A quantized filtering scheme for multi-sensor linear state estimation with non-detectability at the sensors and fusion center feedback

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. It is assumed that detectability does not hold for at least one of the sensors. By allowing the fusion center to broadcast some information back to the sensors, full state estimates can be obtained at the sensors, even without detectability. We prove the stability of the estimation scheme under sufficiently high bit rates, and obtain asymptotic approximations for the error covariance matrix that relates the system parameters and quantization levels used by the different sensors.