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Quantized Filtering Schemes for Multi-Sensor Linear State Estimation: Stability and Performance Under High Rate Quantization

In this paper we consider state estimation of a discrete time linear system using multiple sensors, where the sensors quantize their individual innovations, which are then combined at the fusion center to form a global state estimate. We prove the stability of the estimation scheme under sufficiently high bit rates. We obtain asymptotic approximations for the error covariance matrix that relates the system parameters and quantization levels used by the different sensors. Numerical results show close agreement with the true error covariance for quantization at high rates. An optimal rate allocation problem amongst the different sensors is also considered.