Distributed Filtering for Sensor Networks with Fading Measurements and Compensations for Transmission Delays and Losses

This paper studies a distributed filtering problem for sensor networks, where sensor nodes may suffer from their own fading measurements and random delayed and lost state estimates of their neighbor nodes. A distributed filter is presented based on statistical characteristics of fading measurements of sensors, where an optimal Kalman filter gain for each sensor node and different optimal consensus filter gains for state estimates of neighbor nodes are solved to minimize locally an upper bound of filtering error covariance matrix under given parameters. The proposed filter has reduced computational cost since calculation of cross-covariance matrices between sensors is avoided. Predictors of delayed and lost estimates of neighbor nodes are used for compensations to improve estimation accuracy. To further minimize the upper bound of covariance matrix, optimal parameters are solved, which are nonlinearly coupled with optimal gains. Their approximate numerical solutions can be obtained by nonlinear optimization methods. The boundedness of covariance matrix of the proposed filter is analyzed. As a special case, a distributed filter with constant delays can be obtained, which has the steady-state property. To further reduce online computational cost, two conservative distributed filters are also presented under the steady-state parameters obtained by using the upper bound of delays.