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MMGPS identi es the correct road, on which a vehicle is travelling, and snaps the vehicle position onto that road Furthermore, MMGPS corrects the derived position using its own computed correction parameters, eg Correction Dilution of Precision (CDOP) using the history of previous position estimates and road geometry [Blewitt and Taylor, 2002] Various research experiments utilizing MMGPS have been conducted and results have been fully described in Taylor et al [2001a] The main objectives of the research described in this chapter are to determine both the accuracy and reliability of position of a public transport bus that can be provided using a combination of GPS, odometer and map matching techniques To this end, a new algorithm has been developed that integrates odometer observations with the existing software, now called OMMGPS.

TABLE 7.8 Moving average crossover optimization for COMEX gold out-ofsample study (2003).

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In OMMGPS, height information obtained from digital terrain models (DTM) are used to determined 3D GPS point positions, when only three GPS satellites are visible to the receiver More importantly, height aiding improves the accuracy of GPS point positions with poor satellite geometry (high PDOP), and when severe multipath occurs (multiple re ected GPS satellite signals) The developed method uses absolute GPS positioning, map matched, to locate the vehicle on a road centre-line, when GPS is known to be suf ciently accurate When this is not the case, odometer readings are used to locate the vehicle on a road centre-line The odometer is calibrated using relative GPS positions, based on map-matching criteria, such as the residuals of CDOP, for GPS precision determination (see also Section 2) The accuracy of OMMGPS is a function of the frequency of accurate GPS points, reliable map matching and correct odometer calibration.

The next step is to add the implementation of the new coarse-grained methods to the session:

Standard Ordnance Survey (OS) digital plan and height map products were used for road map matching and height aiding A number of trips along a bus route in central London Baker Street, Oxford Street, etc were made to test the method A typical result of map-matched GPS positioning is shown in Figure 81 The innovative feature of this particular implementation is that map matching is actually used for GPS accuracy determination rather than to identify the correct road the bus is driving on This is achievable, since pre-de ned bus routes.

a limit process, typically Gaussian; and the relevant random variable to compute probabilities becomes its supremum. The literature on this subject has been growing during the recent years, including applications to biology, econometrics, and in general, stochastic models which include nuisance parameters, of which hidden Markov chains have become a quite popular example. The interested reader can see, for example, Andrews and Ploberger (1994), Hansen (1996), Dacunha-Castelle and Gassiat (1997, 1999), Gassiat (2002), Aza s et al. (2006, 2008), and references therein. The rst example in this chapter is extracted from Aza s and Cierco-Ayrolles (2002) and the second from Delmas (2001, 2003a). The theory includes two parts: rst, limit theorems that allow us to nd the asymptotic behavior of certain stochastic processes, and second, computing (or obtaining bounds) for the distribution of the supremum of the limiting process or its absolute value. For the second part, a common practice is to in simulate the paths and approximate the tails of the distribution of its supremum using Monte Carlo. This is not what we will be doing here. Our aim is a better understanding of the behavior of this distribution, and for that purpose we use the results of the rst part of this chapter. Since these concern only one-parameter Gaussian processes, the models in the examples of this chapter have a one-dimensional nuisance parameter, and the asymptotic law of the relevant processes is Gaussian.

j = 1 . . . , m. (12.40)

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