Abstract
In this paper, we study a general multiple-level quantized innovation Kalman filter (MLQ-KF) for estimation of linear dynamic stochastic systems. First, given a multi-level quantization of innovation, we derive the corresponding MMSE filter in terms of the given quantization levels under the assumption that the innovation is approximately Gaussian. By optimizing the filter with respect to the quantization levels, we obtain an optimal quantization scheme and the corresponding optimal MLQ-KF. The optimal filter is given in terms of a simple Riccati difference equation as in the standard Kalman filter. For the case of 1-bit transmission, our proposed optimal filter gives a better performance than the sign-of-innovation filter (SOI-KF) Ribeiro et al. [2006]. The convergence of the MLQ-KF to the standard Kalman filter is established.
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