PixyMon

This expression relates the DAS directly to the aircraft roll rate ωx, and shows the basis of

the DD method for roll rate compensation. However, further investigation is required to determine whether the approximations and assumptions made earlier in the section hold in practice – of particular concern are other sources of DASs which would lead to ambiguities in the roll rate estimates. This is carried out in the next section.

5.3 Experimental Evaluation of Single-Shot Implementation

The first part of this experimental evaluation of the DD method attempts to reproduce the results presented by Currie [1] at the then GEC-Marconi research centre. These consisted of a flat ground interferogram captured by the QinetiQ C-Band InSAR, initially corrupted by a slow roll manoeuvre performed by the pilot, but later compensated using a single application of the DD method. The results showed good compensation of the fringe lines producing the expected flat ground interferogram, but could not be evaluated quantitatively as the data was captured prior to the installation of the auxiliary INU, subsequently used to record the aircraft rotations. The data for the current research comes from the same sensor, but captured more recently with supporting data from the INU, allowing a quantitative comparison of the roll estimated by the DD method.

In the second part, the evaluation is extended to the case of a more typical flight profile in which the pilot attempts to maintain a straight and level flight, with the interferogram being distorted by higher frequency roll perturbations than in the slow roll case, and with the additional restriction of having the range compressed raw data averaged down to a reduced along track sampling rate to alleviate data storage or real-time transmission bandwith requirements (for a UAV for instance) and to reduce processing time for the SAR images.

5.3.2 Roll Compensation Procedure

The DD method for roll compensation consists of four discrete stages, these being estimation of the DASs between the two images, conversion of the DASs to roll rate estimates, integration of the roll rate estimates to reconstruct the roll angle history, and

finally, re-processing of the SAR images and interferogram using the reconstructed roll angle history to provide phase compensation of the range-compressed raw data (this part is integrated into the InSAR processor).

In the first stage the DASs are estimated using cross-correlation of the monostatic and bistatic intensity images on a patch by patch basis, with the images being divided into a grid of along and across-track patches for the cross-correlation procedure. However, the following modifications were made to Currie’s original method: firstly, a maximum limit is set to the permitted DASs using an initial pass, whose results are then discarded. This greatly reduces the effect of spurious results from strong targets (i.e. bright speckle) at the edge of a patch. Secondly, to counteract the triangular weighting of the cross-correlation magnitude resulting from the two rectangular input weightings, which would bias the cross-correlation result to the central position, the bistatic patch is truncated in azimuth at either side of the patch by the maximum permitted DAS. This gives an unbiased estimate of the DAS within the specified range. Thirdly, to remove any topographic influences which cause phase differences between the two images, only the magnitudes of the images are correlated. Finally, rather than averaging the DASs in range which would allow the result to be influenced by weak cross-correlation outputs, the algorithm searches for the strongest cross-correlation output in the patch – i.e. the brightest target - and uses its DAS as the result for the whole patch.

In the second stage, the DAS estimates from the cross-correlation procedure are converted into roll rate estimates using

′ = ′ ω β x xn v t r d 2 2 ₀ 0 Δ ' sin (5.32)

(the dashed terms denoting estimates), which can be obtained by rearranging Eq. (5.31). The sinβ term introduces a weak topographic dependence, but in practice a flat ground topography has to be assumed, with any errors being averaged in range and causing a small ambiguity. However, in theory, this ambiguity can be compensated out using an iterative implementation of the DD method (see Section 5.4). The roll rate estimates are then averaged in range, with the range dependence of Δt₀ allowing the quantisation noise in the DASs (1 pixel, 2 pixels etc.) to be averaged across the range bins.

In the third stage the roll rate estimates are integrated to give an estimate for the along- track roll angle history, minus a constant offset which has to be determined by other means. In practice the roll rate estimates are also subject to DC bias and scaling errors which must be compensated, and are considered in the discussion of results sections.

In the fourth stage, the SAR images and interferogram are reprocessed using the reconstructed roll angle history. The roll compensation is applied inside the InSAR processor by means of phase compensation of the monostatic channel prior to azimuth compression. By compensating the range compressed data before azimuth compression, as opposed to simply compensating the interferogram, scatterers in the two images should align better, improving the interferogram coherence, and hence reducing the noise in the topographic height reconstruction.