Recursive estimation method of cubature Kalman filtering local polynomial coefficients for phase unwrapping

doi:10.11947/j.AGCS.2020.20190385

Abstract

Abstract: Recursive estimation method of cubature kalman filtering(CKF) local polynomial coefficients for phase unwrapping is proposed to retrieve unambiguous unwrapping phase from noisy wrapped phase. First, phase gradient information required is obtained using amended matrix pencil model (AMPM), and then the initial state estimation value of the polynomial coefficients is obtained. Finally, the polynomial coefficients are recursively estimated to obtain the unambiguous unwrapping phase by using the cubature Kalman filter. According to the density of the fringes of the interferograms and the signal-to-noise ratio (SNR) of the interferograms, the row-by-row (or column-by-column) scanning modes or the quality-guide strategy applied in traditional algorithms can be used to guide the cubature Kalman filter to unwrap the wrapped pixels along the suitable paths. The results with the simulated data and the measured data demonstrate that the algorithm in this paper can obtain robust solutions from noisy interferograms, with respect to some other similar algorithms.

Key words: phase unwrapping, local polynomial approximation, cubature Kalman filter, gradient estimate

CLC Number:

P236

XIE Xianming, SUN Yuzheng, LIANG Xiaoxing, ZENG Qingning, ZHENG Zhanheng. Recursive estimation method of cubature Kalman filtering local polynomial coefficients for phase unwrapping[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(8): 1023-1031.

References

[1] GHIGLIA D C, PRITT M D. Two-dimensional phase unwrapping:theory, algorithms, and software[M]. New York:John Wiley and Sons Inc, 1998.
[2] RASTOGI P K, HACK E. Phase estimation in optical interferometry[M]. Boca Raton, FL:CRC Press Inc, 2015.
[3] ITOH K. Analysis of the phase unwrapping algorithm[J]. Applied Optics, 1982, 21(14):2470.
[4] 王超, 张红, 刘智. 星载合成孔径雷达干涉测量[M]. 北京:科学出版社, 2002. WANG Chao, ZHANG Hong, LIU Zhi. Space-borne synthetic aperture radar interferometry[M]. Beijing:Science Press, 2002.
[5] YU Hanwen, LAN Yang, YUAN Zhihui, et al. Phase unwrapping in InSAR:a review[J]. IEEE Geoscience and Remote Sensing Magazine, 2019, 7(1):40-58.
[6] ZHENG Dongliang, DA Feipeng. A novel algorithm for branch cut phase unwrapping[J]. Optics and Lasers in Engineering, 2011, 49(5):609-617.
[7] GOLDSTEIN R M, ZEBKER H A, WERNER C L. Satellite radar interferometry:two-dimensional phase unwrapping[J]. Radio Science, 1988, 23(4):713-720.
[8] ZHAO Ming, HUANG Lei, ZHANG Qican, et al. Quality-guided phase unwrapping technique:comparison of quality maps and guiding strategies[J]. Applied Optics, 2011, 50(33):6214-6224.
[9] FANG Suping, MENG Lei, WANG Leijie, et al. Quality-guided phase unwrapping algorithm based on reliability evaluation[J]. Applied Optics, 2011, 50(28):5446-5452.
[10] 钟何平, 唐劲松, 张森. 一种基于质量引导和最小不连续合成的InSAR相位解缠算法[J]. 电子与信息学报, 2011, 33(2):369-374. ZHONG Heping, TNAG Jinsong, ZHANG Sen. A combined phase unwrapping algorithm based on quality-guided and minimum discontinuity for InSAR[J]. Journal of Electronics & Information Technology, 2011, 33(2):369-374.
[11] 殷爱菡, 张清淼, 姜辉明. 一种改进的加权最小二乘相位展开方法研究[J]. 计算机工程与应用, 2013, 49(3):159-162. YIN Aihan, ZHANG Qingmiao, JIANG Huiming. Study of improved phase unwrapping method based on weighted least squares[J]. Computer Engineering and Applications, 2013, 49(3):159-162.
[12] 陈强, 杨莹辉, 刘国祥. 基于边界探测的InSAR最小二乘整周相位解缠方法[J]. 测绘学报, 2012, 41(3):441-448. CHEN Qiang, YANG Yinghui, LIU Guoxiang. InSAR phase unwrapping using least squares method with integer ambiguity resolution and edge detection[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3):441-448.
[13] GHIGLIA D C, ROMERO L A. Minimum L^P-norm two-dimensional phase unwrapping[J]. Journal of the optical Society of America A, 1996, 13(10):1999-2013.
[14] CHEN C W, ZEBKER H A. Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization[J]. Journal of the optical Society of America A, 2001, 18(2):338-351.
[15] 王丽娟, 蒋厚军, 达汉桥, 等. 统计费用网络流相位解缠并行处理[J]. 武汉大学学报(信息科学版), 2010, 35(9):1061-1064. WANG Lijuan, JIANG Houjun, DA Hanqiao, et al. Parallel computing based on statistical-cost network-flow algorithm for phase unwrapping[J]. Geomatics and Information Science of Wuhan University, 2010, 35(9):1061-1064.
[16] LOFFELD O, NIES H, KNEDLIK S, et al. Phase unwrapping for SAR interferometry:a data fusion approach by Kalman filtering[J]. IEEE Transactions on Geoscience and Remote Sensing, 2008, 46(1):47-58.
[17] 谢先明. 结合滤波算法的不敏卡尔曼滤波器相位解缠方法[J]. 测绘学报, 2014, 43(7):739-745. DOI:10.13485/j.cnki.11-2089.2014.0102. XIE Xianming. An UKF phase unwrapping algorithm with a filtering procedure[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(7):739-745. DOI:10.13485/j.cnki.11-2089.2014.0102.
[18] XIE Xianming, LI Yinghui. Enhanced phase unwrapping algorithm based on unscented Kalman filter, enhanced phase gradient estimator, and path-following strategy[J]. Applied Optics, 2014, 53(18):4049-4060.
[19] 代高兴, 谢先明. 基于修正嵌入式容积卡尔曼滤波的相位展开算法[J]. 测绘学报, 2017, 46(12):1998-2005. DOI:10.11947/j.AGCS.2017.20160665. DAI Gaoxing, XIE Xianming. A fresh phase unwrapping method based on modified embedded cubature Kalman filter[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(12):1998-2005. DOI:10.11947/j.AGCS.2017.20160665.
[20] XIE Xianming, ZENG Qingning. Efficient and robust phase unwrapping algorithm based on unscented Kalman filter, the strategy of quantizing paths-guided map, and pixel classification strategy[J]. Applied Optics, 2015, 54(31):9294-9307.
[21] WAGHMARE R G, MISHRA D, SAI SUBRAHMANYAM G R K, et al. Signal tracking approach for phase estimation in digital holographic interferometry[J]. Applied Optics, 2014, 53(19):4150-4157.
[22] WAGHMARE R G, SAI SUBRAHMANYAM G R K, MISHRA D. Wrapped statistics-based phase retrieval from interference fringes[J]. Journal of Modern Optics, 2016, 63(14):1384-1390.
[23] KATKOVNIK V, ASTOLA J, EGIAZARIAN K. Noisy phase unwrap for fringe techniques:adaptive local polynomial approximations[C]//Proceedings of 20073DTV Conference. Kos Island, Greece:IEEE, 2007:1-4.
[24] KATKOVNIK V, ASTOLA J, EGIAZARIAN K O. Phase local approximation (PhaseLa) technique for phase unwrap from noisy data[J]. IEEE Transactions on Image Processing, 2008, 17(6):833-846.
[25] KULKARNI R, RASTOGI P. Local-polynomial-approximation-based phase unwrapping using state space analysis[J]. Applied Optics, 2017, 56(1):29-34.
[26] KULKARNI R, RASTOGI P. Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter[J]. Applied Optics, 2018, 57(4):702-708.