Optimal sensor data quantization for best linear unbiased estimation fusion

Distributed estimation is useful for surveillance using sensor networks. Due to the capacity constraints at the communication links, the data from the sensors are transmitted at a rate insufficient to convey all the observations reliably. Therefore, the observations are vector quantized and the estimation is done using the compressed measurements. In this paper, under the best linear unbiased estimation (BLUE) fusion rule, we build the optimal sensor quantization scheme for state estimation in a static case, which uses only bivariate probability distributions of the state and sensor observations. For state estimation in a dynamic system, it is shown that, under the communication constraints, the state update reduces to quantizing and estimating the current state conditioned on all of the transmitted quantized measurements. To have a recursive form for state estimation update in a dynamic system, we assume the current quantized measurement is orthogonal to all past ones. For a linear system with additive white Ganssian noise, a close form of recursion for state estimation update is proposed.