having first level of fusion with Kalman filter and second level with error variance based fusion method, is available in the literature. In this work it has been expanded to Extended Kalman Filter—State-Vector Fusion (EKF-SVF) with either error variance based fusion, signal variance based fusion or optimal information fusion as second level. All the three EKF-SVF methods have similar error characteristics, but EKF-SVF with signal variance based fusion, unlike the other two, provides less computational cost since it does not involve matrix inversion. While comparing EKF based fusion and EKF-SVF, EKF-SVF offers increased error minimization.

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

The Kalman filter has earned its fame through its elegance, its compatibility with digital simulation, and its reasonable performance even when the somewhat restrictive assumptions on which it is based are not all met. Extensions of the Kalman filter are varied, and not all estimators dubbed Extended Kalman Filter (EKF) are equivalent. This chapter develops some filter extensions appropriate to target tracking, classification, and command architectures. These include estimation of essentially nonlinear and non-Gaussian motion models for targets, nonlinear conversion of range-bearing measurements into position measurements, and lack of true independence between target state and observation system errors. In target tracking, using models of target motion and a stream of measurements or observations, the Kalman filter provides the conditional distribution of the location of a target following an unpredictable path. From distribution we can not only accurately estimate the location of the target, but we can also place a capture region about the estimate that will contain the target with any pre-specified probability. The Kalman algorithm is based upon a linear-Gauss–Markov (LGM) model of the engagement. Even when there are nonlinearities in the engagement model, an expanded version of the Kalman filter (the EKF) generates plausible position estimates and capture regions. We will contrast realized performance with that predicted by the EKF. The shortcomings of the Kalman filter when used in command architectures are important, but in many cases they can be mitigated. In others alternative approaches like the GWE, explored in later chapters, are much more effective.

Target tracking, nonlinear control, and fault detection are typically evaluated with only a Root Mean Square (RMS). RMS is an absolute measurement of the system performance and does not provide a statistic as to the tracker, controller, or fault detection algorithmic performance. For this paper, we investigate the non-credibility index (NCI) and average normalized estimation error square (ANEES) for nonlinear estimation for the Kalman Filter (KF), the Central Difference Filter (DD1), the unscented Kalman filter (UKF), and the particle filter (PF). Fault detection and target track performance is dependent on target maneuvers, sensor errors, model parameters, and state estimation which need to be understood relative to the filter performance versus the absolute performance (i.e. root mean square) of the system. Utilizing the developments of the Nonlinear Estimation Framework (NEF) toolbox, we develop methods of nonlinear relative comparison performance between nonlinear filters in a unified scenario.

It is well known that passive target tracking by a single observer, commonly referred to as target motion analysis (TMA), can be done using angle and/or frequency measurements. Depending on the measurement set, different passive tracking procedures result: angle-only tracking (AOT), frequency-only tracking (FOT), and angle/frequency tracking (AFT). Whereas the two-dimensional passive tracking problem has been solved for a multitude of scenarios, thus giving a good insight into the parametric dependences, the three-dimensional problem has been discussed only in a few specific cases. To get a deeper insight into the parametric dependences of three-dimensional TMA, this work analyzes AOT and AFT in typical three-dimensional Airborne Warning and Control System (AWACS) scenarios. A Cramer Rao (CR) analysis of the problem reveals the parametric dependences of both methods and gives a clear idea of the increase in estimation accuracy by using AFT instead of AOT. The results obtained in this way are well confirmed by Monte Carlo simulations taking maximum likelihood (ML) as estimation procedure.

It is of great importance to develop a robust and fast tracking algorithm in passive localization and tracking system because of its inherent disadvantages such as weak observability and large initial errors. In this correspondence, a new algorithm referred to as the iterated unscented Kalman filter (IUKF) is proposed based on the analysis and comparison of conventional nonlinear tracking problem. The algorithm is developed from UKF but it can obtain more accurate state and covariance estimation. Compared with the traditional approaches (e.g., extended Kalman filter (EKF) and UKF) used in passive localization, the proposed method has potential advantages in robustness, convergence speed, and tracking accuracy. The correctness as well as validity of the algorithm is demonstrated through numerical simulation and experiment results.

Nonlinear state estimation is a pre-requisite for advanced process control and fault diagnosis tasks. In literature, various recursive nonlinear filtering techniques have been proposed and used for state estimation of nonlinear systems. Over the last few years, Moving Horizon Estimation (MHE) is increasingly being used for state estimation of nonlinear systems. Moving horizon estimation works with a window of data and hence requires additional online computation compared to recursive nonlinear filters. However, MHE performs both smoothing and filtering and thus has the potential to obtain more accurate state estimates as compared to the recursive filters. Most of the available comparisons of MHE with recursive filters are based on simulation case studies where the true states and parameters, as well as noise processes are exactly known. In this work, we apply MHE to a three-tank experimental setup and compare its performance with various nonlinear filters available in literature such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Gaussian Sum EKF (GSEKF). We present some of the challenges in experimental implementation of state estimation approaches. These include presence of unknown disturbances, non-whiteness of noise signals as well as lack of accurate measurements. We then discuss the approach followed for obtaining model parameters and noise characterization to make the models amenable for filter implementation. It is found that EKF, GSEKF and UKF perform as well as MHE as far as accuracy is concerned, but require significantly lower computational efforts.

In underwater, the bearings-only passive target tracking can be done with many available estimators by supplying the noisy bearing measurements from a passive sonar as inputs. The problem here is, all the estimators fail to work in the abnormal conditions which includes the situation of missed bearings, the situation of spurious bearings and the situation in which the noise is non-Gaussian. The algorithm developed in this paper will take care of the above mentioned problems. The main step involved in the algorithm includes preprocessing of the noisy bearing measurements and then supply the preprocessed data along with the variance as input to the advanced nonlinear filter like Modified Gain Bearings-Only Extended Kalman Filter (MGBEKF) to find the target motion parameters. Preprocessing stage involves reducing the amplitude of the noise in the measurements, converting the nongaussian noise to Gaussian and generating the substitute for the missed and spurious bearings using Pseudo Linear Estimator (PLE).

Traditional multiple target tracking (MTT) algorithms such as JPDA, MHT, a basic assume that the targets are points source. This is unrealistic in many cases. We consider targets with certain geometrical shape and they may give multiple measurements using the Markov Chain Monte Carlo (MCMC) approach. We aim at estimating the states of targets, their shape parameters, and number of targets. The proposed approach is based on the clustering process of finite mixture models (FMM), where the parameters of the FMM are obtained by the MCMC sampler. The states of the targets are estimated by equivalent measurement (EQM). The final experiment of three target tracking verifies the proposed algorithm.