Page 192 - NGTU_paper_withoutVideo

Modern Geomatics Technologies and Applications

tracking correction. To detect potentially meaningful peaks, first the mean difference between the single and double powers ( d k
1
k
and d ) and their standard deviations (S1 and S2) by equations 9 to 13.
2
d  k p  p k=1,2,...,N-1 (9)

1 k 1 i
d  k p  p k=1,2,...,N-2 (10)

2 k 2 i


i
(N 1)  N  1 (d )  1 i 2 (  N 1 d ) 2
1

S  k 1 i 1 (11)

1
(N 1)(N  2)
N  2 N 2

k
(N  2)  (d )  k 2 2 (  d ) 2
2
S  k 1 k 1 (12)



2 (N  2)(N 3)
Ε  BS (11)   CS (13)
1 1 2 2

where p is the power of the k-th sampling gate, E1 and E2 are the coefficient of single and double difference standard
k
deviations. B, C coefficients are between 0-1 based on the general shape of the waveforms in study areas. In this study they
have been set as 0.1 and 0.2 according to waveform in this region. The process starts from the first gate, if one half of the
double power difference is greater than E2, the gate would be most likely the primary meaningful sub-waveform. Then If
there are more than three consecutive gate whose the difference of single power is greater than E1, the selected sub-
waveform is the meaningful sub-waveform decisively [25]. According to previous studies, first sub-waveform re-tracking
generally provide the most precise SST [26] therefore, in this study the same approach has been used. In the meaningful
sub-waveform re-tracking with threshold algorithm, the sub-waveform amplitude is considered as of the maximum of the
sub-waveform power [27].

First sub-waveform : MS(i)={1,2,....n} Selected sub-waveform =MS(1) (14)
where MS(i) is the i-th Meaningful Sub-waveform and n in the number of all meaningful sub-waveforms in a waveform.

3..3. Mean Waveform (per each cycle) Re-tracking

Mean waveform per each cycle (Wmean) at the C-th cycle with K number of waveforms using threshold algorithm is
defined by Equation 15.
1 N
W mean (C)   p(i) , i=1,2,..N (15)
K i 1
where P i is the power of i-th gate and N is the number of available gates in a waveform. This waveform re-tracked using to
equations 5 to 8.

3..4. Proposed Method: Maximum Correlation with Mean Waveform

In the developed method, a mean waveform per each pass is defined according to Equation 15 over the study area and
finally a waveform with the maximum correlation with mean waveform is re-tracked using threshold re-tracker. (Equation 16).
Selected waveform = Max Corr{W (j) , w (c)} , W (j)={1,2,...,K} (16)
C C
where Wc(j) is the j-th waveform at C cycle, w (c) is the mean waveform per each cycle and k is the number of all waveforms at
cycle C. Figures 2 shows the re-tracked gates using different re-tracking algorithm in this study. This waveform re-tracked using
to equations 5 to 8.

5