Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex (such as non-Gaussian noise, strong noise, and chaotic noise). This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types (including random noise and chaotic noise) and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations.