In multi-extended target tracking, each target may generate more than one observation. The traditional probability hypothesis density (PHD)-based methods are no longer effective in such scenarios. Recently, the Gaussian mixture PHD approach for the extended target tracking (ET-GM-PHD) has been presented to solve such a problem. The tracking performance of this approach has been restricted by the following disadvantages. First, it only focuses on the linear models. When targets are moving with nonlinear models, it may lead to great tracking errors. Second, the birth intensities are commonly assumed as a prior. In practice, these intensities are always unknown. In order to improve the tracking performance of the traditional ET-GM-PHD approach, a novel extended target tracking approach, namely the ET-cubature information GM-PHD (ET-CIGM-PHD) approach, has been proposed in this paper. To be more specific, we, first, utilize the cubature information filter (CIF) and gating methods to predict and update the Gaussian mixture components of the ET-GM-PHD approach. In the merit of high estimating accuracy of the CIF method, the tracking accuracy of the traditional ET-GM-PHD approach can be significantly improved. Due to the gating method, only part of cells can be used to construct the observation set in the update stage. Thus, the computational load of our approach can be significantly reduced. Then, we propose an adaptive initiating method for the birth intensity initiating. In our method, we utilize the estimated target set to select the most possible partition. Then, we remove cells associated with the estimated targets from the selected partition. The left cells are used to initiate the birth intensity. With the help of the above implementations, the birth intensity can be adaptively initiated. Using such a method, our approach can solve the cases that the prior information of birth intensity is rather little. The simulation results demonstrate the effectiveness of our approach.

In multi-target tracking, the key problem lies in estimating the number and states of individual targets, in which the challenge is the time-varying multi-target numbers and states. Recently, several multi-target tracking approaches, based on the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter, have been presented to solve such a problem. However, most of these approaches select the transition density as the importance sampling (IS) function, which is inefficient in a nonlinear scenario. To enhance the performance of the conventional SMC-PHD filter, we propose in this paper two approaches using the cubature information filter (CIF) for multi-target tracking. More specifically, we first apply the posterior intensity as the IS function. Then, we propose to utilize the CIF algorithm with a gating method to calculate the IS function, namely CISMC-PHD approach. Meanwhile, a fast implementation of the CISMC-PHD approach is proposed, which clusters the particles into several groups according to the Gaussian mixture components. With the constructed components, the IS function is approximated instead of particles. As a result, the computational complexity of the CISMC-PHD approach can be significantly reduced. The simulation results demonstrate the effectiveness of our approaches.

The conventional target tracking approaches are presented under the assumption of the point target. In multi extended target scenarios, the tracking performance of these approaches may be greatly decreased. The the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) (named as the ET-GM-PHD approach) has been presented for applying the GM-PHD approach into extended target tracking. However, it has been proposed under the linear models. In fact, most of targets are moving with nonlinear models. Thus, we, in this paper, present a square-root cubature information filter (SCIF) based ET-GM-PHD approach. To be more specific, we, first, employ the cubature points to predict the mean and the square-root factor of covariance. Then, the information forms of the mean and square-root of covariance has been used to update the mean and covariance of GM component. Meanwhile, we integrate the gating method into our method for saving computational complexity. Owing to the significant tracking performance of the SCIF method, our approach can estimate states and number of multi extended targets in nonlinear scenarios. In addition, we also propose an observation driven method to initiate the birth intensity. As for our method, the conditional probability has been adopted to describe the association between the target and its corresponding observations. With such a probability, the most possible partition, where the estimated targets belong to, can be approximated. Thus, the birth intensity can be estimated by removing the cells associated with the estimated targets. Since we use the estimated targets to initiate the birth intensity, our approach can initiate the birth intensity adaptively. The simulation results prove the effectiveness of our approach.