Many algorithms used for digital signal processing, parameter estimation and digital measurement technology have unsatisfactory accuracy due to the digitalization, unsuitable sampling conditions and approximately mathematical methods etc. The calculation errors of these approximate algorithms are so difficult to be determined theoretically that they cannot easily be compensated by conventional correction methods. Therefore, self-correction (SC) algorithms are proposed to improve the accuracy of digital signal processing and parameter determination.

A self-correction algorithm (Fig. 1) consists of three main parts, i.e., initialization, self-calibration, and errors correction.
In the initialization original output parameters Y_m^* (m=1,2,..., M) are estimated by an approximate algorithm under correction (AUC) using input signals X_k(i) (k=1,2,..., K; i=0,1,..., N-1), where K and N denote the numbers of input signals and the samples number of each input signal. These output parameters deviate from their true values due to the inaccuracy of the AUC. The parameters Y_m^* serve for the self-calibration of the approximate algorithm to determine the calculation errors and for the errors correction.

Fig. 2  Self-calibration of the algorithm under correction

To determine the calculation errors of the AUC, the original output parameters Y _m^* are assigned as reference parameters for the self-calibration (Fig.2). Using the reference parameters Y_m^* reconstruction data X_rk(i) (k=1,2,..., K; i=0,1,..., N-1) are generated with a corresponding model. Reference output parameters Y_rm^* (m=1,2,..., M) are then estimated by the same AUC with the use of the reconstruction data X _rk(i). The errors of the parameters calculated by the AUC can be determined by

The calculation errors of the AUC can thus be self-corrected without any error analysis and external reference.

Fig.3 Scheme of an iterative self-correction algorithm

In this case the reference parameters Y_m,1 for the second self-calibration are more accurate to the true parameters than the reference parameters Y_rm^* for the first self-calibration, so that the errors DY_m,2 are more accurate to the true errors caused by the AUC in the initialization. The final output parameters can be calculated by

where Y^*_rm,1 and Y^*_rm,2 are the reference output parameters in the first and second self-calibrations, respectively.

with J as the number of iterative self-corrections and Y^*_rm,j as the reference output parameters in the j-th self-calibration.

Remark 3: The residual errors of the self-calibration algorithm depends on the original parameter errors caused by the approximate algorithm. A larger residual error is caused by a larger original error. All original errors of calculated parameters must be less than 70 %, otherwise errors convergence of the self-calibration algorithm cannot be guaranteed. Therefore, it is useful to reduce the original errors by using other methods in advance if the original errors are larger than the limit value.

These algorithms are applied to the discrete Fourier-Series/Transformation (DFT) of periodic signals sampled asychronously and to parameter estimation of damped oscillation signals.

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