Multipath Mitigation by Wavelet Analysis for Gps Base Station Applications

It is well known that multipath disturbance is one of the major error sources impacting on high precision GPS positioning. The multipath disturbance is largely dependent on the receiver’s environment since satellite signals can arrive at the receiver via multiple paths, due to reflections from nearby objects such as trees, buildings, vehicles, etc. Although the multipath effect can be reduced by choosing sites without multipath reflectors or by using choke-ring antennas to mitigate the reflected signal, it is difficult to eliminate all multipath effects from GPS observations. Since the geometry between the GPS satellites and a specific receiver-reflector location repeats every sidereal day, multipath tends to exhibit the same pattern between consecutive days. This repetition can then be useful for verifying the presence of multipath through the analysis of observations made at a static receiver on different days. In this study, the authors apply a wavelet decomposition technique to extract multipath from GPS observations. The extracted multipath signature is then applied directly to the GPS observations to correct for the multipath effects. The results show that the proposed method can be used to significantly mitigate the multipath effects at a permanent GPS station. INTRODUCTION GPS carrier phase observations are widely used for all high precision static and kinematic positioning applications. The least-squares estimation method is usually employed for the processing of such GPS observations. The least-squares method is based on the formulation of a mathematical model consisting of the functional model and the stochastic model. If the function model is adequate, the residuals obtained from the least-squares solution should be randomly distributed. However, the GPS observations are contaminated by several types of biases such as the orbital bias, the atmospheric biases, multipath disturbance, and receiver noise. A double-differencing technique is commonly used for constructing the functional model as it can eliminate or reduce many of the troublesome GPS biases (i.e. the atmospheric biases, the receiver and satellite clock biases, and the orbital bias). However, some unmodelled biases still remain in the GPS observations, even after such data differencing. Multipath is a major residual error source in the double-differenced GPS observables, and it can have a significant impact on the positioning results. To obtain accurate positioning results from GPS it is necessary to minimise the magnitude of multipath disturbance of the GPS observations. Recently, some waveletbased techniques have been introduced in the field of GPS data processing (e.g., [4], [5], [11], [13]). These methods have addressed some potential applications such as signal denoising, outlier detection, bias separation and data compression. A new technique using wavelet decomposition is proposed for extracting or modelling multipath from GPS carrier-phase observations. The technique is first applied in order to decompose GPS double-differenced residuals into low-frequency bias and highfrequency noise terms. The extracted bias component is then applied directly to the GPS observations to correct for the trend introduced by this error component. The remaining terms, largely characterised by the GPS range observations and highfrequency measurement noise, are expected to give the best linear unbiased solutions from a least-squares process. This paper is organised as follows. An introduction to existing multipath mitigation techniques is presented. The theory of wavelet decomposition and its application to GPS data processing is then described. A discussion of experimental results and analyses are presented in a subsequent section. Finally, some concluding remarks are made. MULTIPATH MITIGATION TECHNIQUES Mulipath is a phenomenon whereby satellite signals can arrive at the receiver via multiple paths, due to reflections from nearby objects such as trees, buildings, the ground, water surfaces, vehicles, etc. It can be reduced by choosing sites without multipath reflectors or by using choke-ring antennas to mitigate the reflected signal. However, it is difficult to eliminate all multipath effects from GPS observations only through careful site selection and the use of special antenna types. For example, in structural monitoring applications it may not be possible to find suitable antenna sites that are not susceptible to multipath. [17] described two techniques, namely Multipath Elimination Technology and Multipath Elimination Delay Lock Loop, used to mitigate multipath at the receiver signal processing level. Most modern GPS receivers now employ similar algorithms. However, multipath cannot be completely removed and the residuals may still be too large to ignore when high accuracy positioning results are required. It is therefore essential to investigate post-reception data processing techniques for mitigating the effect of multipath. Fortunately the multipath disturbance has a periodic characteristic and is repeated every sidereal day for a static receiver if the antenna environment remains the same. Several post-reception methods to mitigate multipath have been proposed. [8] suggested a technique that requires a preparation of ‘maps’ of the multipath environment surrounding the GPS antenna. The limitation of this technique is that it will only work well if the antenna environment remains unchanged. [1] proposed a technique that relies on the analysis of the signal-to-noise-ratio (SNR) values of GPS signals. However, this technique cannot be used in real-time. [2] proposed the use of a ‘multipath template’ for mitigating multipath. [9] also proposed the use of finite impulse response (FIR) filters to extract or eliminate multipath. However, the limitation of such techniques is that signals (for example, crustal deformation) falling in the same frequency band as the FIR filters will be filtered out [6]. An effective technique based on the use of an adaptive filter to extract and eliminate multipath was suggested by [7]. This is due to the fact that GPS observation noise tends to change with time, it is therefore more appropriate to use an adaptive filter rather than a fixed filter for the purpose of multipath mitigation. The implementation of such a technique is dependent on the selection of appropriate value for the step-size parameter and the filter length. Further investigations are still needed on post-reception techniques. WAVELET TRANSFORM Wavelet Transform (WT) is a new tool for signal analysis that can provide, simultaneously, time and frequency information of a signal sequence. WT has many potential applications in filtering, sub-band coding, data compression and multiresolution signal processing (see, for example, [3], [18]). In particular, the WT is of interest for the analysis of non-stationary signals such as GPS observations because it provides an alternative to the classical Fourier Transform (FT), which assumes stationarity in signals. It can be viewed as an extension to Fourier analysis that is wellsuited for characterising signals whose spectral character changes with time. Such signals are not well represented in time and frequency by the Fourier Transform methods. The method of wavelet analysis is closely related to the time-frequency analysis based on the Wigner-Ville distribution [12]. Mathematical details on wavelet analysis can be found in [3], [12] and [18]. Multi-resolution analysis provides a formal approach to constructing the wavelet basis. The basic concept of multi-resolution analysis is to analyse the signal at different scales by using filters of different cut-off frequencies. The signal is passed through a series of high-pass filters to analyse the high frequencies, and it is passed through a series of low-pass filters to analyse the low frequencies. Therefore, the Wavelet Transform can be used to achieve enough frequency resolution to discriminate these terms in the original GPS observation. Figure 1 illustrates the multi-resolution analysis process using the wavelet transform. Applying a narrow daughter wavelet to the original signal is equivalent to applying a high-pass filter, which completes path 1. Extracting the leading low-frequency requires applying a number of daughter wavelets that are wider than the signal you need to match, then applying a final daughter wavelet that becomes a high-pass filter, completing path 2.