International Journal of Navigation and Observation

Volume 2015, Article ID 983124, 16 pages

http://dx.doi.org/10.1155/2015/983124

## A Ray-Tracing Technique to Characterize GPS Multipath in the Frequency Domain

^{1}Position, Location and Navigation (PLAN) Group, University of Calgary, Calgary, AB, Canada T2N 1N4^{2}European Commission, Joint Research Center, 21027 Ispra, Italy

Received 22 May 2015; Revised 24 August 2015; Accepted 6 September 2015

Academic Editor: David Akopian

Copyright © 2015 Naveen S. Gowdayyanadoddi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multipath propagation is one of the major sources of error in GPS measurements. In this research, a ray-tracing technique is proposed to study the frequency domain characteristics of multipath propagation. The Doppler frequency difference, also known as multipath phase rate and fading frequency, between direct (line-of-sight, LOS) and reflected (non-line-of-sight, NLOS) signals is studied as a function of satellite elevation and azimuth, as well as distance between the reflector and the static receiver. The accuracy of the method is verified with measured Doppler differences from real data collected in a downtown environment. The use of ray-tracing derived predicted Doppler differences in a receiver, as a means of alleviating the multipath induced errors in the measurement, is presented and discussed.

#### 1. Introduction

Ever increasing Global Navigation Satellite System (GNSS) based applications require reliable and accurate navigation solutions in challenging environments such as cities and indoors. In such environments, receiver accuracy and reliability are limited by signal shadowing, blockage, and multipath. These factors lead to increased position errors. Signal shadowing, where the signal is present but attenuated, leads to poor acquisition and tracking performance, while complete signal blockage leads to increased dilution of precision, and, finally, multipath leads to poor measurement accuracy and fading. These challenges and some solutions are discussed in [1–6], for instance. Multipath is one of the major error sources and is a function of the type and number of reflectors in the receiver environment [6]. Many methods have been proposed to alleviate the effects of code multipath by employing various discriminators such as the narrow correlator, the strobe correlator, replica waveform (Double Delta) correlator, and parametric multipath estimation methods such as the multipath estimating delay lock loop (MEDLL) [7, 8]. These methods work on the code (delay) domain and do not completely remove multipath errors and are limited by the radio frequency (RF) signal bandwidth of the GNSS front-end as discussed in [7]. The first two methods work on the composite autocorrelation triangle, the combination of direct, or line-of-sight, (LOS), and reflected, or non-line-of-sight, (NLOS) signals to reduce the errors induced into the measurements; therefore it is not possible to separate direct and reflected signals. The MEDLL attempts to estimate the delay, amplitude, and phase of all reflected signals but it becomes computationally intensive as the number of assumed reflected signals increases [8]. There are methods in the literature to increase the processing speed of correlation, for example, Synthetic Multicorrelators [9] which could be used in relatively open-sky conditions where integration time periods are small. However, other than the computational load, it is difficult to estimate the number of reflected signals in a given environment. The efficiency of these methods also depends on the received signal power, which is greatly affected in such environments, and on the code delay resolution, which is a function of the RF signal bandwidth [7]. Therefore, it is necessary to further understand the characteristics of multipath signals to design more effective multipath mitigating techniques.

Multipath propagation is examined here in the frequency domain. The separation of direct and reflected signals in that domain is studied in [10, 11]. The advantages of the frequency domain approach are that it may separate or* resolve* the direct and multiple reflected signals and allows one to estimate the power, delay, and phase of each reflected signal independently. The degree of separation depends, other than the actual direct-reflected Doppler difference, on the attainable frequency resolution which, in turn, depends on the coherent integration period and receiver motion. Compared to code delay resolution, the frequency resolution is independent of the RF signal bandwidth. The maximum practical integration period is limited by the relative dynamics of the receiver, amongst other factors [12]. With aiding, the effect of relative dynamics can be compensated and then the main challenge is the requirement for a precise oscillator to overcome the oscillator instability affecting the coherent integration period [12–16].

The use of precise oscillators is limited due to cost, size, and power consumption at this time. Hence, there is not much study of multipath characterization done in the frequency domain. There is hope that the development of Chip Scale Atomic Clocks (CSAC) and nano-/microclocks [17] may lead to next generation oscillators which will alleviate cost, size, and power consumption issues. This hope motivates further research in the frequency domain.

In the kinematic case, the Doppler spread of the reflected signals in urban canyons is studied in [10] and it was shown that with a maximum vehicle speed of ~15 m/s the Doppler frequency difference () between the direct and reflected signals was spread between ±40 Hz considering the extreme cases when the direct signal vector is both parallel and orthogonal to the velocity vector of the vehicle. By introducing slow movement in the antenna, in an indoor scenario the frequency separation between direct and reflected signals is increased to improve position accuracy [11]. Due to the variety of possible multipath environments, it is not practically possible to collect and process data in all such scenarios. Hence, extensive studies of reflected signals in the frequency domain using real signals are limited.

Nievinski and Larson [18] list and classify a number of multipath simulation techniques. Eissfeller and Winkel [19] and Franchois and Roelens [20] describe a mathematical model for multipath and discuss numerical results with respect to pseudorange errors. Weiss et al. [21] discuss a GNSS code multipath model for semiurban, aircraft, and ship environments using the ray-tracing technique and present a comparison of simulated and real data results with focus on pseudorange error occurrence, multipath temporal variability, and amplitude. Lau and Cross [22] present a ray-tracing approach to study carrier-phase multipath effects. Irsigler [23] uses a multiray signal model to characterize the Doppler frequency difference in static multipath environments and presents the simulation results discussing the distribution of Doppler frequency for a static antenna scenario for multiple reflector cases. Not much focus is given on using the ray-tracing based technique to study Doppler frequency differences. The ray-tracing technique facilitates accurate simulation of reflected signals in an urban environment using an urban city model [21]. As reported by Irsigler [23], Doppler frequency differences are very small and therefore a standard receiver cannot resolve them in its tracking loops.

This research proposes a method using the ray-tracing methodology to study the between direct and reflected signals in a static receiver with a single static, specular reflector. Using real data collected in a location surrounded by buildings with an ultrastable oscillator to allow for a long coherent integration period, separation of direct and reflected signals in the frequency domain is demonstrated. Ray-tracing has been used for various applications such as evaluating GPS indoor positioning performance [24], modeling code multipath in urban environments using city models [25], developing a hardware emulator to test the effects of multipath on wireless positioning system [26], and improving GPS positioning performance in urban canyons using 3D city models [27]. The proposed method can also be extended to analyze multipath characteristics in an environment where the receiver is moving and the environment consists of multiple reflectors. In a moving case, as shown in [10], receiver velocity greatly influences the frequency characteristics of the multipath signals.

The concept of separating, or resolving, the composite signal is described in Section 2. The assumptions used in this research are discussed in Section 3. The mathematical expression for the between direct and reflected signals is described in Section 4. The theoretical development of the ray-tracing method based computation is presented in Section 5. Simulation results from the developed method for a static case are presented and analyzed in Section 6. Based on the simulation results from the proposed model, real data from a city environment scenario is processed to verify whether or not the static multipath can be resolved in the frequency domain and the corresponding procedure and the results are discussed in Sections 7 and 8. Potential applications of ray-tracing based Doppler difference computation in static positioning are described in Section 9.

#### 2. Resolving Direct and Reflected Signals in the Frequency Domain

As shown by Irsigler [23] even in the static case there is a nonzero Doppler difference between direct and reflected signals that will be a few tens of millihertz. Because the direct and reflected signals arrive at the receiver with small Doppler differences, the autocorrelation function (ACF) of the PRN code computed with a small coherent integration period will be a sum of the ACF of the direct and the reflected signal. The receiver will observe two ACFs with different delays overlapping with each other, resulting in a distorted ACF. To illustrate this, a dataset collected in a city core location surrounded by buildings is used and a cross-ambiguity-function (CAF), also known as Delay-Doppler Map (DDM), was generated for one PRN (PRN 14) using 10 s of coherent integration time. The code and frequency domain views of this CAF are shown in Figure 1 (top subplots). As can be seen, the ACF, is slightly distorted. The frequency domain view, at 0.15 Hz, indicates slight separation of the signals but this is not significant enough to resolve signals with varying delays. This can also be observed in the contour plot, top-view of the CAF, with a coherent integration time of 10 s (Figure 2, top subplot). When the coherent integration time is increased to 120 s, which provides a frequency resolution of 8.3 mHz (1/120 s), multiple peaks are observed in the frequency domain (Figure 1, bottom right subplot) indicating the presence of one or more components in the frequency domain and from the corresponding code domain, it can be observed that there are at least two dominant ACFs with different delays, one at 0 m and the other at −60 m. This is clearly depicted in the contour plot, the bottom subplot in Figure 2, where the zero delay ACF corresponds to a Doppler of 45 mHz and the −60 m delay ACF corresponds to a Doppler of 105 mHz. Hence, with long coherent integration time periods, it is possible to resolve the composite direct and reflected signal into its constituent components. However, this will not directly identify which of the resolved components is a direct signal component and which are reflected signals.