General quantized innovation Kalman filter for stochastic uncertain systems with random packet dropouts

Abstract

Due to of the bandwidth constraint, sensors may only be able to transmit a finite number of bits to save the energy, and the measurement data may have to be quantized before transmission especially in wireless sensor networks (WSNs). This paper studies the problem of the general quantized innovation filtering with random packet dropouts for linear stochastic uncertain systems. The multiplicative uncertainty of system parameters is first converted into additive noises. Then under the Gaussian assumption on the predicted density, the Lloyd-Max quantizer, a general quantized innovation filter with random packet dropouts in the linear minimum mean square error (LMMSE) sense is derived based on the projection theory and Bayes Rule. Furthermore a sufficient condition is provided, under which a general quantized innovation filter with random packet dropouts can be reduced into a standard Kalman filter. An example is simulated to illustrate the effectiveness and correctness of the designed filter.