Parameter Flow Implementation for Probability Hypothesis Density Filter

In most filtering framework applications, estimation is performed under nonlinear measurements and dynamics. A fundamental problem is the accurate and robust incorporation of newly observed measurements. One of the challenges presented by nonlinearities in the measurement is that it often requires a choice of simplifying assumptions for the prior. For nonlinear systems, typically an extended Kalman filter or an unscented Kalman filter is used. To overcome deficiencies in the traditional use of linear-Gaussian models, homotopic corrections have been implemented for a variety of problems, leading to improved results compared to other filters in a single-object estimation scenario. For multitarget approaches, probabilistic approaches based on random finite sets have been popularized. Among them is the use of a probability hypothesis density (PHD) filter and its Gaussian mixture PHD (GM-PHD) implementation. This work develops and demonstrates the fusion of the homotopy via the parameter flow implementation into the framework of the PHD filter in Gaussian mixture form. Two examples of the parameter flow GM-PHD filters are shown to deliver a more accurate posterior intensity compared to the classical GM-PHD.