Frobenius Norm-Based Unbiased Finite Impulse Response Fusion Filtering for Wireless Sensor Networks

This article presents a new approach to designing the Frobenius norm-based weighted unbiased finite impulse response (FIR) fusion filter for wireless sensor networks. The weighted Frobenius norm is employed as a cost function to design a local unbiased FIR filter. The design problem is converted into a constrained optimization problem subject to an equality constraint. The Lagrange multiplier method is used to derive the local FIR filter gain. An alternative Frobenius norm is introduced to determine weights for the local unbiased FIR filters in the design of a global fusion FIR filter. The developed FIR fusion filter is demonstrated to have higher robustness against uncertainties than Kalman filter-based methods, such as the optimal fusion Kalman filter, distributed Kalman filter, and distributed weighted Kalman filter, through a numerical example of moving-target tracking employing seven smart sensors and an experiment with temperature and humidity estimation using eight sensors.