Target motion analysis with unknown measurement noise variance

In this paper, a novel target motion analysis (TMA) method using unscented Kalman Filter (UKF) based on modified polar coordinates (MPC) is proposed to improve the localization accuracy for underwater target with constant velocity. The proposed approach utilizes bearings of two-arrays to estimate the localization and velocity of the target. Unlike extended Kalman filter, unscented Kalman Filter (UKF), which is biased and sensitive to the initial value in Cartesian coordinate, the proposed scheme is much more stable and asymptotically unbiased. Moreover, the performances among these schemes are compared based on the noisy bearings from towed array sonar and flank array sonar via Monte Carlo simulations. Simulation results show that the proposed MPC-UKF has better performances with higher numerical stability and little cost of computational complexity.

To enhance the tracking accuracy of multi-ellipse extended target tracking for maneuvering targets, we propose a Variational Bayesian-based Interacting Multiple Model Maneuvering Extended Target Tracking Algorithm. The algorithm leverages multiple kinematic models within an Interacting Multiple Model framework to predict the target state, enabling better adaptation to various target kinematic modes during the time update. Following the prediction step, variational Bayesian inference, which includes inference of unknown measurement noise, is applied independently within each model to estimate the target’s position and shape. Then, model probabilities are updated based on the likelihood functions, and the model transition probabilities are adaptively learned. Concurrently, an ellipsoid fusion method is employed to combine the shape estimates from different models, while kinematic states are fused using model weights, yielding a robust overall target state estimate. The feasibility and performance of the proposed algorithm are validated by comparing its target tracking simulation results with those of other algorithms under different scenarios.

Underwater acoustic sensor networks (UASNs) play an important role in the ocean's protection. They can realize real-time data collection, monitoring, exploration, and many other underwater applications by connecting and coordinating seafloor sensors and underwater vehicles. To achieve these application objectives, such as fishes tracking in biological monitoring field and submarines tracking in military field, target tracking is one of the key techniques. This paper presents a centralized fusion algorithm based on the interacting multiple models and the adaptive Kalman filter (IMMCFAKF) for target tracking in UASNs. Specifically, by introducing an adaptive forgetting factor into the optimal centralized fusion Kalman filter algorithm, the optimal centralized fusion adaptive Kalman filter (CFAKF) algorithm is obtained first. Then, combining the superiorities of both the optimal CFAKF algorithm and the conventional IMM algorithm, the optimal IMMCFAKF is achieved. The numerical simulations are provided to demonstrate the effectiveness of the proposed optimal IMMCFAKF algorithm.

Fusion identification and estimation of multisensor multichannel AR signals with missing measurements and sensor biases

In this paper, an iterative and joint algorithm is proposed to estimate additive white Gaussian noise (AWGN) variance and channel impulse response (CIR) in orthogonal frequency division multiplexing (OFDM) systems. With the aid of pilots, a rough CIR is firstly estimated by compressed sensing techniques such as sparsity adaptive matching pursuit (SAMP). By exploiting the sparsity of the estimated CIR and the method of orthogonal projection matrix, the noise subspace is obtained to evaluate noise variance. The above two estimator feeds each other, then the estimation of noise variance is used to update the CIR estimation which also updates the noise variance in the following. After several iterations, a perfect performance can be achieved. The operation process is simple and its performance is robust to the noise power. Simulation results show that the propose scheme can obtain better performance than traditional scheme with less pilots.

In this paper we address the joint estimation of the channel impulse response in orthogonal frequency division multiplexing systems with phase distortion, namely phase noise and carrier frequency offset, phase noise bandwidth and the additive noise variance. The estimation algorithm is based on an implementation of the Extended Kalman Filter within the general framework of the Expectation-Maximization algorithm. We focus on the partial training case, where the transmitted signal is not fully known. To tackle this problem, we utilize a Rao-Blackwellized Extended Kalman Filter. We also compare our results with another nonlinear filtering technique, namely Rao-Blackwellized Particle Filtering, applied to this joint estimation problem. The performance of the two filtering techniques considered in this paper is evaluated in terms of the mean square error of the channel estimates and the numerical complexity introduced by each of these techniques.

Probability hypothesis density (PHD) filter has been demonstrated a promising algorithm for tracking an unknown number of targets in real time. However, this method can only be used in the multi‐target tracking systems with known measurement noise variances; otherwise, the tracking performance will decline greatly. To solve this problem, an adaptive PHD filter algorithm is proposed based on the variational Bayesian approximation technique to recursively estimate the joint PHDs of the multi‐target states and the time‐varying measurement noise variances. First, the variational calculus method is employed to derive the multi‐target estimate recursions, and then the Gaussian and the inverse Gamma distributions are introduced to approximate the joint posterior PHD, and achieve a closed‐form solution. Simulation results show that the proposed algorithm can effectively estimate the unknown measurement noise variances and has a good performance of multi‐target tracking with a strong robustness.

This paper addresses the problem of joint tracking and classification (JTC) of a single extended target with a complex shape. To describe this complex shape, the spatial extent state is first modeled by star-convex shape via a random hypersurface model (RHM), and then used as feature information for target classification. The target state is modeled by two vectors to alleviate the influence of the high-dimensional state space and the severely nonlinear observation model on target state estimation, while the Euclidean distance metric of the normalized Fourier descriptors is applied to obtain the analytical solution of the updated class probability. Consequently, the resulting method is called the “JTC-RHM method.” Besides, the proposed JTC-RHM is integrated into a Bernoulli filter framework to solve the JTC of a single extended target in the presence of detection uncertainty and clutter, resulting in a JTC-RHM-Ber filter. Specifically, the recursive expressions of this filter are derived. Simulations indicate that: (1) the proposed JTC-RHM method can classify the targets with complex shapes and similar sizes more correctly, compared with the JTC method based on the random matrix model; (2) the proposed method performs better in target state estimation than the star-convex RHM based extended target tracking method; (3) the proposed JTC-RHM-Ber filter has a promising performance in state detection and estimation, and can achieve target classification correctly.

We investigate cooperative target tracking of multiple unmanned aerial vehicles (UAVs) with a limited communication range. This is an integration of UAV motion control, target state estimation, and network topology control. We first present the communication topology and basic notations for network connectivity, and introduce the distributed Kalman consensus filter. Then, convergence and boundedness of the estimation errors using the filter are analyzed, and potential functions are proposed for communication link maintenance and collision avoidance. By taking stable target tracking into account, a distributed potential function based UAV motion controller is discussed. Since only the estimation of the target state rather than the state itself is available for UAV motion control and UAV motion can also affect the accuracy of state estimation, it is clear that the UAV motion control and target state estimation are coupled. Finally, the stability and convergence properties of the coupled system under bounded noise are analyzed in detail and demonstrated by simulations.

Particle filters for probability hypothesis density filter with the presence of unknown measurement noise covariance

This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track-oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the probability density function (pdf) of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian MHT (hypothesis oriented, based on combinatorial analysis of the general multitarget problem), which is shown to be amenable under some (reasonable) assumptions to the track-oriented MHT (TOMHT). The latter can be implemented efficiently using multidimensional assignment (MDA). The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model (IMM) estimator. The issues of measurements of different dimension and different coordinate systems together with the selection of certain MHT design parameters - the spatial densities of the false measurements and new targets - are also discussed.

A novel T-S fuzzy particle filtering algorithm based on fuzzy C-regression clustering

This paper considers the problem of tracking multiple moving targets on a road network with sparse, highly localized, unattended ground sensor data that are subject to clutter and missed detections. Hidden Markov models for single-target localization with unattended ground sensor data are first derived for road networks, under the assumption of perfect data association. These hidden Markov models are then used to solve the data association problem in the presence of clutter and missed detections for multitarget tracking using a Rao–Blackwellized particle filter. The proposed hidden Markov model tracking approach permits easy generation of accurate probabilistic models from a priori road network structure information, and it naturally enables sparse computationally efficient handling of multimodal target state uncertainties using both positive and negative unattended ground sensor information. The Rao–Blackwellized particle filter provides a fully Bayesian solution to the data association problem, enabling exploration of the association hypotheses space that leverages the computational advantages of exact hidden Markov model inference for multimodal state estimation. Numerical simulations demonstrate the effectiveness of the hidden Markov model/Rao–Blackwellized particle filter on challenging multitarget tracking scenarios with high false-alarm and missed detection rates.

The problem of track to track association in passive sonar with multiple platforms and/or time interruptions is considered. Typical case is a submarine equipped with a hull array (HA) and a towed array (TA). A few methods are applicable and discussed here, coming from detection and estimation theory. Performance of likelihood ratio test are studied for the binary case to associate one track from measurement platform 1 to one another from platform 2. Then it is generalized to two sets of tracks using either a motion representation of the target state (Target Motion Analysis, TMA) or directly the spectrum of frequency lines. Finally, this is also applied to a single antenna like TA where the two origins comes from two different time periods e.g. before/after an ownship maneuver Both applications are supported by a theoretic background and at-sea results.

The significant challenge in shallow water environments is performing reliable target detection and classification while maintaining a reasonable false alert rate. Recent Navy operational experiences in shallow water environments have shown that existing active sonar systems experience excessive amounts of clutter and false alerts which result in a significant reduction in platform tactical advantage and survivability. A target motion discriminator (TMD) technique based on the Interacting Multiple Model (IMM) estimation algorithm is presented to exploit the consistency of position and motion information observed over multiple pings to form a robust classification decision. Several motion class models reside within the TMD, to provide accurate target state estimates and target likelihood functions for both maneuvering and non-maneuvering contacts. Classification performance is dramatically enhanced by using a "no target model" to reject contacts which exhibit erratic motion, i.e., inconsistent with a target motion model while promoting contacts with consistent motion. The accurate estimation of target dynamics obtained by the IMM approach provides the capability to reject stationary clutter resulting from surface and bottom reverberation and reliably detect the slow moving threat. A robust sequential likelihood ratio test which minimizes the classification decision time and improves classification performance is developed and demonstrated using sea test data collected in various environments.