EUSAR’06, European Conference on Synthetic Aperture Radar, Dresden, Germany, May 16-18, 2006. 1 First Evaluations of Airborne InSAR Time-Series Karlus A. C. de Macedo * , Rolf Scheiber, Alberto Moreira Microwaves and Radar Institute (DLR), Germany *The author holds a Grant from CAPES, Brazil Abstract To allow time-series analysis of airborne SAR images using PSs (Permanent Scatterers), this paper has two main objectives. The first is to show, in a quantitative way, that there is a compromise between the number of images used to detect PSs, their probabil- ity of being detected and their stability. This tradeoff is derived based on estimation and detection theories. The second objective is to investigate the possibility of the use of permanent scatterers to estimate undesired phase undulations in airborne data due to residual motion errors. A new technique is proposed, the so-called PS-PGA, where we apply the Phase Gradient algorithm on the PSs in order to obtain sub-wavelength estimations of residual motion errors for both master and slaves, separately, differently from current approaches. Compensation of these residual errors will lead to more reliable airborne D-InSAR measurements. 1 Introduction In order to compensate in interferograms undesired phase con- tributions due to atmospheric effects, DEM errors, [1] pro- poses the Permanent Scatterer technique (PS). The PS tech- nique involves the selection of phase-stable scatterers, At- mospheric Phase Screen (APS) estimation and compensation, parameter inversion of terrain deformation, and DEM errors from a series of SAR data. This technique has been sucessfuly applied to spaceborne data where sets of more then 30 images are oft available. For reliable APS estimation using the PS technique, [2] shows that more than 20 images are necessary. In this paper we investigate for the first time the use of the PS technique in airborne data. Differently from spaceborne case, atmospheric effects are not the main source of undesired phase contribution in airborne data. For the airborne case the accu- racy of the phase measurements are mainly affected by the deviations of the platform from the nominal track. After very precise motion compensation [3], residual motion erros in the order of 5-10 cm are still present in the image causing signif- icant phase undulations turning D-InSAR applications (sub- wavelength measurements) with airborne data impracticable. Due to the low availability of large sets of data from airborne platforms, we start our investigation with a set of 14 images of the E-SAR system acquired in the same day. Due to the dif- ferent nature of phase errors between spaceborne and airborne case, it may be possible, differently from APS estimation, to use less then 20 images to estimate residual motion errors, as we will show. To have a robust and reliable selection of PSs with 14 SAR images we developed and propose a quantitative analysis of the permanent scatterers selection performance. It is shown in [1] and [4] that, the more images available the smaller is the estimation error of the dispersion index estimates ˆ D A . But up to now, there is no quantititive relation showing the tradeoff between the number of images, the desired phase stability and detectibility of the selected permanent scatterers. In section 2, we derive a tradeoff relationship of the compro- mise between the number of images to detect PS candidates, their stability, and their probability of detection. In section 3, we use the selected PSs to estimate undesired phase undula- tions in airborne data due to residual motion errors. We pro- pose a new technique, the so-called PS-PGA, where we apply the Phase Gradient algorithm on the PSs in order to obtain sub-wavelength estimations of motion error. A discussion of the results is included in Section 4. 2 The PS Selection Performance 2.1 Stability The PS technique identifies the stable-phase or permanent scatterers by performing a statistical analysis of the amplitude values of a scatterer along a series of SAR acquisitions. From the amplitude dispersion index D A , it is possible to estimate the phase standard deviation σ ν of a scatterer [1] σ ν  σ n g  σ A m A , D A , (1) where g and σ n are the parameters of the Rice PDF (Probabil- ity Density Function) which models the amplitude of the radar scatterers [1], and m A and σ A are the mean and the standard deviation of the amplitude values of the scatterer, respectively. The selected permanent scatterers are those in which the am- plitude dispersion, D A , is lower than a certain threshold value. Alternatively to D A , the stability of a scatterer can be given by its SNR (Signal to Noise Ratio). It is found by dividing the mean power P of the signal of the scatterer by the power of the noise N o , i.e. P /N o . For a scatterer with Rice distributed amplitudes it becomes SNR = P N o = g 2 2σ 2 n . (2)