The performance assessment of Collective Detection in general is not an easy task as there are many factors that influence the overall method performance, in particular the number of satellites visible, their geometry, and the relation between their signal powers. Furthermore in the SECA approach
also the parametersβ and wb i a s have an influence in the algorithm’s performance, as seen in the
previous section. The performance of the new approach is assessed here in comparison to the
performance of the search grid from[22,119]. The details of this search grid are shown in Table 5.6.
Note that also the search grid from[23] could have been used but this grid is computationally much
heavier with respect to the search grid from[22, 119] and a smaller position uncertainty range is
covered with no noticeable improvements in positioning errors.
For this comparison, a fixed constellation of six GPS satellites is chosen, and the MS position is varied within the uncertainty area. All signals are generated at the same signal power and the mask angle used is 30 degrees. For this simple illustration only 1ms of signal is employed and processed by the SLD detector to generate the individual detection metrics sets. The simulation results are shown in Figures 5.11 and 5.12, where the evolution of the probability of detection and position error of both approaches with the incoming signals’ power is shown. The signals are considered
to be correctly acquired when their final code phase estimation is within±0.5 chips of their true
code phase (calculated from the true MS position/clock bias and the satellites simulated positions).
For reference, a curve representing the sequential acquisition of these signals is also shown, cor- responding to the case when the maximum detection metric corresponds to the true code phase index. Note that the curves respect the correct acquisition of all signals in view.
The main conclusion that can be drawn from the plots in Figures 5.11 and 5.12 is that the perfor- mance of both approaches is dependent on the true MS position and clock bias. This is particularly noticeable for the reference search grid, as in some positions the algorithm’s performance is highly impaired. This is due to the fact that no averaging over a range of code phases is being applied, and the resolution of the first grid (“rough” in Table 5.6) does not assure a maximum code phase estimation error lower than half chip in this first step, so the true code phases can be missed in this step. Nevertheless, it can also be seen that in some cases the fixed grid performs better than the
Table 5.6 – Reference Collective Detection Search Grid
Item Rough Medium Fine
North/East Uncertainty (m) ±1 · 104 ±2000 ±900
North/East Resolution (m) 1000 100 30.0 Clock Bias Uncertainty (m) ±1.5 · 105 ±1200 ±300
(a) Sensitivity Analysis (b) Positioning Error
i) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (0,0,0,0)
(c) Sensitivity Analysis (d) Positioning Error
ii) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (0,0,0,250)
(e) Sensitivity Analysis (f ) Positioning Error
iii) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (0,0,0,500)
(a) Sensitivity Analysis (b) Positioning Error
i) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (250,250,0,0)
(c) Sensitivity Analysis (d) Positioning Error
ii) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (500,500,0,0)
(e) Sensitivity Analysis (f ) Positioning Error
iii) True MS coordinates (in meter):(∆N ,∆E ,∆D ,∆B) = (500,500,0,500)
new approach. This occurs in the cases when the MS position and clock bias coincides precisely with one grid point. However, the averaging approach is more robust, keeping its performance practically independent of the MS true coordinates. In terms of complexity of execution, a compu- tational gain of approximately five times is observed with the new approach, which scans 52.030 points compared to the 252.907 of the reference approach according to Table 5.6.
Through the analysis of the plots in Figures 5.11 and 5.12 it can be concluded that the proposed approach is effective in improving sensitivity over sequential acquisition methods, and that it is
more robust and computationally effective than the reference method[22, 119]. In the section 5.5,
the hybridization of the SECA approach with sequential acquisition techniques is addressed.
5.4.1 Influence of the Vertical Component
In light of the previous results, showing that Collective Detection, at best, provides a positioning
error in the order of tens of meters (also confirmed by[22, 23, 119]), it can be expected that the
vertical component can be safely neglected in the search process, and resort to 2D positioning. A reference vertical displacement could be provided by the BS, corresponding, for example, to the height of the BS antenna, which may be enough for the purposes of Collective Detection. This is also supported by the fact that the vertical error uncertainty will generally be much lower than its horizontal counterpart for land-based applications.
There may be, nevertheless, situations in which this assumption is not entirely correct (po- sitioning within skyscrapers or tall buildings, for example), in which an uncertainty in the verti- cal component needs to be considered as well. In this case, a second weight can be introduced,
wv e r t i c a l, to be added in (5.11), and the algorithm adapted accordingly from there. The vertical
uncertainty should be provided by the BS jointly with the horizontal one. In any case, the vertical uncertainty is not considered in the examples shown here.