Innovative Filter for Nonlinear Multitarget Tracking: Improved SCKF-GM-DLPMBM Filter and Its Implementation

The Poisson multi-Bernoulli mixture (PMBM) filter is capable of estimating the states of multiple targets based on available measurements. To address the limitations of the traditional PMBM filter, which involves the enumeration of assumptions that increases computational time and leads to inaccurate state estimates under noisy conditions, we propose the dual-label PMBM (DLPMBM) filter. This paper enhances the PMBM filter by incorporating labels for both measurements and targets. In the prediction and update phases, the filter is divided into a labeled Poisson point process (LPPP) and a labeled multi-Bernoulli mixture (LMBM) process, which predict and update undetected targets, potential targets, and surviving targets. During the measurement generation phase, each measurement is assigned a unique label, and an improved elliptical gate is used to filter the measurements, embedding them into the LPPP and LMBM measurement update processes. This approach reduces the enumeration of global hypotheses. Furthermore, to address the imprecise estimates of the conventional PMBM filter, an optimization method and its implementation are proposed in this study. To mitigate the uncertainties of conventional filters under nonlinear conditions, we develop an implementation of the Gaussian mixture DLPMBM filter using the square-root cubature Kalman filter (SCKF). The covariance matrix of unknown process noise is improved by integrating the Sage-Husa filter. To ensure the positive definiteness of the estimated covariance, Cholesky decomposition is employed in both the prediction and update phases of the DLPMBM filter. Finally, multitarget tracking experiments are conducted to demonstrate the performance of the proposed DLPMBM filter.