Multipath Mitigation Techniques for Satellite-Based Positioning Applications - Global Navigation Satellite Systems: Signal,Theory and Applications - page 417

Δ ) according to the following equation:

= ± (

M

−

1

)

τ W Δ

(4)

2

For example, in Bhuiyan & Lohan (2010), 193 correlators were used with a correlator spacing
of 0.0208 chips, resulting in a code delay window range of ± 2 chips with respect to prompt

correlator. Therefore, the LOS delay estimate can be anywhere within this ± 2 chips window

range. The ideal non-coherent reference correlation functions are generated for up to L max
paths only for the middle delay index (i.e.,

M + 1

193, the middle
delay index is 97). These ideal correlation functions for the middle delay index are generated
off-line and saved in a look-up table in memory. In real-time, RSSML reads the correlation
values from the look-up table, translates the ideal reference correlation functions at the middle
delay index to the corresponding candidate delay index within the code delay window, and
then computes the Minimum Mean Square Error (MMSE) for that specific delay candidate.
Instead of considering all possible LOS delays within a predefined code delay window as
delay candidates, the search space is first reduced to some competitive peaks which are
generated based on the computed noise thresholds as explained in Bhuiyan & Lohan (2010).
This will eventually reduce the processing time required to compute the MMSE (i.e., MMSE
needs to be computed only for the reduced search space). An example is shown in Fig. 7,
where RSSML estimates a best-fitted non-coherent correlation function at a cost of 3.6

( )

-th delay index; for M

=

2

10 − 4
MMSE in a two-path Rayleigh channel with path delays [0 0.35] chips, path powers [0 -2] dB
at a C/N 0 of 50 dB-Hz.

·

2 Path Rayleigh Channel, Path Delay s:[ 0 0.35 ] Chips, CNR: 50 dBHz

1.2

Received Correlation Function
Estimated Correlation Function
Residual Error

1

0.8

0.6

Peak Threshold

0.4

0.2

0

−0.2

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

Code Delays [Chips]

Fig. 7. Estimated and received non-coherent correlation functions in two path Rayleigh
channel, path delay: [0 0.35] chips, path power: [0 -2] dB, C/N 0 : 50 dB-Hz.