Robust tracking of weak GPS signals in multipath and jamming environments

doi:10.1016/j.sigpro.2009.01.001

Signal Processing

Volume 89, Issue 7, July 2009, Pages 1320-1333

https://doi.org/10.1016/j.sigpro.2009.01.001 Get rights and content

Abstract

In this paper, we address the problem global positioning system (GPS) signals tracking in low signal-to-noise ratio (SNR) and multipath plus interference environments using a two-step approach: a block-averaging pre-processing (BAP) which converts the zero-mean interferences to colored Gaussian noise and a maximum likelihood (ML) based algorithm combined with a whitening transform. We apply the recently proposed BAP technique to improve the SNR. For code tracking with multipath mitigation, we exploit the fact that during a period with no data bit edges, the propagation delay causes only a circular shift to the C/A code block. This allows the decomposition of the averaged data vector into a constant C/A code component plus an undesired signal component. An efficient temporal whitening transform is derived from the sample covariance matrix and applied to suppress strong colored interferers, rendering the ML estimation problem of the multipath parameters tractable. A computationally efficient procedure for solving the complex ML optimization problem is considered using a finite difference maximization technique. By estimating the multipath signals and subtracting their contributions in a sequential scheme, the code synchronization is achieved. The resulting robust ML (RML) tracking procedure is more efficient in mitigating multipath and non-Gaussian interferences. The performance of the developed RML receiver is evaluated through computer simulations to show its superiority over that of narrow correlator and MEDLL approach.

Introduction

It is widely known that the dominant error source in satellite navigation systems is due to the multipath signal propagation [8], [9], [14]. Multipath errors refer to errors in the code-tracking loop due to reception of the direct signal from the satellite and one or more reflections from the ground and objects in the vicinity of the receiver. The respective pseudorange errors are within the tens of meter level and, as such, should be mitigated for high precision positioning. Influence of multipath on the carrier phase is at the centimeter level and is, therefore, negligible relative to code phase errors [5], [17]. For a single antenna receiver, several approaches for code tracking in the presence of multipath have been proposed in recent years [6] , including narrow correlator [33], multipath eliminating technique (MET) [31], multipath estimating delay lock loop (MEDLL) [34], pulse aperture correlator (PAC) [16], vision correlator [11], FIMLA [23] and other techniques that are based on the maximum likelihood (ML) theory [11], [27], [36]. Antenna arrays have also been proposed for multipath mitigation [14], [25]. These techniques differ in their abilities to remove multipath errors, specially at low signal-to-noise ratio (SNR) and/or in the presence of interfering signals. A well-known challenge to existing precision satellite localization approaches is the presence of closely spaced multipath reflections. In addition, most of existing methods are based on the Gaussian noise assumption and, as such, cannot cope with the cases where the global positioning system (GPS) receiver is subject non-Gaussian undesired signals [35]. For these cases, effective, high-resolution, and computationally efficient signal processing tools are required to estimate the parameters of the superimposed signals in GPS receivers. Since MEDLL like receivers are considered to be most effective multipath mitigation methods for GPS positioning [37], the aim of this work is to employ the ML-based approaches for developing a robust maximum-likelihood (RML) algorithm for receiver positioning in multipath and weak signal environments.

In this paper, we consider two useful signal processing techniques for improving GPS synchronization and achieving robustness against weak signal effects and undesired signals [35], [39]. We pre-process the data through block averaging to increase the GPS signal strength [24]. As a block processing technique [10], [18], [38], this scheme enables the acquisition of weak GPS signals. Then, we use the ML approach for signal tracking and multipath mitigation. It is assumed that the received signal has been converted to complex form at baseband, where 50-bps GPS data modulation and Doppler shift have been removed [14]. Block averaging utilizes the replication property of the GPS signal code to reduce the contribution of the colored Gaussian noise interference through the ML delay estimation process. The root square inverse of the estimated covariance matrix acts as a whitening filter that effectively suppresses the strong colored residuals of the undesired signals. The classical estimation problem of superimposed multipath signals in colored noise is efficiently solved by adopting an ML approach, applied to the block-averaged data. The asymptotic Gaussian distribution of the averaged interference and noise term serves to simplify the estimation problem and the development of an alternative parametrization of the GPS signal component which permits the use of computationally efficient techniques for the complex ML optimization task.

The contribution of this work is in the use of the block-averaging pre-processing (BAP) technique to derive a proper signal model for GPS signals tracking in interference and multipath environments. The resulting block-average model is investigated in conjunction with the ML technique. This idea is inspired by the work in [3], where the authors assume that the desired user, in the CDMA context, send a constant during the synchronization period. We adopt the same strategy for the GPS synchronization problem by accumulating and averaging a large number of data blocks during which the C/A code sequence repeats periodically [24]. In [3], a recursive approach based on finite differences was used to optimize the likelihood cost function. We extend this technique to multipath conditions using a sequential procedure for each path parameters estimation.

This paper is organized as follows. The next section describes the general GPS signal model and summarizes the BAP. In Section 3, we develop a block-averaging model with Gaussian distribution, and show that the pre-processing technique reduces the effect of undesired signals to a colored Gaussian noise. A whitening mitigation of the residual colored noise also is discussed. Section 4 addresses the ML time-delay estimation for signal tracking and multipath mitigation. Computer simulations and the conclusions are presented in 5 Performance analysis and simulation results, 6 Conclusion, respectively.

Section snippets

General signal model

In conventional GPS, the received signal in a multipath environment is an $M$ -path model composed of the direct path signal and $(M - 1)$ reflected rays, plus the interference term $J (t)$ , and the Gaussian additive noise $w (t)$ . Each signal path is characterized by its amplitude $A_{k}$ , phase shift relative to the direct signal $φ_{k}$ (i.e. $φ_{1} = 0^{\circ}$ ), and time-delay $τ_{k}$ . All of these parameters are assumed to be constant over the observation period. In the complex form, the received signal is modeled by $r (t) = \sum_{k = 1}^{M} A_{k} s ($

GPS signal processing for robust multipath delay estimation

For simplicity, we ignore the Doppler, phase and data modulation changes over the observation period and we assume that they are being tracked and compensated for by phase lock-loop (PLL) and frequency lock-loop (FLL) [14] or provided by external aid as in assisted GPS [7], [26]. Characterizations of the impact of the phase shifts $φ_{k}$ on direct signal delay ML estimation show that the worst case scenario for delay estimation accuracy is when the direct and reflected signals are in-phase or

Single-path time-delay estimation

With a single-path channel (i.e. $\bar{τ} \equiv τ$ , $S (\bar{τ}) = s (τ)$ and $\bar{α} \equiv α$ ), the ML estimation of $τ$ and $α$ is based on the value of $m_{L}$ maximizing $f_{m_{L} | τ, α} (m_{L} | τ, α)$ with respect to $τ$ and $α$ . The solution of this standard signal parameter estimation in colored Gaussian noise is well known and is given by [30] $\hat{τ} = \arg \max_{τ} \frac{| s^{H} (τ) {\hat{K}}_{L}^{- 1} m_{L} |^{2}}{s^{H} (τ) {\hat{K}}_{L}^{- 1} s (τ)},$ $\hat{α} = \frac{s^{H} (\hat{τ}) {\hat{K}}_{L}^{- 1} m_{L}}{s^{H} (\hat{τ}) {\hat{K}}_{L}^{- 1} s (\hat{τ})} .$ Once the delay estimate $\hat{τ}$ is obtained via Eq. (20), $\hat{α}$ can be immediately computed using Eq. (21). Below, we present a low-complexity

Performance analysis and simulation results

In the majority of the multipath scenarios, the amplitudes of secondary path signals are smaller than that of the direct path. To exploit this fact, we observe through extensive simulations that the performance can be significantly improved by introducing a constraint on the power of the reflected signal to enhance the GPS receiver performance. This constraint is formulated as $20 \log (\frac{A_{1}}{A_{k}}) < 10 dB .$ This means that when the SMR is greater than 10 dB, the influence of the reflected signal can be

Conclusion

To mitigate the multipath effect on the direct line-of-sight time-of-arrival estimation, a RML approach was proposed using the developed block-averaging model. This approach is based on applying a sample mean model to reduce all zero-mean interferers to a colored Gaussian noise effect. This reduction was made possible by utilizing the repetitive structure of the C/A code and a block-averaging technique prior to correlation with the receiver local codes. A whitening processing was then used to

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To illustrate the contribution, and without loss of generality, the example of transient change detection (TCD) is considered in the context of GNSS SQM. This is an application where the propagation conditions may vary quite rapidly, and the user terminal needs to promptly react to detect the presence of deleterious effect such as multipath [12], non-line-of-sight (NLOS) or signal attenuation [13], as well as potential threats such as spoofing [14] and interference attacks [15]. For illustration purposes, we will consider some generic SQM metric exhibiting a simultaneous change in mean and variance when some threat or signal distortion appears.
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These approaches concern the use of multi sensor aided systems, the long integration of the signal, the modeling of the CDMA autocorrelation function alteration in the design of the processings. For example the new processing of multipath and interference signal takes into account the shape distortion of the auto correlation function in the design of the code delay estimate [24,19]. The new aided systems use a vector tracking loop to estimate the delays of the GNSS signal of each satellite with the global navigation solution obtained with or without the integration of external sensors [31,21].
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In general, time–frequency synchronization as well as signal detection is tackled in GPS receivers during the acquisition/detection stage via a parallel search over the binned delay-Doppler space across all the satellite C/A codes [5,6]. In many practical scenarios, signals might arrive at the receiver with multipath components instead of the line of sight (LOS) component [3,6,7]. Constructive and destructive superpositions of randomly delayed and faded replicas, leads to distorted correlation peaks.
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^☆: This work is supported by ONR/NSWCCD under Contract no. N65540-05-C-0028, and in part by NSF, Grant no. EEC-0332490.

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Robust tracking of weak GPS signals in multipath and jamming environments☆

Abstract

Introduction

Section snippets

General signal model

GPS signal processing for robust multipath delay estimation

Single-path time-delay estimation

Performance analysis and simulation results

Conclusion

International Journal of Electronics and Communications

Journal of Digital Signal Processing

Subspace array processing for the suppression of FM jamming in GPS receivers

IEEE Transactions on Aerospace and Electronic Systems

A novel interference suppression scheme for global navigation satellite systems using antenna array

IEEE Journal on Selected Areas in Communications

Maximum-likelihood synchronization of a single user for CDMA communication systems

IEEE Transactions on Communications

GPS receiver architectures and measurements

Proceedings of IEEE

Performance comparison of multipath mitigating receiver architectures

Indoor GPS positioning: challenges and opportunities

Introduction to GPS: The Global Positioning System

GPS receiver block processing

The theory and performance of NovAtel Inc.'s vision correlator

Elements of Signal Detection and Estimation

Performance analysis of narrowband interference rejection techniques in DS spread-spectrum systems

IEEE Transactions on Communications

Block acquisition of weak GPS signals in a software receiver

A simple multipath delay estimator based on alternating projection algorithm