Restoration of input signals of dynamic measuring systems using digital reverse f ltering

The problem of synthesizing an optimal input signal restoration operator for linear dynamic measuring systems whose operators do not have zeros in the bandwidth of these systems is considered. An algorithm for restoring the input processes of measuring systems for the dynamic measurement mode in the form of an inverse digital fi lter is proposed. The inverse fi lter is represented by a series connection of a regularizing pre-fi lter (low-pass fi lter) and an inverse measurement system operator. It is shown that the procedure for minimizing the generalized discrepancy of the output signal of the measuring system can be constructed using only one regularization parameter, the cutoff frequency of the prefi lter, by fi xing its order. Such a construction, combined with the homogeneity of the representations of the initial data, the inverse operator of the measuring system, and the regularizer, ensures low computational costs when implementing the recovery algorithm. Based on the simulation results, it is shown that the pre-fi lter signifi cantly increases the convergence of recovery algorithms. An important advantage of the proposed recovery algorithm compared to the Kalman fi lter apparatus under conditions of high a priori uncertainty about the measured value is that the recovery accuracy is practically independent of the input signal model. The amount of a priori information is limited by the maximum frequency of the spectrum of the controlled process, as well as by the statistical characteristics of the measurement errors and the task of the operator of the measuring systems. These errors are estimated approximately from noise information and the identifi cation procedure. The simulation performed showed a high stability of the recovery procedure to the level of output noise of measurements and changes in the dynamics of the input signal with good accuracy characteristics of the recovery algorithm. The research results can be used to improve the accuracy of measuring systems in the dynamic measurement mode with a high a priori uncertainty about the measured value. 

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