The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part BI. Beijing 2008 
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4.1.2 Start values 
The correctness of the initial values of flj , p j and O' y is 
important for the EM algorithm to generate a good estimate. 
The initial value for fi . , is found by smoothing the 
pre-processed signal and First derivative of waveform, Figure 6. 
The initial values for jj. . are placed in the positions of the 
local maxima. If there are more components to estimate than the 
number of local maxima, the extra start values are put in the 
position of the local maxima with the greatest number of 
consecutive nonzero samples. Figure 7 illustrates a waveform 
(solid) and its initial estimates (dashed). The start values for p . 
are set so that all components have an equal weight and (7 is 
set to 7. 
Waveform (solid) and Three gauss components(dashed) have 
been estimated from the waveform in Figure 8. The estimated 
parameter: fl { = 54^ (T 1 =9.0> JU 2 = 8^ <T 2 =8.5> // 3 =13k 
<T 3 =7.2. 
Figure 9, Automated last return detection software is applied to 
the backscatter waveform to identify the start, peak, and end of 
the last return, inferred to be from the ground. In Figure 9 the 
laser pulse hits the canopy first and creates one echo pulses. A 
fraction of the laser pulse also hits the ground giving rise to a 
twice echo pulse. The vertical lines in the figure illustrate the 
positions of the ground extracted by the SLICER. 
250 
200 
150 
100 
50 
X»" 
1 i 
V , . ... i 
0 
100 200 300 400 500 
Fig.9 Ground location of SLICER 
250 
200 
150 
100 
50 
] 
or...L-.-J. 
0 100 200 300 400 500 
Fig. 10 Simulated waveform 
Fig.6 First derivative of waveform