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Evaluation of a Cubature Kalman Filtering-Based Phase Unwrapping Method for Differential Interferograms with High Noise in Coal Mining Areas.

Liu W, Bian Z, Liu Z, Zhang Q - Sensors (Basel) (2015)

Bottom Line: Phase unwrapping can have a dramatic influence on the monitoring result.The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study.The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

View Article: PubMed Central - PubMed

Affiliation: School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China. liuliucumt@126.com.

ABSTRACT
Differential interferometric synthetic aperture radar has been shown to be effective for monitoring subsidence in coal mining areas. Phase unwrapping can have a dramatic influence on the monitoring result. In this paper, a filtering-based phase unwrapping algorithm in combination with path-following is introduced to unwrap differential interferograms with high noise in mining areas. It can perform simultaneous noise filtering and phase unwrapping so that the pre-filtering steps can be omitted, thus usually retaining more details and improving the detectable deformation. For the method, the nonlinear measurement model of phase unwrapping is processed using a simplified Cubature Kalman filtering, which is an effective and efficient tool used in many nonlinear fields. Three case studies are designed to evaluate the performance of the method. In Case 1, two tests are designed to evaluate the performance of the method under different factors including the number of multi-looks and path-guiding indexes. The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study. Two case studies are then designed to evaluate the feasibility of the proposed phase unwrapping method based on Cubature Kalman filtering. The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

No MeSH data available.


Prediction principle of two-dimensional CKFPU.
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sensors-15-16336-f001: Prediction principle of two-dimensional CKFPU.

Mentions: The CKFPU is combined with a path-following strategy and omnidirectional local phase slope estimation, to guide the CKFPU by the phase quality so that it operates from high-quality regions to low-quality regions. The prediction estimation of any pixel will be calculated by weighting the corresponding unwrapped adjacent pixels, as shown in Figure 1. Hence, for the two-dimensional CKFPU algorithm, the prediction equation can be modified as follows:(22)x→m,n−=∑(a,s)∈(B,L)d(a,s)x→[(m,n)/(a,s)](23)Pm,n−=∑(a,s)∈(B,L)d(a,s)(P[(m,n)/(a,s)]+Q(a,s))whereis the predicted state vector of pixel (m,n) andis its corresponding error matrix;denotes the estimated state vector of the adjacent unwrapped pixels andis the corresponding error matrix; Q(a,s) is the estimated error variance matrix for phase slope at pixel (a,s); B denotes eight adjacent pixels for pixel (m,n) and L denotes the whole image. The optimal weight d(a,s) can be calculated as follows [21]:(24)d(a,s)=[P(a,s)×1SNR(a,s)]−1g(a,s)∑(a,s)∈(B,L)([P(a,s)×1SNR(a,s)]−1g(a,s))(25)g(a,s)={1,(a,s)pixel−unwrapped0,(a,s)pixel−wrapped


Evaluation of a Cubature Kalman Filtering-Based Phase Unwrapping Method for Differential Interferograms with High Noise in Coal Mining Areas.

Liu W, Bian Z, Liu Z, Zhang Q - Sensors (Basel) (2015)

Prediction principle of two-dimensional CKFPU.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4541881&req=5

sensors-15-16336-f001: Prediction principle of two-dimensional CKFPU.
Mentions: The CKFPU is combined with a path-following strategy and omnidirectional local phase slope estimation, to guide the CKFPU by the phase quality so that it operates from high-quality regions to low-quality regions. The prediction estimation of any pixel will be calculated by weighting the corresponding unwrapped adjacent pixels, as shown in Figure 1. Hence, for the two-dimensional CKFPU algorithm, the prediction equation can be modified as follows:(22)x→m,n−=∑(a,s)∈(B,L)d(a,s)x→[(m,n)/(a,s)](23)Pm,n−=∑(a,s)∈(B,L)d(a,s)(P[(m,n)/(a,s)]+Q(a,s))whereis the predicted state vector of pixel (m,n) andis its corresponding error matrix;denotes the estimated state vector of the adjacent unwrapped pixels andis the corresponding error matrix; Q(a,s) is the estimated error variance matrix for phase slope at pixel (a,s); B denotes eight adjacent pixels for pixel (m,n) and L denotes the whole image. The optimal weight d(a,s) can be calculated as follows [21]:(24)d(a,s)=[P(a,s)×1SNR(a,s)]−1g(a,s)∑(a,s)∈(B,L)([P(a,s)×1SNR(a,s)]−1g(a,s))(25)g(a,s)={1,(a,s)pixel−unwrapped0,(a,s)pixel−wrapped

Bottom Line: Phase unwrapping can have a dramatic influence on the monitoring result.The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study.The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

View Article: PubMed Central - PubMed

Affiliation: School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China. liuliucumt@126.com.

ABSTRACT
Differential interferometric synthetic aperture radar has been shown to be effective for monitoring subsidence in coal mining areas. Phase unwrapping can have a dramatic influence on the monitoring result. In this paper, a filtering-based phase unwrapping algorithm in combination with path-following is introduced to unwrap differential interferograms with high noise in mining areas. It can perform simultaneous noise filtering and phase unwrapping so that the pre-filtering steps can be omitted, thus usually retaining more details and improving the detectable deformation. For the method, the nonlinear measurement model of phase unwrapping is processed using a simplified Cubature Kalman filtering, which is an effective and efficient tool used in many nonlinear fields. Three case studies are designed to evaluate the performance of the method. In Case 1, two tests are designed to evaluate the performance of the method under different factors including the number of multi-looks and path-guiding indexes. The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study. Two case studies are then designed to evaluate the feasibility of the proposed phase unwrapping method based on Cubature Kalman filtering. The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

No MeSH data available.