State estimation with quantized innovations in wireless sensor networks: Gaussian mixture estimator and posterior Cramér–Rao lower bound

Since the features of low energy consumption and limited power supply are very important for wireless sensor networks (WSNs), the problems of distributed state estimation with quantized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function (PDF) with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algorithms for WSNs, the posterior Cramér–Rao lower bound (CRLB) with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.