This chapter considers the nonlinear filtering problem involving noises that are unknown and bounded. We propose a new filtering method via set-membership theory and boundary sampling technique to determine a state estimation ellipsoid. In order to guarantee the online usage, the nonlinear dynamics are linearized about the current estimate, and the remainder term is then bounded by an optimization ellipsoid, which can be described as the solution of a semi-infinite optimization problem. It is an analytically intractable problem for general nonlinear dynamic systems. Nevertheless, for a typical nonlinear dynamic system in target tracking, some certain regular properties for the remainder are analytically derived; then, we use a randomized method to approximate the semi-infinite optimization problem efficiently. Moreover, for some quadratic nonlinear dynamic systems, the semi-infinite optimization problem is equivalent to solving a semi-definite program problem. Finally, the set-membership prediction and measurement update are derived based on the recent optimization method and the online bounding ellipsoid of the remainder other than a priori bound. Numerical example shows that the proposed method performs better than the extended set-membership filter, especially in the situation of the larger noise.
Part of the book: Nonlinear Systems
Since there has been an increasing interest in the areas of Internet of Things (IoT) and artificial intelligence that often deals with a large number of sensors, this chapter investigates the decision fusion problem for large-scale sensor networks. Due to unavoidable transmission channel interference, we consider sensor networks with nonideal channels that are prone to errors. When the fusion rule is fixed, we present the necessary condition for the optimal sensor rules that minimize the Monte Carlo cost function. For the K-out-of-L fusion rule chosen very often in practice, we analytically derive the optimal sensor rules. For general fusion rules, a Monte Carlo Gauss-Seidel optimization algorithm is developed to search for the optimal sensor rules. The complexity of the new algorithm is of the order of OLN compared with OLNL of the previous algorithm that was based on Riemann sum approximation, where L is the number of sensors and N is the number of samples. Thus, the proposed method allows us to design the decision fusion rule for large-scale sensor networks. Moreover, the algorithm is generalized to simultaneously search for the optimal sensor rules and the optimal fusion rule. Finally, numerical examples show the effectiveness of the new algorithms for large-scale sensor networks with nonideal channels.
Part of the book: Functional Calculus