Indoor Positioning with GNSS-Like Local Signal Transmitters - Global Navigation Satellite Systems: Signal,Theory and Applications - page 326

fact that the left part of the ACF is the one that is the least modified by multipath, but that in
addition the prompt replica is modified by the presence of multipath. Thus, the new
discriminator uses the Early correlator that is less modified and a modified form of the
prompt correlator. Expressions (4) represent the way the prompt correlator is modified and
are in fact obtained from the analysis of the general form of the multipath contribution to
the discriminator. Indeed, for multipath of less than half a chip, one can show that

( ) ∑

ˆ

⎧ +=−

( )

IE IL 2 Δ A cos θθ −

k k

⎨

0 ≤≤ kN

(5)

( )

ˆ

( )

∑

⎩ QE + QL =− 2 Δ A sin θθ −

k k

0 ≤≤ kN

The various sums in (5) being the multipath contributions, considering there are N reflected
paths of amplitudes A k and delay (θ k -θ). The limitation of the efficiency of the method to
reflected paths of less than half a chip is due to the validity domain of these approximations.

Let us now give the main results obtained for multipath mitigation. The proposed code loop
is compared to the standard code loop and the Narrow Correlator (NC). The signal received
is assumed to be the sum of a direct signal and a single reflected signal whose amplitude is
half that of the direct signal. The following curves show the envelopes of the pseudo-range
errors in a similar way as in figure 10.

With an unlimited front-end bandwidth receiver , the results are given in figure 20. The half chip
limit is quite clear for the SMICL. Nevertheless, performances are better than SDLL and NC
for short multipath 24 .

0,5

In-phase multipath SMICL
Out-of-phase multipath SMICL
In-phase multipath NC
Out-of-phase multipath NC
In-phase multipath SDLL
Out-of-phase multipath SDLL

0,4

0,3

0,2

0,1

0

-0,1

-0,2

-0,3

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 1 1,125 1,25 1,375 1,5

Multipath relative delay (chips)

Fig. 20. Comparison of discriminators for an unlimited bandwidth
24 Many simulations, carried out with Ergospace, have shown that this assumption concerning the
delays of the reflected paths indoors is acceptable almost all the time.