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We propose an efficient method for the detection of Line of Sight (LOS) and Multipath (MP) signals in global navigation satellite systems (GNSSs) which is based on the use of virtual MP mitigation (VMM) technique. By using the proposed method, the MP signals' delay and coefficient amplitudes can be efficiently estimated. According to the computer simulation results, it is obvious that our proposed method is a solution for obtaining high performance in the estimation and mitigation of MP signals and thus it results in a high accuracy in GNSS positioning.

In GNSS systems such as Global Positioning System (GPS) and future Galileo the positioning accuracy is seriously degraded in the presence of MP propagation [

In the absence of MP signals, the CF of C/A-GPS and BOC(1, 1)-Galileo codes can be approached by the following expressions, respectively:

Figure

Correlation functions in the absence of MP signals for both C/A-GPS and BOC(1, 1)-Galileo.

In the presence of MP signals the baseband signal model is defined as follows [

Some important characteristics of the MP signals are summarised as follows:

The MP signals arrive after the LOS signal because it must travel a longer propagation path.

If the delay of the MP is less than one

The MP signals can be stronger or weaker than the LOS signal.

In all the figures of the paper, the delays are normalized with respect to the LOS. In effect, “0” represents

In presence of a single MP component, the normalized input signal with respect to

The relationship between the amplitudes of LOS and MP signals is given as

In presence of a LOS and single weak MP signals, the receiver tries to correlate with these two components. The resulting CF is distorted as shown in Figure

The mathematical expression of the MCF can be obtained from (

The VLOSCF has peak amplitude equal to the maximum value of the CCF and has a width of two code chips on the horizontal axis.

The mathematical expression of VLOSCF can be derived from (

As shown in Figure

The peak location of the VMCF corresponds to the MP delay

LOS, MP and CCF (weak MP “GPS-code”).

Concept of VMM (weak MP “GPS-code”).

In this case, the relationship between the amplitudes of the LOS and MP signals is given as

In presence of a strong MP signal, the CCF is not aligned with LOSCF but with the MCF as shown in Figure

As shown in Figure

The mathematical expression of VMCF can be derived from (

In this case, to estimate the delays

LOS, MP, and CCF (strong MP “GPS-code”).

Concept of VMM (strong MP “GPS-code”).

The relationship between the amplitudes of the LOS and MP signals is given as

The maximum of the VLOSCF and CCF is given as

The obtained VMCF (A1A2A3A4A5A6 in Figure

To estimate the delays

LOS, MCF, and CCF (weak MP “BOC(1, 1)-Galileo-code”).

Concept of VMM (weak MP “BOC(1, 1)-Galileo-code”).

With the same discussion and as the case of C/A-GPS signals, the resulting CCF and the concept of the VMM are illustrated in Figures

The delays

LOS, MCF and CCF (strong MP “BOC(1, 1)-Galileo-code”).

Concept of VMM (strong MP “BOC(1, 1)-Galileo-code”).

In presence of two MP and a LOS signals, the received signal can be expressed by the following equation [

The relationships of the amplitudes and the delays is:

Here, the mathematical expression MCF2 can be obtained from (

LOSCF, MCF1, MCF2, and CCF (two MP signals “GPS-code”).

Concept of VMM (two MP signals “GPS-code”).

In the presence of two MP and LOS signals, the peak position of the CCF can be located on the peak of LOSCF or MCF1 or MCF2. In this paper, we discuss only the second case. Another discussion can be done for the first and the third cases.

With a similar discussion, Figures

LOSCF, MCF1, MCF2, and the resultant CCF “BOC(1, 1)-Galileo-code.”

Concept of VMM (case of two MP signals “BOC(1, 1)-Galileo-code”).

The values of the delays

The impact of MP on code tracking accuracy is often represented as an error envelope which represents the maximum error resulting from one single MP with a certain phase delay and amplitude. The same method of analysis applied to the MP-induced error will be used for the discriminators considered herein. It is worth noting that computing the MP-induced code tracking error envelope (CTEE) is equivalent to finding the point, where the discriminator output crosses the origin because it represents the point where the DLL will lock. It is obvious that both the finite-bandwidth filter and the correlator spacing have an influence on the envelope. So, a large correlator spacing will result in a greater susceptibility of the tracking loop with respect to MP. Usually, a narrow finite-bandwidth filter will tend to increase the MP-induced error envelope. Thus, the GNSS positioning accuracy requires a rigorous choice of these two parameters.

In order to demonstrate that our RCMPM method performs better than a single NC, two schemes have been simulated: an NC with 0.1 chip spacing and our RCMPM method. For these simulated schemes, we consider a LOS and single MP signals and a band-limited CF of 20 MHz. The errors are computed versus MP signal that has amplitude of 0.5 and a delay that varies from 0 to 1.5 chips with respect to the LOS. The MP error envelopes are calculated at the maximum points when the MP signal is at

Code error envelope of NC.

Code error envelope (RCMPM-Galileo and NC-Galileo).

Multiple correlator sampling of the CF.

Block diagram of the bank of correlators.

As illustrated in Figure

An efficient method for the detection and mitigation of MP signals is proposed in this paper. This method is derived from the VMM technique [

The samples of the CCF of both C/A-GPS and BOC(1, 1)-Galileo which are obtained by the use of the bank of correlators are shown in Figure

In fact, we use the bank of correlators to calculate the CCF. The block diagram of the bank of correlators is shown in Figure

The received signal is correlated with a number of correlators to get samples of the input correlation function