Optimal integrated discrete-time processing of continuous random process samples in view of correlated Markov noise observations

Abstract

Algorithms for integrated optimal processing of random processes are implemented using discrete-type signal processing tools in current Radio Engineering and Telecommunication Systems (RES and TCS). Therefore, these algorithms must be synthesized as discrete-type and suitable recurrence relations for such implementation. However, mostly mathematical models of random processes evaluated and observed in RES and TCS have a continuous recording form, which is due to the physical nature of these processes. Thus, there arises a task of synthesizing optimal algorithms for discrete-type integrated processing of continuous random processes’ samples. Yet, current hardware components permit using high sampling frequency in RES and TCS resulting in measurement samples’ autocorrelation. Therefore, measurement noise correlation should be taken into account during steady-state synthesis of multichannel digital filters as it significantly affects the generated filtering estimates. This paper proposes a new multichannel digital filter based on difference measurements and statistically equivalent discrete-type representation of continuous state vector models and observation for solving the problem of optimal linear integrated processing for samples of a continuous vector Markov random process considering the known statistical characteristics of an additive vector Markov correlated noise. Mathematical model’s structures of the measuring channel with analog-to-digital conversion (ADC) and of the multichannel digital filter are presented. ADC key aspect is the accumulation (integration) of continuous observations at time intervals between adjacent selections of the estimated state vector. To illustrate the synthesized algorithm efficiency there is examined a simple example of optimal integrated processing of a continuous Gaussian-Markov random process of the second order with Markov correlated noise of two meters having different physical nature and a different degree of measuring samples’ autocorrelation. The integrated processing efficiency is indicated. Using difference measurement method does not result in computational costs raise in a multichannel digital filter, since state vector dimension remains unchanged in the same way as for filtering continuous random processes amid white Gaussian noise. That said ADC analog part of the measuring channel is significantly simplified compared to known algorithms, since the single-cycle delay is implemented in the digital part. It should also be noted that there is no analog differentiation procedure common to classical filtering algorithms for continuous random processes in continuous time by the difference measurements’ method. Joining meters (radio engineering and non-radio engineering) with different bandwidths (autocorrelation functions) increases noise immunity, because the latter are not affected by radio jamming, and information redundancy enables to reduce the measurement error and thereby to enhance RES and TCS accuracy.