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CN-121978687-A - Phase unwrapping method based on extended Kalman filtering

CN121978687ACN 121978687 ACN121978687 ACN 121978687ACN-121978687-A

Abstract

The invention aims to provide a phase unwrapping method based on extended Kalman filtering, which comprises the following steps of A, constructing a two-dimensional phase unwrapping program MCC-EKFPU; and B, performing phase unwrapping treatment on the interferogram by using a two-dimensional phase unwrapping program MCC-EKFPU to obtain an unwrapped phase of the interferogram. The method introduces the maximum correlation entropy criterion extended Kalman filtering theory into the interferogram winding phase unwrapping, combines the interferogram phase gradient estimation technology and the robust path tracking strategy, has higher phase unwrapping precision and better robustness, and has better application potential in interferogram phase unwrapping application with higher accuracy requirement.

Inventors

  • XIE XIANMING
  • ZHANG YIFAN
  • HUANG XIANGYI
  • HUANG WEIWEI

Assignees

  • 广西科技大学

Dates

Publication Date
20260505
Application Date
20260107

Claims (6)

  1. 1. The phase unwrapping method based on the extended Kalman filtering is characterized by comprising the following steps of: A. the two-dimensional phase unwrapping procedure MCC-EKFPU is constructed and the system equation of the two-dimensional phase unwrapping procedure MCC-EKFPU is as follows: (1) Wherein, the For the picture element to be unwound Is used as a state variable to be estimated by the MCC-EKF phase unwrapping procedure, Representing picture elements Pixel in neighborhood (eight contiguous pixels) Unwrapping phase of the unwrapped pixels; And Respectively represent the slave neighborhood pixels To the picture element to be unwound And phase gradient estimation errors thereof; Representing picture elements The observed value of the state variable is used to determine, Representing interferometric image elements The state variable is free of observations of noise pollution, Representing picture elements Observing a noise vector by a state variable; B. and carrying out phase unwrapping treatment on the interference pattern by using a two-dimensional phase unwrapping program MCC-EKFPU to obtain unwrapped phases of the interference pattern.
  2. 2. The extended kalman filter based phase unwrapping method of claim 1, wherein: The solving process of the two-dimensional phase unwrapping program MCC-EKFPU is as follows: a. predicting the state and solving the target pixel Is the unwrapped phase prediction value of (2) And unwrapped phase prediction error variance ; B. State update based on target pixel Is the unwrapped phase prediction value of (2) And unwrapped phase prediction error variance Calculating to obtain final unwrapped phase estimation value And final estimation error variance 。
  3. 3. The extended kalman filter based phase unwrapping method of claim 2, wherein: in the step a, the target pixel is solved Is the unwrapped phase prediction value of (2) The formula of (2) is as follows: (2) (3) (4) Wherein, the Representing the two-dimensional labels of the picture elements to be unwound, And (3) with Respectively represent disentangled pixels Is used for unwrapping the phase and the estimation error variance of the unwrapping phase; representing a center picture element Coordinate set of disentangled pixels in the field; for disentangled picture elements Weight of (2); Representing target pixel Disentangled picture element in the field And target pixel A phase difference between adjacent phases; The representation is composed of Disentangled picture elements in the field of picture elements An initial unwrapping phase predicted value obtained by the phase information; The representation is composed of Disentangled picture elements in the field of picture elements Initial unwrapping phase prediction value obtained from phase information And carrying out weighted summation to obtain the unwrapped phase predicted value.
  4. 4. The extended kalman filter based phase unwrapping method of claim 2, wherein: in the step a, the unwrapped phase prediction error variance is calculated The formula of (2) is as follows: (5) in the formula (i), Is the target pixel And disentangled picture elements The variance of the phase gradient estimation error; Is the target pixel Unwrapping phase prediction error variance.
  5. 5. The extended kalman filter based phase unwrapping method of claim 2, wherein: In the step b, calculating a target pixel Is used for unwrapping phase estimation And final estimation error variance The formula of (2) is as follows: (6) (7) (8) (9) (10) Wherein, the Representing the two-dimensional labels of the picture elements to be unwound, As a gaussian kernel with weighted mahalanobis distance, The representation is composed of Target pixel obtained by phase information of all unwrapped pixels in pixel field Is used for the unwrapping phase prediction value of (a), Representing picture elements Unwrapping a phase measurement noise error covariance matrix; Representing an observation function Jacobian matrix of (b) is in A value at; Representing picture elements Is a gain matrix of (a); Is that The phase estimate for the unwrapping of the picture element, Is that The pixel unwrapping phase estimates the error variance.
  6. 6. The extended kalman filter based phase unwrapping method of claim 5, wherein: Gaussian kernel function with weighted mahalanobis distance The expression of (2) is: ; in the above-mentioned formula(s), For the weighted square mahalanobis distance formula, Representative of Pixel unwrapping phase estimate Or observe the phase , Can represent a target unwrapping phase prediction value Or observe the predicted value ; Representing unwrapped phase prediction error Or observation noise Is the inverse of the covariance matrix of (a).

Description

Phase unwrapping method based on extended Kalman filtering Technical Field The invention relates to the technical field of phase unwrapping, in particular to a phase unwrapping method based on extended Kalman filtering. Background Measurement values of physical parameters of measurement targets in various interferometry techniques, including interferometric synthetic aperture radar (InSAR), optical interferometry, and digital holographic interferometry are often measured by their corresponding interferometric phases. However, the measured phase data obtained from various interferometry techniques is typically presented in modulo 2 pi form, resulting in an integer multiple of 2 pi difference between the measured phase (commonly known as the wrapping phase) and its true unwrapping phase, so that the measured wrapping phase cannot be used directly in the inversion of the physical parameter of the object being measured. The wrapping phase is restored to the true unwrapping phase representing the physical parameter of the measurement target through Phase Unwrapping (PU) processing. Thus, as a core step in interferometry, the accuracy of Phase Unwrapping (PU) directly determines the accuracy of measurement target physical parameter estimation. How to accurately recover unwrapping phases reflecting target physical parameters from interference patterns of different fringe patterns has become a key link for improving the application reliability of various interferometry techniques. Disclosure of Invention The invention aims to provide a phase unwrapping method based on extended Kalman filtering, which introduces the maximum relevant entropy criterion extended Kalman filtering theory into interferogram wrapping phase unwrapping, combines an interferogram phase gradient estimation technology and a robust path tracking strategy, has higher phase unwrapping precision and better robustness, and has better application potential in interferogram phase unwrapping application with higher accuracy requirement. The technical scheme of the invention is as follows: The phase unwrapping method based on the extended Kalman filtering comprises the following steps: A. the two-dimensional phase unwrapping procedure MCC-EKFPU is constructed and the system equation of the two-dimensional phase unwrapping procedure MCC-EKFPU is as follows: (1) Wherein, the For the picture element to be unwoundIs used as a state variable to be estimated by the MCC-EKF phase unwrapping procedure,Representing picture elementsPixel in neighborhood (eight contiguous pixels)Unwrapping phase of the unwrapped pixels; And Respectively represent the slave neighborhood pixelsTo the picture element to be unwoundAnd phase gradient estimation errors thereof; Representing picture elements The observed value of the state variable is used to determine,Representing interferometric image elementsThe state variable is free of observations of noise pollution,Representing picture elementsObserving a noise vector by a state variable; B. and carrying out phase unwrapping treatment on the interference pattern by using a two-dimensional phase unwrapping program MCC-EKFPU to obtain unwrapped phases of the interference pattern. The solving process of the two-dimensional phase unwrapping program MCC-EKFPU is as follows: a. predicting the state and solving the target pixel Is the unwrapped phase prediction value of (2)And unwrapped phase prediction error variance; B. State update based on target pixelIs the unwrapped phase prediction value of (2)And unwrapped phase prediction error varianceCalculating to obtain final unwrapped phase estimation valueAnd final estimation error variance。 In the step a, the target pixel is solvedIs the unwrapped phase prediction value of (2)The formula of (2) is as follows: (2) (3) (4) Wherein, the Representing the two-dimensional labels of the picture elements to be unwound,And (3) withRespectively represent disentangled pixelsIs used for unwrapping the phase and the estimation error variance of the unwrapping phase; representing a center picture element Coordinate set of disentangled pixels in the field; for disentangled picture elements Weight of (2); Representing target pixel Disentangled picture element in the fieldAnd target pixelA phase difference between adjacent phases; The representation is composed of Disentangled picture elements in the field of picture elementsAn initial unwrapping phase predicted value obtained by the phase information; The representation is composed of Disentangled picture elements in the field of picture elementsInitial unwrapping phase prediction value obtained from phase informationAnd carrying out weighted summation to obtain a final unwrapping phase predicted value. In the step a, the unwrapped phase prediction error variance is calculatedThe formula of (2) is as follows: (5) in the formula (i), Is the target pixelAnd disentangled picture elementsThe variance of the phase gradient estimation error; Is the target pi