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A real-time processing method for GB-SAR monitoring data by using the dynamic Kalman filter based on the PS network

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Abstract

Ground-based synthetic aperture radar (GB-SAR) has been widely used in the safety monitoring of slopes, dams, and buildings due to its high precision, large coverage area, and fast image acquisition. The real-time processing of high frequency and continuous deformation monitoring data is particularly important for early warning of landslides and high-risk buildings. Yet very limited studies have been conducted on the real-time processing method of GB-SAR monitoring data. In this study, a novel real-time processing method of GB-SAR monitoring data is proposed by using the Kalman filter based on the permanent scatterer (PS) network. The proposed method starts from the radiation characteristic and the phase composition of the GB-SAR monitoring data and instantaneously processes the acquired radar image by using the dynamic Kalman filter based on PSs and PS network. Then, a real-time processing Kalman mathematical model can be established, the model parameters are initialized, and the recursive Kalman filter to solve the timely deformation monitoring. By continuously updating the image data, the real-time and high-efficient calculation of PS deformation parameters can be achieved, which realizes the high accuracy and continuous deformation monitoring. The proposed novel method fills the gap in the real-time processing techniques of GB-SAR monitoring data and solves key problems of PS network updating, phase unwrapping, atmospheric phase correction, deformation calculation, etc.

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Abbreviations

PS:

Permanent scatterer

PSI:

Persistent scatterer interferometry

CPSS:

Combined permanent scatterer selection

N :

The number of single-view images

PSCs:

Permanent scatterer candidates

ADI:

Amplitude Deviation Index

\({\varphi }_{i}\) :

Interference phase at PS point i

\({\psi }_{i,j}\) :

Double-difference phase observation matrix of two adjacent \({\text{PS}}_{i}\) and \({\text{PS}}_{j}\)

\(\Delta {\varphi }_{i,j}\) :

A member of matrix \({\psi }_{i,j}\)

\({t}_{k}\) :

Time

\({\mathbf{x}}_{k}\) :

State vector at the time \({t}_{k}\)

\({\mathbf{T}}_{k-1}\)  :

State transition matrix from time \({t}_{k-1}\) to time \({t}_{k}\)

\({\mathbf{w}}_{k}\) :

Dynamic noise at time \({t}_{k}\)

\(\mathbf{Q}\) :

Covariance matrix of dynamic noise

\({\mathbf{z}}_{k}\) :

Observation vector at time \({t}_{k}\)

\({\mathbf{H}}_{k}\) :

Observation matrix at time \({t}_{k}\)

\({\mathbf{n}}_{k}\) :

Observation noise at time \({t}_{k}\)

\(\mathbf{R}\) :

Variance matrix of the observation noise at time \({t}_{k}\)

\(\Delta {\mathbf{r}}_{\mathrm{k}}\) :

Displacement increment between two adjacent PSs

\(\Delta {\mathbf{v}}_{k}\) :

Increment of deformation rate between two adjacent PSs

\(\Delta t\) :

Time baseline of the interference images

\(\lambda\) :

Wavelength of GB-SAR

\({\widehat{\mathbf{x}}}_{0}^{-}\) :

Initial state vector

\({\mathbf{P}}_{0}^{-}\) :

Covariance matrix of \({\widehat{\mathbf{x}}}_{0}^{-}\)

\({\widehat{\mathbf{x}}}_{k}^{-}\) :

Prior estimate of the state vector

\({\mathbf{P}}_{k}^{-}\) :

Covariance matrix of \({\widehat{\mathbf{x}}}_{k}^{-}\)

\({\mathbf{d}}_{k}\) :

Modified value

\({\mathbf{D}}_{k}\) :

Covariance matrix of \({\mathbf{d}}_{k}\)

\({\widehat{\mathbf{x}}}_{k}^{+}\) :

Posterior estimate of the state vector

\({\mathbf{P}}_{k}^{+}\) :

Covariance matrix of \({\widehat{\mathbf{x}}}_{k}^{+}\)

\({\mathbf{K}}_{k}\) :

Kalman gain matrix

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Funding

This research was substantially supported by the General Program of National Natural Science Foundation of China (Grant No. 42277181), the Sichuan Science and Technology Program (2022YFS0539), and the State Key Program of National Nature Science Foundation of China (Grant No. 52130904).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, Sichuan, 610065, China

    Xia Xiang, Chen Chen, Heng Lu, Han Zhang & Jiankang Chen

  2. College of Hydraulic and Hydroelectric, Engineering, Sichuan University, Chengdu, Sichuan, 610065, China

    Xia Xiang, Chen Chen, Heng Lu, Han Zhang & Jiankang Chen

  3. Sichuan Provincial Station, of Surveying and Mapping Product Quality Supervision and Inspection, Chengdu, Sichuan, 610041, China

    Hui Wang

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  1. Xia Xiang
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Correspondence to Chen Chen.

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Xiang, X., Chen, C., Wang, H. et al. A real-time processing method for GB-SAR monitoring data by using the dynamic Kalman filter based on the PS network. Landslides 20, 1639–1655 (2023). https://doi.org/10.1007/s10346-023-02057-z

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