Multisensor management optimization for multitarget tracking based on Hausdorff distance minimization

In multi-hypothesis target tracking, given the time-predicted tracks, we consider the sensor management problem of directing the sensors' Field of View (FOV) in such a way that the targets detection rate is improved. Defining a (squared) distance between a sensor and a track as the (squared) Euclidean distance between the centers of their respective Gaussian distributions, weighted by the sum of the covariance matrices, the problem is formulated as the minimization of the Hausdorff distance from the set of tracks to the set of sensors. An analytical solution for the single sensor case is obtained, and is extended to the multiple sensors case. This extension is achieved by performing the following: (1) It is first proved that for an optimal solution, there exists a partition of the set of tracks into subsets, and an association of each subset with a sensor, such that each subset-sensor pair is optimal in the Hausdorff distance sense; (2) a brute force search is then conducted to check all possible subset-partitions of the tracks as well as the permutations of sensors; (3) for each subset-sensor pair, the optimal solution is obtained analytically; and (4) the configuration with the smallest Hausdorff distance is declared as the optimal solution for the given multi-target multi-sensor problem. Some well established loopless algorithms for generating set partitions and permutations are implemented to reduce the computational complexity. A simulation result demonstrating the proposed sensor management algorithm is also presented.