For extended object tracking, the random matrix approach is a computationally efficient framework that is capable of estimating the kinematic state and extension of the object jointly, and thus is gaining momentum in recent years. Existing random matrix approaches have an underlying assumption that scatter centers are symmetrically distributed around the centroid. In many real scenarios, however, they are often distributed on particular portions of the object since these parts reflect more radar energy, and measurement distributions over an object are skewed. To effectively describe such a phenomenon, this paper proposes a new measurement model using a skew normal distribution. Based on the proposed model, a variational Bayesian approach is derived to recursively estimate the kinematic state and the extension through convergent iterations. The resultant algorithm inherits the simplicity of the random matrix approach. To cope with the possible abrupt change of kinematic state, extension, and measurement distribution over an object (especially the skewness) when a target maneuvers, a multiple model approach is presented in the information theoretic interacting multiple model framework. Effectiveness of the proposed algorithms is evaluated using simulated data and real experimental data. Results show that the proposed algorithms outperform the existing random matrix methods when measurement distributions are skewed.

Extended object tracking (EOT) is gaining momentum in recent years. The random matrix method is a popular EOT method, which has a simple yet effective framework. The existing random matrix approaches usually assume that scatter centers are uniformly or symmetrically distributed on the object. However, due to weak signal strength and limited measuring angles, scatter centers are densely distributed on several (separated) parts rather than uniformly distributed on the whole object. This results in several measurement-densely-distributed parts. To address this problem, this paper proposes a new conditional Gaussian mixture model. Each component of the model characterizes a single measurement-densely-distributed part. The object extension is modeled as an ellipse by a random matrix. As a portion of the object, each measurement-densely-distributed part is modeled by scaling and shifting that ellipse and transforming that random matrix. This modeling can effectively describe the non-uniformly distributed measurements, but also inherit the simplicity of the random matrix model. Based on the new model and utilized the random matrix framework, a variational Bayesian approach is derived, which recursively and efficiently estimates kinematic and extension states. From the simulation and real experimental results, the proposed approach has a significant performance improvement over some existing random matrix approaches.

Hidden Markov models are widely used for target tracking, where the process and measurement noises are usually modeled as independent Gaussian distributions for mathematical simplicity. However, the independence and Gaussian assumptions do not always hold in practice. For example, in a typical target tracking application, a radar is utilized to track a non-cooperative target. Measurement noise is correlated over time since the sampling frequency of a radar is usually far greater than the bandwidth of measurement noise. Besides, when target is maneuvering, the process and measurement noises are heavy-tailed and non-Gaussian due to intrinsic data generation mechanism. In this paper, we consider a linear pairwise Markov model (PMM) with Student's t noise to model non-cooperative single target tracking without clutter and missed detections. A PMM is more general than an HMM and can be used to model correlated measurement noise or correlated process and measurement noises. The Student's t distribution is one of the most commonly used heavy-tailed distribution and can be used to address irregular target motion. We mainly focus on solving the filtering problems for the model. First, we develop a filter for the case where noise statistics are accurately known. Second, we further consider the case of non-stationary Student's t noise, and propose a novel robust filter by employing a variational Bayesian method. Finally, the effectiveness of the proposed filters is illustrated via simulation results.

Least squares (LS) estimation is simple yet effective for parameter estimation. Most real-world problems are nonlinear. In practice, nonlinear LS problems are linearized first and then solved by a linear LS estimator. However, since these methods solve a nonlinear LS problem by a linear way, there is room for improvement only if estimators being nonlinear in the original measurement. In this article, an LS approach is proposed for nonlinear LS problems, along with theoretical analysis and justification. First, for a general nonlinear measurement model with any form of noise, a unified linearization (UL) approach is proposed under certain assumptions and a linearized least squares (LLS) estimator is defined based on the UL model. Second, an augmented nonlinear least squares (ANLS) estimator is proposed based on LLS estimation. In the ANLS estimator, the original measurement is augmented by its nonlinear conversion intended to further utilize the nonlinear measurement. Moreover, we prove that the ANLS estimator outperforms LLS estimation-based estimators. Finally, the UL and the ANLS estimator are applied to source localization with time difference of arrival and/or frequency difference of arrival measurement, and a two-step ANLS localization algorithm is developed. The performance of the proposed algorithm is evaluated via simulation of some typical localization scenarios.

Extended object tracking (EOT) jointly estimates the object’s kinematic state and extension including the shape, size, and orientation based on measurements from the sensor. For elliptical and rectangular objects, length and width are important parameters of the extension. However, directly modeling and estimation of the length and width may suffer from the uncertainties in resolution of the sensor and the observing angle and the distance between the sensor and object. The aspect ratio (ratio of length to width or width to length) is a key quantity for describing the shape, a constant for rigid body, and an inherent feature that can be directly used for object classification. Moreover, this ratio is insensitive to the above uncertainties. This paper focuses on modeling the extended object and utilizes the aspect ratio in the tracking approach. New dynamic and measurement models are proposed, and the aspect ratio is modeled by a gamma distribution. Then a variational Bayesian approach is derived, which gives estimates of the kinematic state and extension in an analytical way. The approach is evaluated by a simulated and three experimental data sets. Results show that utilizing the aspect ratio can improve the EOT performance in both single- and multiple-sensor cases, compared with the random matrix method and the parameterized elliptical object tracking method.