Target Tracking using Robust Sensor Motion Control

We consider the problem of tracking moving targets using mobile wireless sensors (of possibly different types). This is a joint estimation and control problem in which a tracking system must take into account both target and sensor dynamics. We make minimal assumptions about the target dynamics, namely only that their accelerations are bounded. We develop a control law that determines the sensor motion control signals so as to maximize target resolvability as the target dynamics evolve. The method is given a tractable formulation that is amenable to an efficient search method and is evaluated in a series of experiments involving both round-trip time based ranging and Doppler frequency shift measurements

Transport based particle methods for the Fokker-Planck-Landau equation

We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy, and decay of estimated entropy. We prove that matching the gradient of the logarithm of the approximate solution is enough to recover the true solution to the Landau equation with Maxwellian molecules. Several numerical experiments in low and moderately high dimensions are performed, with particular emphasis on comparing the proposed method with the traditional particle or blob method.