Tracking performance and average error analysis of GPS discriminators in multipath

doi:10.1016/j.sigpro.2009.01.007

Signal Processing

Volume 89, Issue 6, June 2009, Pages 1224-1239

https://doi.org/10.1016/j.sigpro.2009.01.007 Get rights and content

Abstract

Signal multipath in GPS leads to undesirable tracking errors and inaccurate ranging information. The extent of the tracking error in compromising the receiver performance depends on the multipath amplitude, delay, and phase relative to the direct path. The coherent discriminator and the noncoherent early-minus-late power discriminator offer different tracking accuracy and sensitivity to multipath parameters. In this paper, we develop analyses of the effect of multipath carrier phase offset on GPS tracking error bounds as well as statistical average error values. Although the two receiver discriminators share the same performance bounds, they differ in their response to the multipath within these bounds. The analytical expressions for this response provide the framework to assess the average performance of the two discriminators over the multipath phase distribution and other important propagation channel variables.

Introduction

The multipath problem in geolocation can cause severe degradation of the performance of GPS receivers [1], [2], [3], [4]. In reality, a GPS receiver must replicate the coarse acquisition (C/A) code that is transmitted with the carrier frequency L1=154×10.23 MHz by the satellite vehicles (SV) and thereafter acquired by the receiver. The receiver must then shift the phase of the replica code until it fully correlates with the SV C/A code. This operation is executed by the receiver delay lock loop (DLL). The DLL reaches the maximum correlation between the incoming SV code and the local replica code during the tracking phase by using an early–late discriminator. However, multipath attributed to reflections of the GPS signal from ice, water, building structure, or glass surface compromises the DLL discriminator function, producing tracking errors [5], [6], [7]. Therefore, it becomes important to evaluate the GPS receiver performance as a function of multipath amplitude, phase, and time delay.

Both coherent and noncoherent discriminators can be applied in the GPS receivers. Various studies on multipath effects for the DLL discriminators have been performed [8], [9], [10], [11]. This paper provides detailed analytical treatment of the GPS multipath effect on both the coherent discriminator and the noncoherent early-minus-late power discriminator. It compares the average as well as the worst tracking error performance of the two discriminators under one dominant multipath. Specifically, the role of carrier phase offset due to multipath propagation is demonstrated and its contribution to the tracking error is examined. This paper analyses the receiver performance for direct line-of-sight case. The corresponding analytical error expressions for obstructed line-of-sight propagation environments follow similar derivation steps, although, in the final form, they assume different structures and behaviors. Computer simulations of the impact of a dominant multipath on the discriminator tracking performance are provided. It is assumed that there is an infinite front-end precorrelation bandwidth, the early and late correlations are performed within the same navigation symbol, and no symbol transitions are encountered over the correlation interval. It is shown that in direct line-of-sight case, the noncoherent discriminator offers a better performance than the coherent discriminator; however, in obstructed line-of-sight case, the result turns out to be the opposite.

The paper considers stand-alone receivers and does not deal with assisted GPS [12], [13], [14]. It focuses on GPS receivers, although the developed analysis may be examined and expanded to other satellite systems, navigation code structures, and properties [15]. Section 2 of this paper provides an overview of DLL in-phase and quadrature outputs in multipath. Closed form expressions of the tracking error as a function of multipath parameters using the coherent and the early-minus-late power (noncoherent) discriminators, are provided in 3 Performance analysis for coherent discriminator, 4 Performance analysis for noncoherent discriminator, respectively. A performance comparison of the two discriminators in multipath based on averaged error values in multipath is provided in Section 5. The conclusion is given in Section 6.

Section snippets

DLL in multipath

The GPS DLL tracks the GPS signals and provides the corresponding time delays. It is implemented by a simple cross-correlation process. At the receiver, the DLL cross-correlates the received GPS navigation data, which is modulated onto the C/A code, with a copy of the C/A code. In the absence of noise, interference, multipath, and Doppler shift, the received GPS signal after downconversion and phase tracking is given by $s_{db} (t) = Ag (t - γ) \exp [j (φ - \hat{φ})]$ where A is the signal amplitude, g(t) the ±1

Performance analysis for coherent discriminator

First, we examine, in details, the effect of multipath on the coherent discriminator performance. Substituting (20) into (5), the discriminator function becomes $D_{M} = \frac{A}{\sqrt{2}} {\cos (ψ) [R (τ + d / 2) - R (τ - d / 2)] + α \cos (ψ + β) [R (τ + d / 2 - Δ τ_{m}) - R (τ - d / 2 - Δ τ_{m})]} = D_{c} + D_{err}$ which consists of two terms. The first term, D_c, is identical to (8), and represents the multipath-free discriminator component. It is referred to as the regular discriminator function. Accordingly, the multipath induced error component function, D_err, is $D_{err} = \frac{α A}{\sqrt{2}}$

Performance analysis for noncoherent discriminator

Although the early-minus-late power discriminator provides the same tracking error envelope of the coherent discriminator, it has different multipath phase dependency between performance bounds, leading to an average behavior different than its coherent discriminator counterpart. Based on (5), (20), the corresponding discriminator function under multipath for $α < 1$ is $D_{M} = \frac{A^{2}}{2} [R^{2} (τ + d / 2) - R^{2} (τ - d / 2)] + \frac{A^{2}}{2} {α^{2} [R^{2} (τ + d / 2 - Δ τ_{m}) - R^{2} (τ - d / 2 - Δ τ_{m})] + 2 α \cos (β) [R (τ + d / 2) R (τ + d / 2 - Δ τ_{m}) - R (τ - d / 2) R (τ - d / 2 - Δ τ_{m})]} = D_{nc} + D_{err}$ In

Performance comparison of discriminators

Examining (24), (30), the tracking errors for both discriminators for α<1 over the multipath relative time delay from 0 to $([1 + 2 α \cos (β) + α^{2}] d) / (2 [1 + α \cos (β)])$ are the same. However, over the range $([1 + 2 α \cos (β) + α^{2}] d) / (2 [1 + α \cos (β)])$ to 1+d/2, the two errors are different in most cases. The difference is very evident in Fig. 7 which shows the tracking error over a Δτ_m for $α = 0.56$ under different values of β. In this figure, each curve of the tracking error consists of four segments, out of which the

Conclusion

In this paper, we have analyzed the problem of multipath for the GPS DLL. We provided a comprehensive treatment of tracking performance for the DLL coherent discriminator and the DLL noncoherent early-minus-late power discriminator when the GPS receiver is subject to a single dominant multipath. This analysis has enabled the computation of the average tracking performance over random distribution of multipath parameters, including the carrier phase offset. It is shown that the noncoherent

Acknowledgment

This work is sponsored by the Office of Naval Research, Grant no. N65540-05-C-0028 and NSF Grant no. EEC-0332490.

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Signal Processing

Tracking performance and average error analysis of GPS discriminators in multipath

Abstract

Introduction

Section snippets

DLL in multipath

Performance analysis for coherent discriminator

Performance analysis for noncoherent discriminator

Performance comparison of discriminators

Conclusion

Acknowledgment

Evaluation and reduction of multipath-induced bias on GPS time-of-arrival

IEEE Transactions on Aerospace and Electronic Systems

Spatial and temporal processing for global navigation satellite systems: the GPS receiver paradigm

IEEE Transactions on Aerospace and Electronic Systems

GPS code and carrier multipath mitigation using a multiantenna system

IEEE Transactions on Aerospace and Electronic Systems

Short-delay multipath mitigation technique based on virtual multipath

IEEE Antennas and Wireless Propagation Letters

Code tracking architecture influence on GPS carrier multipath

IEEE Transactions on Aerospace and Electronic Systems

GPS positioning in a multipath environment

IEEE Transactions on Signal Processing

Spread-spectrum ranging multipath model validation

IEEE Transactions on Aerospace and Electronic Systems

Spread-spectrum code and carrier synchronization errors caused by multipath and interference

IEEE Transactions on Aerospace and Electronic Systems