For extended-object/group-target tracking (EOT/ GTT), the random-matrix approach assumes that measurements are linear in the state and noise with a covariance being a random matrix to represent the object extension or target group. In practice, however, most measurements are nonlinear in the state and noise. This paper proposes a random-matrix approach for EOT/GTT using nonlinear measurements. First, a matched linearization (ML) is proposed to linearize nonlinear measurements. The linearized form has two parts. The first is linear in the state, and it is optimized in the sense of minimum mean square error (MMSE). The second part is linear in the extension-related noise with a preserved second moment, which is important since extension information is contained in the covariance of this noise. The linearized measurements can be incorporated into existing random-matrix algorithms after a simple conversion under certain conditions. Second, a variational Bayesian (VB) scheme is proposed for EOT/GTT using the linearized measurements. This approach can be generally applied no matter whether the linearized measurements are converted or not. The effectiveness of the proposed ML and VB approach is demonstrated by simulation results compared with existing random-matrix algorithms.

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.

For automotive radar-based extended object tracking, this paper proposes a new approach, which jointly estimates the kinematic state and the extension of a vehicle. The vehicle’s shape is described as a rectangle with its vertices treated as the extension state. “Having a rectangular shape” is described as a quadratic equality constraint on the state. To deal with the challenging problem of modeling measurement (scattering center) distribution over a vehicle, we partition the rectangular area into multiple regions and assume that in each region the scattering centers have a simple distribution. An approach is proposed to associate measurements with these regions. Given an association, the target state is estimated in a linear minimum mean-square-error framework with the shape constraint treated as a pseudo measurement. The probabilities for these regions to generate measurements are updated online. The estimate is then projected into the constraint space. The effectiveness of the proposed approach is illustrated using both simulated and real data.

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.

For extended object tracking (EOT), a fluctuating number of measurements are generated by a sensor at a time instant. In practice, the measurement number depends on the object extension, sensor resolution, and sensor-to-object geometry. Given the sensor resolution, the number thus contains information on the object state and extension. This paper proposes a random-matrix approach to EOT utilizing this information to improve the performance of state and extension estimation. First, a Gamma-alike distribution of the measurement number is proposed to model the dependency of the number on sensor resolution and the object state and extension. This model also fits the random-matrix framework. Second, a Bayesian approach to jointly estimating the state and extension based on an extension-dependent number of measurements. Facilitated by the form of the distribution, the derived approach has an analytical form and it can naturally reduce to an EOT approach without directly using measurement numbers. The proposed number model can also be incorporated with different random-matrix approaches. The effectiveness of the proposed approach is demonstrated by evaluation results using one simulation and two real-data experimental scenarios compared with existing random-matrix algorithms.