Characterization and mitigation of multipath fading on multi-frequency GNSS signals in urban environment

Abstract

The global navigation satellite systems (GNSS) receiver is likely to experience performance degradation in the presence of multipath interferences in indoor and urban canyon environments. There will be multiple reflected signals arriving at the receiver antenna from different paths and directions regarding the different locations of the nearby constructions, causing significant fluctuations and distortions on the amplitude and phase of the direct signals. This is the so-called multipath fading effects and usually exhibit with the random features of temporal, spatial, and frequency diversity across the signal bands. To have a better understanding of the multipath fading effects, a live test was conducted near Lujiazui CBD area in Shanghai. The collected data were processed to characterize the signal attenuations and phase fluctuations on multi-frequency GNSS signals via the detrend code delay, carrier phase, and navigation bit errors. The resulting scintillation index on amplitude, code delay, and carrier phase, e.g., S₄, ${\sigma }_{\varphi }$ and ${\sigma }_{\tau }$ can be calculated. Based on these multipath features, the inter-frequency aiding strategy will be utilized for the multipath mitigations in the multi-frequency tracking loop design. The results demonstrate the effectiveness of the multi-frequency tracking algorithm in the urban environment.

1 Introduction

With the development of the global navigation satellite system (GNSS), the widespread applications of the high precision navigation terminal will become a reality. However, the performance of the GNSS receiver will be severely compromised in challenging environments, such as indoor, urban canyons, boulevard, and tunnels. Multiple reflected signals arrived at the receiver antenna from different paths and directions regarding the different locations of the nearby constructions, causing significant fluctuations and distortions on the amplitude and phase of the direct signals. In some extreme cases, the line-of-signal (LOS) signals will be completely blocked. Only non-line-of-sight (NLOS) reception is available. All these factors, i.e., signal interruption, NLOS, and multipath can refer to the so-called multipath fading or shadowing effects and usually exhibit the random features of temporal, spatial, and frequency diversity across the signal bands. More importantly, these effects can introduce code and carrier tracking errors, leading to cycle slips or loss of lock, and in turn degrading GNSS positioning accuracy and robustness.

A lot of effort has been devoted to characterize, detect, and mitigate the multipath effects. Bellad et al. [1] found that in some urban scenarios, the LOS signal is weaker than the composite multipath signal. They characterized the distortions in the GNSS signal correlation peak due to multipath and proposed a novel method to separate LOS and multipath signals under static and low dynamic conditions. Xie et al. [2] characterized the multipath distributions in urban canyon environments and identified the LOS and multipath signal components from the correlation map with long coherent integration. Strode et al. [3] developed a GNSS multipath detector using three-frequency signal-to-noise measurements. Wang et al. [4] built a signal feature vector including mean and standard deviation, blockage coefficient, geometric dilution of precision (GDOP) expansion ratio, and strength fluctuation to characterize different environmental interferences. They utilized the support vector machine (SVM) algorithm to recognize the urban environment type. Guermah et al. [5] have developed a machine learning algorithm to classify the LOS, NLOS, and multipath signals based on the fusion of information provided by right-handed circularly polarized (RHCP) and left-handed circularly polarized (LHCP) antennas. Quan [6] also developed a machine learning-based multipath detector by investigating the double difference (DD) carrier phase residuals from all available signals of multi-GNSS (GPS, GLONASS, Galileo, BDS, and QZSS). Chen et al. [7] investigated and compared three known multipath mitigation methods, i.e., coupled amplitude delay lock loops (CADLL), high-resolution correlator (HRC), and multipath mitigation technique (MMT) and found that CADLL is superior to other methods. To improve the positioning accuracy in the urban environment, some advanced multi-sensor fusion technologies have been developed to aid GNSS receiver for mitigation on multipath interruptions. For example, Suzuki et al. [8] proposed a method to directly estimate GNSS satellite visibility using Google Earth based on so-called virtual fish-eye sky image generation. Wang et al. [9] utilized a shadow matching approach on an Android smartphone and presented better performance over the conventional GNSS positioning in the cross-street direction with a 5 m cross-street position accuracy. Gu et al. [10, 11] integrated the inertial sensor and 3D city map to separate the LOS and NLOS signals and realized a lane-level vehicle self-localization in dense urban canyon.

The existing approaches for multipath characterization, classification, and mitigation highly relay on the accurate multipath features. The widely used indicators, e.g., GDOP, C/N₀, and elevations in the current studies, are oversimplified. It is known that with the development of modernized GNSS, there will be more satellites and more signals available to provide high-accuracy navigation services. Due to the difference on signal bands, modulations, and structures, the GNSS signals will exhibit inconsistent characteristics in the urban environment. The characterization of the multipath fading effects on each frequency is necessary to facilitate the detection and mitigation of the multipath interferences. Different from the existing methods, the signal fluctuation index S₄, $\sigma_{\varphi }$, and $\sigma_{\tau }$ are introduced in this paper to characterize the multipath effects on the signal amplitude, carrier phase, and code delay. The amplitude fluctuation S₄ and carrier fluctuation $\sigma_{\varphi }$ were originally adopted in ionosphere scintillation studies [12,13]. The reason for doing so is that they are good measures to indicate the fast fluctuations on the signal intensity and phase and the ionosphere scintillations are the refraction and/or diffraction phenomenon caused by the irregular structures, which is very similar to the multipath effects. Therefore, these indicators can be used for fast-varying multipath characterization, e.g., the selective fading channels in the urban canyon. Considering that the multipath effects have a strong impact on the code tracking performance, we use $\sigma_{\tau }$ to represent the code delay fluctuations in the urban environments. Then based on the realistic signal characteristics, the multi-frequency tracking will be used to mitigate the multipath errors.

The organization of the paper is as follows. Section 2 describes the methodology and urban experiment setup. Section 3 characterizes the multipath features, including the fluctuations on the signal strength, carrier phase, code delay measurements, etc. Section 4 presents the multipath mitigation performance with inter-frequency aiding technique. Section 5 concludes the paper.

2 Methodology description and data collection

In this section, the methodology adopted in the analysis will be introduced, including the calculation of S₄, $\sigma_{\varphi }$, and $\sigma_{\tau }$. Then the data collection system and the experiment setup will be given.

2.1 Methodology description

Typically during the GNSS signal propagation, the received measurements contain several components, e.g., relative receiver-satellite dynamics, ionosphere delay, troposphere delay, multipath, receiver and satellite clock errors, thermal noise, and platform vibrations. For the users in high latitude and equatorial regions, the ionosphere scintillations will be a serious problem to the receiver. However, in the urban environment, the multipath will be the dominant error source. To characterize the multipath effects, we need to remove the other components via a detrending process. Then the fluctuation index can be calculated according to the detrended measurements. Note that the detrending process is based on the assumption that the multipath-induced scintillations or fluctuations are much more rapid and intense than the other error components. This assumption is only applicable to the kinetic measurements in urban environment, but not suitable for the static condition where the multipath variation is much slower than the dynamic case.

There are several detrending methods used in the literature: Butterworth (BW) filtering [14], polynomial fitting [13], continuous wavelet transform (CWT) filtering [15], and discrete wavelet transform (DWT) [12]. In this paper, the BW filtering method is adopted to separate multipath scintillations from other slowly varying trends in the receiver measurements.

• 1. Signal intensity and amplitude fluctuation index S₄

The signal intensity (SI) can be obtained from the correlation values in in-phase (I) channel and quadrature (Q) channel from the receiver baseband tracking loop outputs [14, 16]:

$${\text{WBP}}_{k} = \mathop \sum \limits_{{20 \times \left( {k - 1} \right) + 1}}^{20 \times k} [(I_{i}^{{}} )^{2} + (Q_{i}^{{}} )^{2} ],$$

(1)

$${\text{NBP}}_{k} = \left( {\mathop \sum \limits_{{20 \times \left( {k - 1} \right) + 1}}^{20 \times k} I_{i}^{{}} } \right)^{2} + \left( {\mathop \sum \limits_{{20 \times \left( {k - 1} \right) + 1}}^{20 \times k} Q_{i}^{{}} } \right)^{2} ,$$

(2)

$${\text{SI}}_{{{\text{raw}},k}} = {\text{NBP}}_{k} - {\text{WBP}}_{k} ,$$

(3)

$${\text{SI}}_{{{\text{norm}},k}} = 10 \times {\log}10\left( {\frac{{SI_{{{\text{raw}},k}} }}{{SI_{{{\text{trend}},k}} }}} \right),$$

(4)

where WBP and NBP represent the wide band power and narrow band power, respectively. i denotes the coherent integration interval number and k denotes the navigation bit number. SI_raw denotes the raw signal intensity and can be obtained as (3). The low-frequency trend SI_trend is estimated by a sixth-order BW high-pass filter with 0.1 Hz cutoff frequency, the same value as in Van Dierendonck et al. [14]. Then the raw intensity SI_raw is normalized by the trend SI_trend to form the normalized signal intensity SI_norm in (4).

The S₄ index can then be computed as follows [14]:

$$S_{4} = \sqrt {\frac{{\left\langle {{\text{SI}}_{{{\text{norm}}}}^{2} } \right\rangle - \langle {\text{SI}}_{{{\text{norm}}}} \rangle^{2} }}{{\langle {\text{SI}}_{{{\text{norm}}}} \rangle^{2} }}} ,$$

(5)

where <·> represents the averaging operation over the interval of interest [16]. A moving window with length of 10 s is used to obtain the value of $S_{4}$ in each second.

• 2. Detrended phase and carrier phase fluctuation index $\sigma_{\varphi }$

The carrier phase estimations from the carrier tracking loop output are taken as the original measurements for phase detrending process. Similarly, the sixth-order BW high-pass filter with cutoff frequency at 0.1 Hz is used to detrend the carrier phases $\varphi$. Then given the detrended phase $\varphi_{{{\text{detrend}}}}$, the std of $\varphi_{{{\text{detrend}}}}$ can be obtained as [13]):

$$\sigma_{\varphi } = \sqrt {\left\langle {\varphi_{{{\text{detrend}}}}^{2} } \right\rangle - \langle \varphi_{{{\text{detrend}}}} \rangle^{2} } ,$$

(6)

where <·> represents the moving averaging operation over the interval of interest [16]. The moving window size relates to the phase measurement rate, such as 50–100 Hz, which corresponds to the integration time range as 10–20 ms.

• 3. Detrended code delay and code delay fluctuation index $\sigma_{\tau }$

It is known that the multipath effects have a strong impact on the code tracking performance. We take the code delay $\tau$ estimated from the code tracking loop as the input to the detrending process. Again, the sixth-order BW high-pass filter with cutoff frequency at 0.1 Hz is adopted to detrend the code delay sequence ${ }\tau$. Therefore, the detrended code delay $\tau_{{{\text{detrend}}}}$ can be obtained. Then the std of $\tau_{{{\text{detrend}}}}$ can be calculated as:

$$\sigma_{\tau } = \sqrt {\left\langle {\tau_{{{\text{detrend}}}}^{2} } \right\rangle - \langle \tau_{{{\text{detrend}}}} \rangle^{2} } ,$$

(7)

where <·> represents the moving averaging operation. The moving window size relates to the code measurement rate, such as 50–1000 Hz, which corresponds to the integration time range as 1–20 ms.

2.2 Data collection system and experiment setup

To capture the multipath disturbance features, a vehicular field test in dense urban canyons near Lujiazui CBD in Shanghai was conducted. The field test was performed on Jan 12, 2020. The data collection system concludes a high gain antenna and a data collection radio front end. As can be seen in Fig. 1, the antenna is placed on the top of the vehicular. It is an AT340 full band geodetic antenna with about 40 dB gain produced by ComNav Technology Ltd (https://www.comnavtech.com/AT340.html). The front end is LabSat Wideband-3. It is a configurable device controlled by the software interface in PC or laptop. It can support multi-frequency and multi-constellation intermediate frequency (IF) data collection. The real sample and complex sample patterns are according to the user configuration. In this study, the GPS triple-frequency (L1/L2/L5) complex data are collected with configuration of 0 Hz IF, 30.69 MHz sampling rate, and 2-bit quantization.

Fig. 1

Land vehicle with data collection system for field test. a GNSS Geodetic Antenna AT340. b LabSat Wideband-3 hardware and software

The self-developed software receiver is used to process the IF data. The positioning results are shown in Fig. 2. It can be seen that we drove along the Pudong South Road toward the north until the cross to the Binjiang Road. Then we drove along the East Garden Road, Lujiazui Ring Road, Yincheng Middle Road and d toward the west in the end. The overall drive time was about 11 min. As can be seen in Fig. 2, there are dense skyscrapers in this area and the received signals will be strongly disturbed by the NLOS signals, and in some cases the signals can be completely blocked by these buildings. To have a better understanding of the signal reception environment, the drive path is divided into each minute segment and plotted in geodetic coordinate as shown in Fig. 3a. The visible satellite spatial distribution is plotted in Fig. 3b. There are nine GPS satellite visible during the driving. The satellites that are capable of broadcasting triple-frequency signals are marked in blue color. The rest are shown in black color in Fig. 3b.

Fig. 2

Drive trajectory near Lujiazui CBD on Google map

Fig. 3

a Drive path on the geodetic coordinate, b sky plot

Taking GPS L1 signals as an illustration, it can be seen in Fig. 4 that all the signal strengths are disturbed during the field test. With the different receiver-satellite relative geometry and the nearby buildings’ locations, these signals exhibit the random temporal features. For example, PRN #8 and PRN #27 are located in the similar azimuth zone toward the south direction relative to the receiver. However, in the first 6 min, the signals from PRN #8 are completely blocked by the tall buildings, while the signals from PRN #27 are available during the entire test. It is probably because the elevation of PRN#27 is over 60°, which is about 30° higher than PRN#8. However, PRN#27 showed a severe attenuation during 7–8 min. Combining the corresponding drive segment, the sky plot, and the Google Map in Figs. 2 and 3, the signals during this time interval are probably blocked and reflected by the buildings on both sides.

Fig. 4

Signal C/N₀ of the visible satellite during the field test

3 Multipath characterization

There are four satellites, i.e., PRN#8, #9, #26, and #27, which carry triple-frequency signals. We pick PRN#27 as an illustration because it has the highest elevation angles and therefore should have the least signal blockage as compared to the other three satellites. The signal C/N₀ on PRN#27 L1, L2, and L5 are plotted in Fig. 5. It shows that L5 has the strongest signal strength, while L2 is generally 20 dB weaker than the L1 and L5. The attenuation on L2 is probably caused by hardware issues. To avoid the contamination from abnormal measurements on L2, the signal effects on L1 and L5 are only characterized in this study. If we look into the variation pattern of L1 and L5, it can be found that although these two signals’ strengths dropped occasionally, there are difference on their attenuation durations and behaviors. For example, L5 is over 10 dB stronger than L1 in the first 1 min, showing that L1 has obvious multipath fading effects. Since L5 has a higher code rate which is ten times over the L1 signals, L5 should have better anti-multipath capability. However, during 7–8 min, the L5 signal is almost 10 dB weaker than L1, demonstrating the frequency diversity features in the presence of the signal blockage and NLOS event.

Fig. 5

Signal C/N₀ on PRN#27 L1, L2, and L5 during the field test

The correlation values in I and Q channels on L1 and L5 are obtained to calculate the normalized signal intensity as well as amplitude fluctuation index S₄ according to the calculation method described in Sect. 2.1. As shown in Fig. 6, the ${\text{SI}}_{{{\text{norm}}}}$ plots confirm that L1 experienced severe multipath interferences within the 1 min. During the 7–8 min, there was an enhancement on L1 and L5, indicating that the scattering and reflection caused defocus and refocus transformations. Intense multipath fading presented on the GPS signals in the urban environment. Most of the attenuations are over 20 dB, and in some extreme cases, the fading is over 40 dB. The corresponding index S₄ plots show that the PRN #27 signals suffered strong amplitude fluctuations at around 0.5–1, 2–3, 4–5, and 7–8 min. The S₄ values in these intervals are larger than 1. For the rest of the time interval, the average S₄ value is at 0.2 level below, which corresponds to the typical index value in nominal thermal noise conditions.

Fig. 6

${\text{SI}}_{{{\text{norm}}}}$ and S₄ on PRN#27 L1 and L5 during the field test

The detrended carrier phase $\varphi_{{{\text{detrend}}}}$ and detrended code delay $\tau_{{{\text{detrend}}}}$ are calculated by using the sixth-order BW filter as described in Sect. 2.1. After that, the std of carrier phase and code delay, i.e., $\sigma_{\varphi }$ and $\sigma_{\tau }$, are estimated as well. Note that the original carrier and code measurements are obtained from 10 ms integration in carrier and code tracking. The corresponding results are displayed in Figs. 7 and 8, respectively. Figure 7 shows that most of the multipath-induced errors are within ± 120°, which may cause half cycle slip in carrier signal tracking, except that between 1 and 2 min, the phase transition on L1 exceeded a full cycle but L5 had a relatively small phase error below 60°. The $\sigma_{\varphi }$ plot shows that the phase error deviation exceeded 30° when the multipath fading occurred. This is the tracking threshold of a four-quadrant arctangent discriminator which is applicable to the pilot signal carrier tracking, e.g., L5Q. For a two-quadrant arctangent discriminator used in L1 carrier tracking, the threshold value is decreased to 15 degrees. Therefore, the GNSS carrier tracking on either L1 or L5 are all fragile to lose lock in the urban environment. Long integration time strategy and multipath mitigation algorithms should be adopted to improve the receiver’s robustness.

Fig. 7

$\varphi_{{{\text{detrend}}}}$ and $\sigma_{\varphi }$ on PRN#27 L1 and L5 during the field test

Fig. 8

$\tau_{{{\text{detrend}}}}$ and $\sigma_{\tau }$ on PRN#27 L1 and L5 during the field test

The code delay variations in Fig. 8 are consistent with the carrier trends in Fig. 7 as well as multipath fadings in Fig. 6. The large errors are associated with the deep amplitude fadings. The code delay error is equivalent to the pseudorange measurement accuracy, which determines the navigation performance. It can be seen that the general code delay errors are within ± 50 cm, which identify with the pseudorange measurement accuracy requirements in the commercial receivers under the nominal conditions. However, the code delay errors exceed ± 2 m when the multipath occurred. The code delay fluctuation $\sigma_{\tau }$ shows that L5 performance is not as good as expected, because there are no obvious difference between L1 and L5 code delay errors, indicating that in the presence of severe multipath interference, the positioning errors will be over several meters even with L5 observations.

The navigation bit decoding error is an important indicator to measure the receiver performance in the urban environment. The receiver requires the measurements from at least four visible satellites to fix the navigation solutions. Each satellite should have at least its first three subframes to be successfully decoded from the correlation output. Each subframe contains 300 bits with 20 ms for each bit, which means the receiver requires at least 18 s to realize the initial localization in cold start mode. However, in the urban environment, the initialization time will increase due to the signal blockage, NLOS and multipath interferences. To have a direct vision, the L5Q measurements are used to illustrate the phase transition and the bit decoding error in the presence of the multipath effects, since L5Q is a pure pilot signal without navigation message modulation. The correlation on I channel of the L5Q signals should keep positive when the signal tracking loop is locked. However, due to the multipath fading effects, there will be phase transitions and correlation values on I channel will turn negative, as shown in Fig. 9. Meanwhile, the data signal on L5I will also experience phase transitions, which brings the data bit decoding errors. The averaged bit errors rate is calculated within each 6 s time interval and the statistical results are plotted in Fig. 10. We can see that the maximum bit errors can reach 95% from 1 to 2 min. This is the reason why we only obtain the positioning results after first 2 min in Figs. 3 and 4.

Fig. 9

I and Q correlation values on PRN#27 L5Q during the field test

Fig. 10

Bit decoding error percentage per sub frame on PRN#27 L5 during the field test

4 Multipath mitigation

Based on the previous analysis, we intend to use the multi-frequency tracking (MT) algorithm to perform inter-frequency aiding from uncompensated signals to the interfered signals and mitigate the strong amplitude attenuations. This MT algorithm has been investigated in our recent work [17, 18]. Therefore, only a brief summary is presented here. Figure 11 shows the state vector on each frequency ${\varvec{x}}_{Li}$ including the code delay $\tau$, carrier phase $\varphi$, Doppler $f_{{\text{d}}}$, and Doppler rate $f_{{\text{d}}}$. The measurements are obtained from the discriminator outputs, e.g., code error $\Delta \tau$, carrier phase error $\Delta \varphi$ and Doppler error $\Delta f_{{\text{d}}}$. Given the state vector ${\varvec{x}}_{Li}$, the corresponding system model and measurement model can be built with incorporation of clock noise and thermal noise models. The Kalman filter can be designed and implemented based on the signal models on each frequency. This is the so-called single frequency tracking (ST) algorithm. Since the multi-carrier signals carry the same range information, the state vector on each frequency ${\varvec{x}}_{Li}$ can be associated via the corresponding frequency dependency relation. Then virtual reference signal can be constructed to link the multi-frequency signals. The corresponding state vector, measurement, as well as signal models can be obtained by mapping the real signal into the reference plane as shown in the right part of Fig. 11. Therefore, a joint filter can be designed with respect to the virtual signal models. This is the fundamental of MT algorithm design. More details can be found in Yang [17, 18]. In this study, we alter the MT algorithm to a dual-frequency tracking version for L1 and L5 joint tracking due to the hardware issues on L2.

Fig. 11

The signal models in single-frequency tracking (ST) and multi-frequency tracking (MT)

The L1 and L5 Doppler tracking results from ST and MT outputs are plotted in Fig. 12. It shows that the Doppler fluctuations caused by the multipath fading effects are mitigated by using the inter-frequency aiding strategy in the MT implementation than the conventional ST method. For example, a 20 Hz Doppler error on L5 is removed with the aid of L1 measurement within 7–8 min.

Fig. 12

Doppler tracking results on PRN #27 L1 and L5 with ST and MT modes

5 Conclusion

This paper introduced several indices including amplitude fluctuation index S₄, carrier phase fluctuation index $\sigma_{\varphi }$, and code delay fluctuation index $\sigma_{\tau }$ to characterize the multipath effects across the signal bands in the dense urban environment. The index calculation as well as detrending methodology is described. The live data collected from the road test near Lujiazui CBD area in Shanghai are analyzed with the proposed characterization indicators. In addition, the preliminary investigation of the navigation bit decoding errors in the urban environment is also given. The results show that in some extreme cases, there will be over 40 dB signal attenuation and the multipath-induced carrier phase and code errors are over 120 degrees and 2 m, respectively. In addition, the maximum bit decoding errors can be up to 95%. To improve the tracking performance in the presence of severe multipath fading, the multi-frequency tracking (MT) algorithm is applied. The results demonstrated that over 20 Hz Doppler fluctuations can be mitigated by using the inter-frequency aiding strategy in the MT implementation than the conventional ST method.

However, due to the hardware issues, the L2 collected data are 20 dB weaker than the L1 and L5 signals. To avoid the contamination from the abnormal measurements on L2, the signal effects on L1 and L5 were characterized in this study. In future, this issue should be fixed, and more field tests will be conducted to further investigate the multipath characterization and mitigation technology.