Interferometric Stereo Radargrammetry: Absolute Height Determination from ERS-ENVISAT Interferograms Richard Bamler German Aerospace Center (DLR) Oberpfaffenhofen, D-82234 Wessling, Germany e-mail: richard.bamler@dlr.de Phone: +49-8 153-28-2673 Fax: +49-8 153-28-1420 ABSTRACT Absolute phase determination in SAR interferometry as well as stereo radargrammetry relies on the accurate esti- mation of mutual range shifts (or residual delays) of SAR data pairs. If two SARs with appropriately different radar frequencies are available, baselines can be large and the regimes of interferometry and stereo radargrammetry overlap; Then radargrammetry can take advantage of the coherence of the two data sets and can employ complex speckle correlation. Hence, speckle becomes an informa- tion rather than a nuisance. In the paper the lower bound for the estimation error of residual delay is derived and compared with simulations. The result is relevant also for absolute phase determination and speckle tracking. An example for height accuracy in an ERS-ENVISAT interferometric scenario is given. Index Terms - SAR interferometry, stereo radargramme- try, maximum likelihood delay estimation, co-registration error, speckle tracking INTRODUCTION In order to make full operational use of SAR interferome- try (InSAR) and differential InSAR a world-wide dense network of reference areas of known elevation is required. Large baseline stereo radargrammetry can provide absolute height measurements. Also algorithms have been proposed to derive the absolute phase from interferograms [l]. In any case, and no matter which particular implementation is chosen, the problem boils down to estimating mutual range shifts (or: residual delays) between two (possibly complex) SAR images to the best achievable accuracy. However, the approaches of stereo radargrammetry and interferometry differ considerable: In stereo radargrammetry [2] the baselines are usually much larger than the critical interferometric baseline ren- dering the two images to be non-coherent. Therefore, de- tected images must be used to estimate shifts (‘macro- scopic’ stereo parallaxes). The estimation accuracy strongly depends on image content (points, edges) and speckle is a nuisance. In interferometry, on the other hand, shifts are estimated based on partially coherent complex images, i.e. speckle 0-7803-6359-O/OO/$lO.OO 0 2000 IEEE 142 and phase patterns are the information used. No image features are required. The achievable accuracy of these ‘residual delay estimation’ [ 13 or ‘speckle tracking’ 131 algorithms is much higher than in the radargrammetry case. However, due to the small baselines, the shifts to be estimated are much smaller than in radargrammetry. In order to resolve the absolute phase, the shift estimation accuracy must be smaller than half of a wavelength, i.e. about U600 of a range resolution element in the ERS case. The radar frequency of ENVISAT/ASAR will differ from the one of ERS by 31 MHz allowing for interferometric baselines of up to 3 km. In this regime the mutual shifts become large enough that sufficient height information can be extracted even if the absolute phase was not recovered to an accuracy of less than a phase cycle. Since partially coherent complex images are used to retrieve the shifts or stereo parallaxes in this case, the distinction between ra- dargrammetry and interferometry is no longer applicable, hence the term ‘interferometric stereo radargrammetry’. SHIFT OR DELAY ESTIMATION ACCURACY No matter whether we want to determine the absolute phase offset in an interferogram or whether we want to estimate tiny parallaxes in the ERS-ENVISAT scenario sketched above, the accuracy of shift (delay) estimation is a crucial factor. Several methods have been proposed in the past (see, e.g. [ 1,4,5]). The optimum (maximum likelihood) estimator (MLE) for mutual shift of partially correlated stationary circular Gaussian signals is known to be the cross-correlation op- eration. The error of this estimator is derived in the Ap- pendix for the case of homogeneous image patches, i.e. without image features. The result is: ( 1) a, =&gosf 312 where a, is the standard deviation of the estimate Ai of a mutual shift Ax in units of samples, y is the coherence of the interferometric data pair and N is number of sam- ples in the estimation window, and osf is the oversampling