Greedy Sensor Selection for Nonlinear Models with Performance Guarantees

Abstract

This paper focuses on developing a low-complexity greedy method to address the sensor selection problem with a generic nonlinear model. The optimal subset of sensors is chosen to satisfy specific performance constraints, which are functions of the Fisher information matrix (FIM) and depend on unknown parameters due to the nonlinear measurement model. Therefore, the sensor selection problem is a multi-constrained optimization problem, which is challenging to be addressed in a greedy way. In this paper, we design a performance metric, which is an average of truncated submodular functions, to ensure that all performance constraints are satisfied. An auxiliary term is introduced to the performance metric to make it well-defined. A greedy algorithm with optimality guarantees is proposed accordingly. In contrast to existing optimality guarantees, the proposed optimality guarantees are independent of the auxiliary term. Numerical results demonstrate the superiority of our proposed optimality guarantees and show that the proposed algorithm achieves similar performance to the convex methods in various scenarios with lower computational complexity.