Gini Ketelaar

Initial point selection and validation in PS-InSAR using integrated amplitude calibration

SAR amplitude calibration is performed prior to the selection of potential Persistent Scatterers (PS) to avoid amplitude variations due to sensor characteristics and viewing geometry. As only the interferometric phases of a small percentage of the radar pixels in an image is used in the PS-InSAR analysis, it is investigated if this time and storage space consuming step can be omitted. We present an integrated method which does not perform amplitude calibration explicitly, but integrates it into the PS point selection procedure for validation purposes by evaluating the hypothesis that a point would have been selected if all images were calibrated beforehand. Its performance assessment is based on coherent phase behavior of the selected potential PS and indicates that empirical calibration validation is an alternative for calibrating full images based on physical sensor parameters. I. INTRODUCTION Persistent Scatterer (PS) (1) InSAR is based on a network of point scatterers with a non-random phase behavior in time. As their interferometric phase contributions due to deformation are obscured by other effects, their identification is based on the amplitude behavior in time. For an unbiased selection of potential PS, a preceding SAR calibration is performed to isolate the amplitude observations corresponding with phys- ical PS properties from amplitude variations due to viewing geometry and sensor characteristics. Since the amount of PS is generally a small percentage of the full image and only their interferometric phase observations are used in the PS- InSAR analysis, the necessity of calibrating full images can be questioned. This study investigates the integration of amplitude calibration in the selection procedure of potential PS as a validation tool to determine if the potential PS would have been selected if the SAR images were calibrated beforehand.

Recursive data processing and data volume minimization for PS-InSAR

PS-InSAR has proven to be an accurate and ef- ficient technique for the joint estimation of topographic and displacement signal from stacked interferometric combinations. In this contribution a new method for PS-Insert processing is introduced, which enables the recursive estimation of parameters of interest. The method is based on the ILSQ PS-InSAR concept and makes use of the estimation vector and corresponding variance-covariance matrix of the initial estimation epoch. The presented methodology systematically adds a new acquisition (or set of acquisitions) to the existing stack, updates the solution of the previous run, and analyzes whether the behaviour of the (pre-) selected points fits the expected one. This contribution focuses on a mathematical framework, rather then on specific applicational problems. Nevertheless, the performed numerical analysis on simulated data sets is analyzed and discussed, which shows that the preset aims of the recursive PS-InSAR estimation technique is achieved. I. INTRODUCTION Time series InSAR analysis using persistent scatterer (PS) techniques aims at the joint estimation of topographic and displacement signal from a number of interferometric com- binations, (1), (2). Since the estimates of both parameters are correlated and error signal due to, e.g., atmospheric signal can significantly affect the adjustment, an accurate estimation depends on the availability of a large data stack, i.e., more than 20-30 images. A smaller number of images usually results in problems like detecting the potential PS, reducing the atmospheric signal, separating topography and displacement, and phase ambiguity estimation. An additional problem for all current multi-image pro- cessing concepts is that the parameter estimation is usually performed in batches, i.e., by using all available acquisitions at once. Hence, in order to incorporate a newly available acquisition into the processing chain, and consequently update the estimates, the whole processing (at least the PS part) has to be performed again. Such an approach consequently leads to an increase of processing time, limits the application to the areas where only a sufficient number of images is available, and reduces the potential application of the method to a semi- real-time deformation monitoring. The two main processing concepts of PS-InSAR are the concept of the ambiguity function, (1), and Integer Least Squares (ILSQ) method, (2). The main drawback of the first one is that the propagation concept of observations to the unknown parameters is suboptimal. Moreover, the method strongly depends on the discretization of the solution space and it treats unknown ambiguities as deterministic parameters instead of stochastic ones. The ILSQ approach is based on the principles of Best Linear Unbiased Estimation (BLUE) - it is based on the minimization of the mean squared error and it is formulated as a constrained minimization problem on the integer nature of the unknowns, (6). By means of the ILSQ method, the quality description of estimated parameters is the one of the end products of the analysis, which can conse- quently be used to determine the significance and reliability of the estimated parameters. The ILSQ PS-InSAR processing framework sets the basis for a recursive data processing strategy, where new acquisi- tions can be easily added to an existing data stack, significantly reducing the computational requirements. This implies that the presented methodology systematically adds a new acquisition to the existing stack, updates the solution of the previous run, and analyzes whether the behaviour of the (pre-)selected points fits to the expected behaviour of parameters of interest. If not, an alternative hypothesis is tested against the prior solution, leading to the rejection of the point, adaptation of the model, or manual intervention. For the conditions on the practical application of recursive PS-InSAR processing, it can be referred to the block-diagonal structure of the variance-covariance matrix of the introduced recursive model (the estimates from the initialization run and phase observations of the additional acquisition are assumed to be uncorrelated). Secondly, the atmospheric and non-modelled displacement contributions to the interferometric phase have to be modelled and incorporated into the variance matrix by means of covariance functions, (4), (5) - in the presented study the covariance functions are not further elaborated on. Moreover, in numerical experiments, phase contributions are isolated by low-pass filtering in the spatial domain and high- pass filtering in the temporal domain. Furtheron, in order to correctly perform the initialization run (candidate selection and unwrapping), a sufficient number of images (15-20) is needed. In the following sections the concept of the recursive PS- InSAR is presented. Examples on simulated data are used

Land subsidence monitoring in city area by time series interferometric SAR data

In this paper, the time series multi-image stack processing technique is implemented based on the ERS-1, ERS-2 SAR data set of cities of Las Vegas in America. A single master approach is used in the stack data processing based on the permanent scatterers processing technique invented by Ferretti et al. (1,2). After the differential phase model establishment and stable points selection, linear subsidence velocity and digital elevation model errors are estimated, non-linear subsidence velocity and atmospheric artifacts related to each SAR acquisition are separated, so a land subsidence history covering all the SAR data acquisitions in each city can be achieved. In our research, more test data in cities of China will be implemented in the next step.