Elliptic fitting non-linear error correction method based on Kalman filtering

Abstract

The invention belongs to the technical field of phase generation carrier demodulation, and discloses an elliptic fitting non-linear error correction method based on Kalman filtering. The method comprises the following steps: randomly selecting five data points, and substituting into an elliptic equation to construct a five-element algebraic equation set; selecting the deviation of an elliptic parameter estimated value to serve as a state vector; continuously updating the state vector and a state covariance matrix with data points to be fitted by a Kalman filter algorithm; using a newly-updatedcovariance matrix as an error covariance matrix at a next moment; adding the deviation value of an updated new parameter with an initial parameter estimated value to obtain a new elliptic parameter estimated result; when the changes of the results of two adjacent estimates in the update process are less than a given error 10<-8>, considering that a convergence state is reached, and stopping iteration; and using the estimated value as an optimal estimated value, that is, an optimal elliptic parameter. The relative amplitude and the harmonic suppression ratio are greatly improved; non-linear errors can be effectively corrected; and the demodulation accuracy is improved.

Description

Technical field [0001] The invention belongs to the technical field of phase generation carrier demodulation, and in particular relates to a Kalman filter-based ellipse fitting nonlinear error correction method. Background technique [0002] Phase Generation Carrier Demodulation (PGC) technology is a homodyne demodulation method widely used in interferometric optical fiber sensors. PGC mainly includes arctangent and cross differential multiplication (DCM) algorithms. Compared with DCM, the arctangent demodulation method has the advantages of being less affected by the fluctuation of the light source intensity, less affected by the filter passband ripple, good linearity, and large dynamic range. It has been used as a practical demodulation technology in optical fiber Hydrophone array demodulation. Because the arctangent demodulation is a nonlinear algorithm process after the interference signal is multiplied by the carrier and low-pass filtering. Non-linear error has become a k...

AI Technical Summary

Problems solved by technology

[0003] To sum up, the problems existing in the existing technology are: susceptible to the influence of outliers and noise, a small number of outliers can make the results change greatly, the robustness is relatively poor, and when the data to be fitted is concentrated in a shorter arc During the period, the noise of different deviation sizes will also change the fitting results

And when the number of sample points given is relatively large, the amount of calculation is too large, and the cost of time and space is too large, which is not suitable for real-time ellipse fitting

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