Especificación de casos de uso

It w as decided that the exact cause o f the linear trend betw een e and A/z,,;. observed in se c tio n 4 .3 .3 sh ould be in v estig a ted further in a m ore c o n tr o lle d sim u la tio n environm ent. A sim ulation o f the w aveform averaging process under the control o f just the HTL w as carried out in order to isolate the cause. The basis o f this sim ulation w as the repeated application o f equation 3 .1 6, x representing height, over the period o f w aveform averaging, that is with n ranging from 0 to 49. a , p and T w ere set to the appropriate values for the ERS-1 tracker, and /zq and ho were taken to be zero.

Pure specular w aveform s w ere used in this sim ulation. The flat surface im p u lse respon se, PfsiO, and surface height pdf, q{z), in equation 3.2 , w ere taken as 5-

functions, resulting in a return pulse identical to the SPTR. Each 1020 H z w aveform w as m o d elled on the SPTR usin g a G aussian fu n ction , and co u ld th erefore be represented m athem atically as:

p ,(/z) = exp f \2' ( h ~ K f 2 2 _{\ p V} _ 4.8

w here g., = 1.28788 ns and h„ is given by: = n a e + - { n + \)p£ 4.9 2 0 (e /1 0 + 1) 10 05 fhrtk-VT) E -0.5 - ■1 .0 - - 20 0 2 4 6 8 10 T im e (s) (b) (e /1 0 + 1) 1.5 1 0 - 0.5 E -05 -2.0 6 10 0 2 4 8 T im e (s)

F igure 4.9 R etracked heights and H TL error signals along-track for (a) sim ulated data, and (b) specular w aveform data from the S alar de Uyuni salt-pan (scaled and offset for clarity).

E ach averaged w aveform can therefore be represented as:

49 / \2"

( h - K f

2

CG„

_

4.10

A series o f such averaged w aveform s was generated for values o f £ b etw een -5 m and

-1-5 m, in increm ents o f 10 cm. The height difference, betw een the telem etered

height at the tim e o f the 37th pulse and the retracking point, at 50% o f the peak

pow er, was calculated for each averaged waveform . A plot o f the height error signal,

£, against this height difference can be seen in figure 4.10, which reveals a linear trend sim ilar to that seen in the real data and the output o f the full tracker sim ulation. The slope o f the trend was m easured as -3.5. The reason for this linear trend will now be discussed in the light o f the results from the HTL sim ulation.

A h 3 „ g ( m )

F igure 4 .1 0 Fleight error signal, e, versus height difference, betw een the

telem etered height and the 50% retracking point.

The initial w aveform was distributed about the centre o f the range w indow , w hich corresponds to the true tracking point in the case of a pure specular reflection. It is im portant to note that not all so-called specular w aveform s are the result o f a pure specular reflection. This has the effect o f shifting the tracking point aw ay from the peak tow ards the half-pow er point on the leading edge. This is the source o f the retracking bias discussed in section 4.4.2.

As the averaging process takes place, the range w indow m oves quadratically in tim e, its position being governed by the H TL (equation 4.9). The degree o f m ovem ent betw een the arrival o f individual pulses depends entirely on the H T L erro r signal, £, for a given set o f tracking param eters. Due to the m ovem ent o f the range w indow , the pulses are not perfectly superim posed, and are effectively sm eared across the range w indow . A fter the arrival o f the 50th pulse, at the end o f the averaging sequence, the final averaged w aveform will be in a position determ ined purely by £. Figure 4.11 shows this final situation w hen £ = +4 m, 0 m and -4 m. Also show n is the position o f the centre o f the range w indow when n = 36, that is w hen the range is w ritten to the telem etry, and the 50% threshold retracking point.

a

Bin num ber

63

Figure 4.11 Positions o f the final averaged w aveform s and retracking points relative to the centre o f the range window in the HTL sim ulation, for (a) e = +4 m, (b) e = 0 m and (c) e = -4 m. A typical averaged w aveform w hich requires retracking is also shown in (c).

It can be seen from figure 4.11 that in each case a distinct offset exists betw een the 50% threshold retracking point and the range w indow centre. In this sim ulation, we know that the w aveform is initially at the correct tracking p osition, and that the averaged w aveform is offset from this true tracking point due to the m otion o f the range window. This sim ulation therefore tells us w here the averaged w aveform will be located with respect to the centre o f the range w indow for a com plete range o f e,

w hen the first w aveform in the averaging sequence is at the correct tracking point. The current retracking algorithm s work under the assum ption that w aveform s should be retracked to the centre o f the range w indow , but this result tells us that they should be retracked to a position dependent on e.

In figure 4 .1 1(c), a typical averaged waveform is show n w hich requires retracking in o rd er to m ake the associated range m easurem ent m eaningful. The cu rrent 50% threshold retracking schem e has the effect o f increasing the range by an am ount

as shown. These sim ulations show that the range should be increased by an am ount

\r r ’ w hich takes into account the additional offset due to the range w indow motion.

It should also be noted that the asymm etry about the £ = 0 axis in figure 4.10 is due to the fact that we have chosen to retrack to the half-pow er point on the leading edge. This choice o f retracking point is in fact arbitrary, and a different point w ould yield different results. The biases introduced by this schem e w ill be discussed in section 4.4.2.