On linear encoder-decoder design for multi-sensor state estimation subject to quantization noise and channel erasure

We consider remote state estimation of a scalar stationary linear Gauss-Markov process observed via noisy measurements obtained by two sensors. The sensors can construct a causal linear function of their measurements, which are quantized and transmitted to a decoder (or fusion centre (FC)) over channels which are prone to packet erasures. We design linear encoding and decoding strategies for estimating the state of the linear system that allow improved estimation performance in the presence of packet erasures and quantization errors. To this end, we construct and compare various distributed encoding and decoding methods without any feedback from the FC regarding the channel erasures. We also design various decentralized benchmark methods that either assume perfect feedback from the FC or in addition co-location of the two sensors resulting in a centralized scheme with diversity. These benchmark methods provide various lower bounds for the distributed encoding-decoding schemes designed without feedback. Numerical results indicate i) that optimal decentralized design of the encoders and the decoder in the absence of feedback can provide a remote state estimation performance that is comparable to those achieved by the lower bounds (with feedback) particularly when the sensors are identical and their channels are symmetric, and (ii) a little feedback from the decoder can improve the performance considerably when the channels are asymmetric (i.e. the packet erasure probabilities are unequal).