Sensor Selection for Nonlinear Systems in Large Sensor Networks

In this paper, we consider multistage look-ahead sensor selection problems for nonlinear dynamic systems such as radar target tracking systems. We investigate the problem for large sensor networks for both independent and dependent Gaussian measurement noises in the presence of temporally separable as well as inseparable constraints, e.g., energy constraints. First, when the measurement noises are uncorrelated between sensors, we derive the optimal solution for sensor selection when the constraints are temporally separable. When constraints are temporally inseparable, we can obtain near-optimal solutions by relaxing the nonconvex problem formulation to a linear programming problem so that the sensor selection problem for a large sensor network can be solved in a computationally efficient manner. For illustration, a radar target tracking problem is considered where it is shown that the new method presented for nonlinear dynamic systems performs better than the method based on linearizing the nonlinear equations and using previous sensor selection methods for large sensor networks. Finally, when the measurement noises are correlated between the sensors, the sensor selection problem with temporally inseparable constraints can be relaxed to a Boolean quadratic programming problem problem,, which can be efficiently solved by a Gaussian randomization procedure along with solving a semidefinite programming problem. Numerical examples show that the proposed method that includes consideration of dependence performs much better than the method that ignores dependence of noises.