Time-Matching Random Finite Set-Based Filter for Radar Multi-Target Tracking

Radar nonlinear multi-target tracking method with parallel PHD filter

Since probability hypothesis density (PHD) filters do not need explicit data association, they have recently been widely used in radar multi-target tracking (MTT). However, in existing PHD filters, sampling times are generally considered the same for all targets. Due to the limitation of antenna beam width in radar applications, the same sampling time for all targets will lead to a mismatch between the predicted data and measurement data, reducing the accuracy of radar MTT. In order to eliminate the estimation error with less computational cost, a radar nonlinear multi-target tracking method with a parallel PHD filter is proposed in this article. The measurement area is divided into several subspaces according to the beam width of the radar antenna, and the PHD of all subspaces is calculated in parallel. Then, multi-feature information in radar echo assists tracking and improves real-time performance. Experimental results in various scenarios illustrate that the proposed method can eliminate the estimation errors introduced by sampling time diversity at the cost of less computation cost, especially in cluttered environments.

Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation

In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate.

A Labeled GM-PHD Filter for Explicitly Tracking Multiple Targets

In this study, an explicit track continuity algorithm is proposed for multitarget tracking (MTT) based on the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) filter. Trajectory maintenance and multitarget state extraction in the GM-PHD filter have not been effectively integrated to date. To address this problem, we propose an improved GM-PHD filter. In this approach, the Gaussian components are classified and labeled, and multitarget state extraction is converted into multiple single-state extractions. This provides the identity label of the individual target and can shield against the negative effects of clutter in the prior density region on the estimates, thus realizing the integration of trajectory maintenance with state extraction in the GM-PHD filter. As no additional associated procedures are required, the overall real-time performance of the proposed filter is similar to or slightly lower than that of the basic GM-PHD filter. The results of numerical experiments demonstrate that the proposed approach can achieve explicit track continuity.

Low-Complexity Joint Range and Doppler FMCW Radar Algorithm Based on Number of Targets

A low-complexity joint range and Doppler frequency-modulated continuous wave (FMCW) radar algorithm based on the number of targets is proposed in this paper. This paper introduces two low-complexity FMCW radar algorithms, that is, region of interest (ROI)-based and partial discrete Fourier transform (DFT)-based algorithms. We find the low-complexity condition of each algorithm by analyzing the complexity of these algorithms. From this analysis, it is found that the number of targets is an important factor in determining complexity. Based on this result, the proposed algorithm selects a low-complexity algorithm between two algorithms depending the estimated number of targets and thus achieves lower complexity compared two low-complexity algorithms introduced. The experimental results using real FMCW radar systems show that the proposed algorithm works well in a real environment. Moreover, central process unit time and count of float pointing are shown as a measure of complexity.

Refined PHD Filter for Multi-Target Tracking under Low Detection Probability

Radar target detection probability will decrease as the target echo signal-to-noise ratio (SNR) decreases, which has an adverse influence on the result of multi-target tracking. The performances of standard multi-target tracking algorithms degrade significantly under low detection probability in practice, especially when continuous miss detection occurs. Based on sequential Monte Carlo implementation of Probability Hypothesis Density (PHD) filter, this paper proposes a heuristic method called the Refined PHD (R-PHD) filter to improve multi-target tracking performance under low detection probability. In detail, this paper defines a survival probability which is dependent on target state, and labels individual extracted targets and corresponding particles. When miss detection occurs due to low detection probability, posterior particle weights will be revised according to the prediction step. Finally, we transform the target confirmation problem into a hypothesis test problem, and utilize sequential probability ratio test to distinguish real targets and false alarms in real time. Computer simulations with respect to different detection probabilities, average numbers of false alarms and continuous miss detection durations are provided to corroborate the superiority of the proposed method, compared with standard PHD filter, Cardinalized PHD (CPHD) filter and Cardinality Balanced Multi-target Multi-Bernoulli (CBMeMBer) filter.