Constrained robust Kalman filtering for passive source localization

In this paper, a constrained robust Kalman filter (CRKF) approach to passive target localization based on a geometrically constrained sensor network is newly proposed. Our approach is strongly motivated by the inherent problem of the previous stochastic robust Kalman filters (RKFs) which are very sensitive to the inaccurate a priori statistical information on the stochastic parametric uncertainties. To solve this sensitivity problem, an additional state-equality constraint comes from the given sensor geometry is augmented with the conventional stochastic RKF cost using Lagrange multipliers. A minimizing solution to this constrained optimization problem gives us a new CRKF recursion. From the resultant filter structure, it is shown that the use of additional state-equality constraint corrects the imperfect statistical knowledge on the stochastic uncertainties and plays an important role in ensuring both the optimality and the reliability of the proposed filter. Computer simulations for the passive target tracking based on geometrically constrained sensor network demonstrate the reliable estimation performance of the proposed method compared to the existing ones.