Practical multivariate statistical multipath detection methods
|Phase multipath is one of the most crucial error sources in centimetre or millimetre level GNSS high precision positioning. Short-delay multipath is still especially difficult to detect or mitigate by the state-of-the-art hardwarebased techniques. Therefore, processing algorithm-based multipath mitigation methods are crucial for the further improvement of positioning accuracy, either integrated with other techniques or in a stand-alone mode. The effectiveness of some of these is, however, limited by the degrees of freedom in currently available solutions, i.e. insufficient satellites and signals. This problem is similar to the un-robustness and unreliability of some outlier detection techniques used in RAIM and other integrity algorithms in the current GPS system.
Fig. 1 Simulated GPS three-frequency (red: L1, blue: L2, green: L5) multipath error in PRN02 in the LCPC dataset (relative permittivity =3.9)
GPS modernization is being undertaken. The GPS Block IIR-M satellites are already transmitting an unencrypted civil signal (L2C) on L2 frequency and Block III satellites will transmit a new civil signal (L1C) on L1. Moreover, the signal power of L2 will be increased. This will make tracking of L2 much easier and more reliable and will increase the use of L2 in high precision kinematic applications. An additional signal, the so-called L5, will be available on GPS Block IIF satellites scheduled for launch beginning in late 2009. Both the modernised L2 and the new L5 civil signals allow coherent tracking of code and phase and so avoid the losses that occur when tracking the current P(Y) code in L2. This had led to the extensive current interest, e.g. (Hatch et al., 2000) in investigating the potential of three-frequency data for a wide range of applications. On the other hand, the European GNSS, named Galileo, is being developed to provide four carrier frequencies and its Full Operational Capability (FOC) is scheduled to be in 2013. Galileo signals are expected to be available to users in four categories: Open Service (OS), Safety-of-Life (SoL) service, Commercial Service (CS), and Public Regulated Service (PRS).
This paper investigates the application of a sophisticated multiple outlier detection technique, which the author refers to as the cocktail multiple outlier detection algorithm, to multipath contaminated measurements in the three-frequency GPS and Galileo systems (only OS Galileo signals are used in this investigation, i.e., L1, E5a, and E5b) and a combined multiple-frequency GPS and Galileo system. It is tested with simulated data as real GPS L5 (only available in one Block IIR-M satellite now) and Galileo data are not yet available. The results, possibilities and weaknesses of the method are analysed. Note that the results of this investigation are not affected by the movement of the roving receiver because single-epoch data processing is used. Moreover, ambiguity resolution is not the main research interest in this paper, which assumes that ambiguities are fixed before the proposed algorithms are applied therefore no ambiguities are simulated in the carrier-phase data.
Cocktail multiple outlier detection algorithm
For high precision GPS positioning, the observation equations used in parameter estimation are usually linearized as:
Description of testing
Description of simulated test datasets
The first two simulated datasets are referenced to the setup of a real multipath experiment carried out at the Laboratoire Central des Ponts et Chaussées (LCPC) near Nantes in France during May 2002 . The real data was used in the validation of the multipath model used in the simulation of multipath data for the investigations of this paper, the validation results show that the model can generate very realistic phase multipath error (Lau and Cross, 2007). In the experiment, two Leica Geosystems System 530 receivers attached to lightweight AT502 antennas were used and a 5m by 2.5m steel panel
was constructed and placed about 5m to one of the receiving antennas in order to create a sufficiently large multipath signal. The antenna-reflector geometry is shown in Fig. 2. The geometry of the first two simulated datasets are the same but the reflectors with the assumed relative permittivities of 10 (e.g. flint glass) and 20 are used in multipath simulation. Therefore, the test datasets are denoted as LCPC-10 and LCPC-20 according to the relative permittivity used. The baseline length is about 86 m. The information used in multipath simulation is summarised in Table 1. The sky plot of the satellites-reflector-antenna geometry is shown in Fig. 3. Moreover, details of the satellites whose signals are contaminated by multipath are shown in Table 2.
Another virtual test site is at the IGS global tracking station LBCH in Long Beach, United States. In the LBCH test dataset, a concrete wall (reflector) is set 5m to the north of the antenna and a reference station 100m to its south. A relative permittivity of 7 (see Table 1) was used in the simulation of multipath in order to create strong multipath. This value is based on Stavrou and Saunders (2003), which found that the real part of the complex permittivity of concrete varied from 6.2 to 7 (for signals in the range of 1 to 95.9 GHz). Table 2 summarises the multipath simulation.
Also a kinematic data set, denoted as K-HK7-300, was simulated based on a 720m trajectory along a real street in Hong Kong. The roving antenna was assumed to set about 29cm (measured to L1 phase centre) above a 1m by 1m steel carry platform that travel at 1ms-1. The buildings were assumed to be made of concrete with a relative permittivity of 7. The reference station was assumed to be about 500 m to the north of the road. Table 3 summarises the simulation – note that some satellites are blocked for some of the time.
In the all of the test datasets, Leica System 530 receivers and AT502 antennas were assumed to have been used in data collection. Moreover, normal distributed random measurement noise with the standard deviation of 1 mm was generated in each
phase measurement. It should be pointed out that it was necessary to assume the use of a particular receiver and antenna because factors such as receiver correlator spacing and antenna gain pattern have an impact on the simulated multipath. The author does not believe the choices the author has made affect the overall conclusions of this research. Testing methodology Five scenarios with different GNSSs or combinations of frequencies have been tested and results compared with the known positions in all cases:
• Scenario 1: the current single
frequency GPS data;
• Scenario 2: the modernised
dual-frequency GPS data,
• Scenario 3: the future threefrequency
• Scenario 4: the future OS threefrequency
Galileo data, and
• Scenario 5: the future OS Galileo
Note that the reason for Scenario 1 is that
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