Importancia de las ciencias en la educación primaria

Two data sets captured by the QinetiQ C-Band InSAR are used here to evaluate the DD method for roll compensation. Both the areas imaged consist mainly of flat ground to allow easy identification of roll patterns in the interferograms, and easy qualitative assessment of the effectiveness of roll compensation. However, both areas also contain portions of raised topography allowing the ability of the roll compensation algorithm to separate roll-distortions from the topography to be tested, which is a key feature of both the DD and 2-look methods for roll compensation described in this thesis, and a key deficiency of existing data driven methods based on interferogram filtering, such as [4]. All the processed images are shown in the results section to allow easy side-by-side comparison of before and after results.

The first data set was captured over Pershore Airfield and is generally flat with a steeply banked strip on the left hand side of the image (see Fig. 5.5 (a) and (b)). This data set has a high pulse PRF (1250 Hz) and is corrupted by slow roll manoeuvre consisting of approximately half a cycle of quasi-sinusoidal roll with a peak amplitude of about 1.4˚ over a duration of 12.8 s, as shown in Fig. 5.7 (b). The signature of the aircraft roll history is shown characteristically repeated across the uncompensated interferogram of Fig. 5.5 (b), increasing in amplitude with range. However, there is a strip of banked ground down the left hand side of the image which is clearly visible in the INU roll compensated interferogram of Fig. 5.5 (d), but visually has characteristics similar to aircraft roll, and would certainly be mistaken as such by any technique for roll compensation based on interferogram filtering if the image were a little shorter in range (i.e. if the banked strip extended across the whole image). Therefore this data provides an interesting challenge to test the DD method for separability of roll and topographic effects. The relevance of the high sampling rate and long roll period are to provide a data set in which sensitivity and bandwidth problems, described in Section 5.5, can be neglected.

The second data set was captured not far from the English coast at Weston-Super-Mare, with typical straight and level flight characteristics, consisting of small amplitude (to approximately ±1˚) roll perturbations about 0˚, with frequency components much higher than in the Pershore Airfield data, as shown in Fig. 5.13 (b). The topography consists of fairly flat farmland except for a slightly raised band (< 10m according to the spot heights and contours marked on the Ordnance Survey map [5]) corresponding to a lightly developed area running from top to bottom of the image, slightly to the left of centre-line. This is clearly visible in the SAR image of Fig. 5.12 (a) and INU compensated interferogram of Fig. 5.12 (d). The characteristics of the two data sets are summarised in Table 5.1.

Slow roll manoeuvre (Pershore Airfield)

Straight and level flight (Weston-Super-Mare) Azimuth No. of samples 16000 8192 Pulse PRF 1250.00 Hz 208.33 Hz Mean vx 82.575 m s -1 80.013 m s-1 Azimuth sample spacing 6.6 cm / 0.0008 s 38.4 cm / 0.0048s

Image length / duration 1057 m / 12.8 s 3146 m / 39.32 s

Processed resolution 0.8 m (near-range) 0.8 m (near-range)

Synthetic aperture time TSA 0.68 s (fixed) 0.7 s (fixed)

Range

No. of range bins processed 512 1184 (512 shown)

Sample spacing / resolution 1.5 m / 2.1 m 1.5 m / 2.1 m

Slant ranges processed 1708 - 2475 m 1708 – 3482.5 m

Nominal aircraft height, H 1218 m 1280 m

Table 5.1: Parameters for the Pershore Airfield and Weston-Super-Mare Data sets.

The track length for the second image is long compared to the first image at 3146 m against 1057 m, in order to show a reasonable and representative sample of the typical roll perturbation characteristics of the BAe Andover platform. In order to keep the data to a manageable size it was compressed by the coherent pre-summing of 48 consecutive pulses. In general, an efficient choice of sampling rate is just higher than the Doppler bandwidth of the received signal, corresponding to the first null in the physical antenna beamwidth. However, in this case, the range compressed raw data was compressed to a PRF of just over 208 Hz compared to a Doppler bandwidth of 500 Hz (see Fig 4.7), at the

expense of a small amount of aliasing at the edges of the synthetic aperture. Here, the effect of the aliasing has been minimised by restricting TSA to a constant 0.68 s (so ρaz =

0.8 m at near range), giving a Doppler bandwidth for the matched filter of only 100 Hz at

v_xn = 80 ms-1

(from Eq. 3.41) at near range. The low sampling rate is also a potential limit to roll rate sensitivity (see Section 5.3.7), which invites an interesting comparison between the incoherent DD method and the coherent 2-look method for roll compensation described in Chapter 6 which does not suffer from this limitation.

Track compensation was applied to the range compressed raw data before SAR processing. In range this involved both phase compensation and resampling in range to account for across-track movements, whilst along-track this involved using the along-track velocity to resample for a constant spatial PRF. Due to a bandwidth bottleneck in the asynchronous RS422 interface connecting the navigation instruments to the digital tape recorder, apart from the priority measurements of INU roll pitch and yaw angles and rates, much of the other INU data was unreliable. However, limited track compensation could still be achieved by interpolating the irregularly sampled INU v_y and v_z velocity data and combining it with along track velocity measurements from the GPS, and limited height information from the barometric altimeter (at roughly one sample per second). This allowed point targets in the image to be focused to an azimuth resolution of around half a metre (greater than used here). The final pre-processing stage was to apply range curvature compensation (see Section 3.5.5 for a description of this problem) using a frequency domain range/Doppler pre-warping technique.

SAR processing was carried out using a custom-built range/Doppler InSAR processor written in ‘C’ by the author, using FFT based cross-correlation for fast execution. This purpose-built processor allowed the flexibility to provide integrated roll compensation (either from the INU roll measurements or from the data-driven roll history reconstructions) and other refinements such as radiometric compensation.

The InSAR images were processed as conventional SAR images except for the synthetic aperture being of fixed duration (so the azimuth resolution degrades with range) rather than being increased with range to give a constant azimuth resolution. This ensured a constant bandwidth for the roll rate estimator across the track (see Section 5.5.1). Visually, the SAR images appeared well focused at this resolution. After processing, the data was saved at the original sampling rate to preserve the minimum detectable DAS. However this resulted in unusually large SAR images (16000x512 pixels at 8 bytes/pixel = 65.5 Mbytes per image for the Pershore airfield images), as the images would normally have been averaged in azimuth after SAR processing to say 1000-2000 pixels for viewing.