Differential state quantization of high order Gauss-Markov process

Analyzes a differential technique of tracking and quantizing a continuous time Gauss-Markov process using the process and its derivatives. By using fine quantization approximations the author derives expressions for the time-average smoothed error. Analytical bounds are derived on the overall smoothed error and it is confirmed that the differential scheme outperforms vector quantization of the scalar process, state component quantization, and state vector quantization. It is shown that when the overall rate R in bits per second is high, the optimal smoothed error varies as 1/R³ for the differential scheme. This is better than the performance of DPCM and a modified vector DPCM, analyzed under the same framework. For both these schemes the asymptotic variation of the smoothed error is 1/R² at rate R. For differential state quantisation, the resulting optimal size of the vector quantizers are small and can be used in practice