Restoration of the Input Signals of Dynamic Measurement Systems Using Digital Inverse Filtering

The article considers the problem of synthesizing the optimal input signal restoration operator for linear dynamic measurement systems whose operators are zero-free within their bandwidth. An algorithm is proposed for restoring the input processes of measurement systems for the dynamic measurement mode in the form of an inverse digital filter. The inverse filter is represented by a series connection of a regularizing prefilter (low-pass filter) and an inverse operator of measurement systems. It is shown that the procedure for minimizing the generalized discrepancy of the output signal of a measurement system can be designed only for one regularization parameter, the cut-off frequency of the prefilter, by setting its order. Such a design combined with the homogeneous representations of the initial data, the inverse operator of the measurement system, and the regularizer ensures low computational costs in the implementation of the restoration algorithm. The simulation results show that the prefilter significantly improves the convergence of restoration algorithms. As compared to the Kalman filter apparatus, the proposed restoration algorithm offers an important advantage under the conditions of high a priori uncertainty about the measurand: the restoration accuracy is virtually independent of the input signal model. The amount of a priori information is limited by the maximum spectrum frequency of the controlled process, as well as the statistical characteristics of errors associated with performing measurement and setting the operator for a measurement system. These errors are estimated approximately using data on noise and the identification procedure. The conducted simulation shows a high stability of the restoration procedure to the output noise of measurements and changes in input signal dynamics with good accuracy characteristics of the restoration algorithm. The study results can be used to improve the accuracy of measurement systems in the dynamic measurement mode at high a priori uncertainty of the measurand.