Since the early days of optical SAR processing and stabilised antenna platforms [6] InSAR motion compensation has been carried out using data from on-board Inertial Navigation Units (INUs) which offer a simple and convenient method for measuring the actual aircraft track and orientation [7]-[10]. These unambiguous track measurements are
used to compensate for the variation in along track velocity and to calculate a phase and (if necessary) a range correction, to be applied to the range compressed data before azimuth compression. This reduces geometrical distortions in the processed SAR image as well as improving focus [3],[4]. The roll measurements from the INU may also be used to provide a phase correction to the range compressed data [14], or used directly to correct the height errors in the topographic reconstruction.
This ability of the INU to provide absolute measurements of the platform motion, combined with the availability of computationally efficient algorithms for six-axis (three rotations and three translations) motion compensation, and an excellent high frequency performance [5], makes INU based motion compensation the preferred choice for most modern SAR and InSAR systems [14]-[17]. Motion compensation can be further enhanced by using GPS, or preferably Differential GPS (DGPS), to compensate for INU drift and generally improve low frequency performance. However, DGPS is slightly restrictive as it requires the use of a synchronised ground receiver at a surveyed location somewhere in the region of the SAR (e.g. within 200 km for the ERIM IFSARE [16]), which may limit flexibility.
4.2.2 Doppler Centroid Compensation
The development of data driven algorithms for SAR motion compensation started in the early 1980s with the development of clutterlock and an early form of map-drift autofocus for processing data from Seasat [23]. Clutterlock is used for estimating Doppler centroid offsets in the SAR azimuth spectrum due to antenna beam pointing errors or across track drift, which if uncompensated lead to a loss in SNR and SALR (Signal to azimuth Ambiguity Level Ratio). Techniques for Doppler centroid estimation were refined by [24],[25] and [26] and are now used for both satellite and aircraft-borne systems.
In a single channel SAR, Doppler centroid estimation is used to estimate a linear phase error correction to be applied to the range compressed data before SAR processing, in order to steer the Doppler centroid back to the zero Doppler position, with the intention of re-aligning it with the matched filter and improving the SNR and SALR. The data can then be azimuth compressed using a standard SAR processor, which typically involves bulk processing using efficient FFT algorithms, rather than having to adjust the filter characteristics along track to match the data, which would then require processing using time domain convolution, which is inefficient for large data sets.
In a dual antenna InSAR, the coherence between the two SAR channels is critical, so in order to preserve coherence, any Doppler centroid compensation has to be applied identically to both channels. This also preserves any small differences in the phase and Doppler characteristics of the two received signals due to the slightly different motion through space of the two antennas, which can be exploited by more sensitive techniques to estimate the aircraft roll rate (see Chapters 5 and 6).
4.2.3 Autofocus
The development of autofocus techniques started with incoherent methods such as map- drift autofocus and contrast optimisation [1]. These have been extended to multiple aperture techniques in order to detect higher orders of phase error (see [27], [28]). These have such good performance up to second order that they are used by QinetiQ (Malvern) to improve the low order performance of their INU based motion compensation system [5] for their L-Band spotlight data archive, which was collected before the advent of DGPS. This system has produced images at 6 cm azimuth resolution at a range of 20-30 km, where motion compensation is critical.
More recently, coherent methods such as Phase Difference (PD) [29] and Phase Gradient Autofocus (PGA) [30]-[32] have emerged. According to Carrara et al [28], PGA is a superior algorithm for higher orders of phase error, whilst PD autofocus produces similar results to map-drift autofocus, but with fewer iterations. However, these techniques were developed for spotlight mode SAR, and have to be heavily adapted for strip-map SAR, with possible performance implications. Some of the latest research into autofocus makes use of higher order statistics to further improve high frequency performance [33].
The phase error estimates derived from the autofocus procedure are used to compensate the range compressed SAR data, which is then re-compressed in azimuth. Usually, this autofocus and re-compression procedure is iterated until the residual phase errors are sufficiently small. However, the quadratic phase errors may be caused by either along- track velocity errors or across-track accelerations (see Section 4.3) and in practice the SAR images suffer from geometrical distortions unless this ambiguity is resolved using on- board instrumentation [1]-[4]. Typically, the PRF of the radar is tied to the along-track velocity to give a constant spatial PRF [10], with the along-track velocity being obtained from a Doppler navigator or INU. In the case of a lightweight or low budget UAV this function could be provided by DGPS or in the future, a lower performance (compared to an INU) inertial system based on solid-state accelerometers (see Section 1.2). In this way the remaining quadratic phase errors detected by autofocus can now be attributed to across
track accelerations and double integrated to give a track correction.
Ideally, autofocus would be applied to both channels of an InSAR independently to obtain the best possible focus in each image. Unfortunately, InSAR is sensitive to even small differential distortions between the two SAR images which result in a loss of interferogram coherence [37]. A better method is to autofocus one channel only, and apply the phase corrections equally to both channels. If necessary, a specialised residual focusing technique can then be employed to improve the interferogram coherence [11].