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Multipath is one of the most important sources of positioning error in GNSS. Well-designed antennas can mitigate multipath signals and enhance the performance of GNSS receivers. This paper concentrates on methods to assess multipath mitigation performance for GNSS antennas. We propose a model to describe multipath environment in GNSS ground stations. The model analyzes effects caused by inclined reflective surfaces and multipath mitigating algorithms in receivers. A method to assess multipath mitigation performance is put forward by analyzing pseudorange code phase errors caused by multipath signals after signal processing. Based on the model and method, principles in site selection for GNSS antenna are introduced to minimize effects caused by multipath.

Global Navigation Satellite System (GNSS) plays a significant role in military, industry, and civil field. In GNSS the precision of pseudorange measurement is highlighted in most applications. Pseudorange error has impact on both availability and integrity of navigation and positioning. Among all the factors that may cause pseudorange error, multipath is one of the factors that cannot be compensated for by observations provided by monitoring data [

Because the model of multipath signal is an important reference to multipath mitigation, it should be studied first. Pattern of multipath signals in different multipath environments was studied in [

To mitigate multipath signals in signal processing stage, many algorithms were proposed. The narrow correlator spacing method [

Algorithms mentioned above focus on signal processing in receivers and provide general conclusions of multipath mitigation performance. Every method has disadvantages in multipath mitigation or accessibility. Meanwhile multipath mitigation provided by antenna is ignored. Effect of multipath mitigation antenna can be a reinforcement for multipath mitigation.

The most widespread method to evaluate the performance of multipath mitigation for antennas is the front-to-rear ratio [

Hence it is necessary to develop an accurate assessment method for antennas. This paper concentrates on antennas sited at ground stations. A model of multipath environment in ground station is provided and assessment method for antennas is developed. Data measured from real antennas is adopted to demonstrate the assessment method and the dependence of site selection.

The rest of this paper is organized as follows. In Section

In this section, an antenna located at the center of a semiopen land is discussed. Semiopen land refers to an area with no inclined mirror reflective surface within a radius range of

This figure shows how multipath signal is produced. Multipath signals are mainly produced by two kinds of reflective surfaces: horizontal surfaces and inclined surfaces. Elevation angles of multipath signals caused by horizontal surfaces equal to negative elevation angles of direct signals. Elevation angles of multipath signals caused by inclined surfaces depend on both the elevation angles of direct signals and the dip angles of the surfaces.

Propagation delay of the multipath signal is related to the difference in path length between direct signal and its multipath replica. Difference in path length can be calculated via geometry in Figure

When dip angle

While the width of the pseudo-random noise code (PRN code) correlation peak is the same as the chip width

Since dip angles

Let

Propagation time delays of multipath signals can be demonstrated in Figure

In this figure, the height

Under the environment of GNSS monitoring station, elevation angles of multipath signals are restricted. There are only multipath signals with elevation angles larger than

In this section, effects of multipath mitigation algorithms deployed in receivers are analyzed. Double-delta algorithm is picked up as an example. Principles of the algorithm will not be discussed in this paper. Detailed process of derivation has been shown in [

The direct signal can be represented by

In this case, signals in receivers can be represented as a combination of direct signals and multipath signals.

This figure shows the structure and the performance of the double-delta algorithm. (a) is the assignment of two pairs of correlators in double-delta algorithm. (b) is a plot of (

It can be found in Figure

Double-delta algorithm can effectively mitigate PPE caused by multipath signal when multipath delay meets the condition that

At horizontal surfaces

Therefore, Figure

In this figure, the chip width

Model of multipath signal in GNSS monitoring station has been discussed in Section

While the installation height

Assuming that

Analytical calculations of

Radiation patterns of practical antennas are measured and displayed in Figure

In this figure, all of the data is measured in an anechoic chamber. Elevation angles ranged

This photo is the two antennas used in the test. The left one is a chocking ring antenna designed and manufactured by Ashtech. The right one is a Trimble ZEPHYR™-Model 2 antenna.

It was mentioned in [

Multipath signals are mainly caused by a reflection form air to soiled materials. Shift in polarization model can be calculated by (

In this figure the relative permittivity

We use tolerance of the PPE to evaluate multipath mitigation performance of antennas. The tolerance denotes the maximum PRN code phase error that is acceptable. For a fixed tolerance, there is a range of elevation angle. Within this range, PPE at any elevation angles are below the tolerance. This evaluation represents that there would never be a multipath error which is larger than the tolerance within the range. For a fixed tolerance, a better antenna provides a wider elevation angle range. For a fixed elevation angle range a better antenna provides a lower tolerance instead. The tolerance-based indicator is much more intuitive than the legacy front-to-rear ratio approach.

When the tolerance of the maximum PPE

With conclusion in this section, antennas can be designed to match multipath mitigation algorithm. A matched design may be a reinforcement of the multipath mitigation performance of the receiver.

The model of multipath signals at GNSS monitoring station has been analyzed in Section

Heights of antennas mainly influence mitigation performance in multipath signals produced by horizontal reflective surfaces. The PPE in this scenario can be calculated via conclusions in Section

This figure shows how the PPE varies with the antenna height

There are some discontinuities in Figure

Form Figure

This figure shows the variety of the PPE with the satellite elevation angle

An impropriate height may cause a larger error. For a fixed tolerance of maximum or average PPE, the proper range of height can be determined by this method. Detailed phase error diagram with elevation angles can be a reference for the selection of the height

From Figure

The radius of the open area has effects on mitigating multipath signals caused by inclined reflective surfaces. The PPE in this scenario can be calculated via conclusion in Section

This figure shows the variety of

From Figure

We pick double-delta algorithm under BPSK modulation as an example to analyze multipath mitigation in this paper. There are many other algorithms and modulations in GNSS application. In this section, we make a brief of how the proposed assessment method works in other algorithms and modulations.

Besides the double-delta approach, there are many other algorithms for multipath mitigation. The narrow correlator and the early-late slope are also multipath mitigation algorithms applied in receivers. These algorithms are mainly different with the double-delta approach in the expression of PRN code phase error function. For example, (

Hence, the proposed method can also be adopted to help select a proper multipath mitigation algorithm for a certain type of antenna. We can run the proposed assessment for the same antenna under different multipath mitigation algorithms to find the best algorithm to match the radiation pattern of the antenna.

The BOC is adopted in modern GPS signals. Different from BPSK, the primary correlation peak of the BOC signal is more narrow than BPSK. Hence, early-late spacing

Double-delta approach is based on the evaluation of slopes on both sides of the primary correlation peak of the receiving signal. The space between E2 and L2 (

Hence, the proposed method is still available when the multipath mitigation algorithm is available under other modulations.

In this paper, we studied the model of multipath signals in GNSS monitoring stations. The involving of inclined reflective surfaces increases the precision of the multipath model in semiopen areas. The calculation of multipath delay shows that multipath signals will only happen at a specific range of elevation angles. This range can be expressed by a function of signal properties and environment characteristics.

Multipath mitigation algorithms were studied. By deploying multipath mitigation algorithm, certain ranges of multipath signals can be eliminated. This range can be calculated via arguments of the modulation and the algorithm. Thus, specific elevation angles of antennas may be ignored to enhance performance for antenna design.

We calculated the results of two practical antennas. An accurate approach to evaluate the multipath mitigation performance for antennas is proposed. With the method, developers may assess antennas in a precise way.

We simulated different installation sites of antennas. Principles for site selection are introduced based on methods proposed above. Effects of antenna height and semiopen land radius are analyzed. A proper range of both arguments is put forward to optimize the site. With these principles effects caused by multipath can be mitigated.

We also analyze the availability of the proposed method under other algorithms and modulations. The result shows that our method still works under most major algorithms and modulations in GPS applications.

Global Navigation Satellite System

Delay lock loop

The PRN code phase error

Global positioning system

Multipath estimating delay lock loop

Maximal measurement tree

Right-hand circular polarization

Left-hand circular polarization.

The authors declare that there are no conflicts of interest regarding the publication of this paper.