Set-membership multiple-source localization using acoustic energy measurements

Multiple-source localization problem based on acoustic energy measurements is investigated by set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurement is a complicated nonlinear function of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. The main contribution of this paper is as follows. Firstly, to deal with the nonlinear function, it is linearized by the first-order Taylor expansion with a remainder error. The point is that the bounding box of the remainder is derived in each iteration based on the convex bounding set of the state. Especially, when the state can be bounded in a cylinder, the remainder bound can be achieved analytically. Secondly, based on the separate property of the nonlinear observation function, an efficient estimation procedure is developed to deal with the high-dimensional state estimation problem by using an alternately optimization iterative algorithm. In the process of iteration, the remainder bound requires to be known on-line. Finally, a typical numerical example in multiple-source localization demonstrates the effectiveness of the set-membership localization algorithms. In particular, it shows that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the maximum likelihood localization algorithm.