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information is available about the data sets. There are also unsupervised methods, such as hierarchical clustering, which can be used to determine the components in a data set without any prior information about the data. The use of calibration methods in infrared spectroscopy is illustrated here by an example of the application of PCR to the analysis of vegetable oils [11]. Figure 3.15 shows the superposition of the infrared spectra of ve different types of vegetable oil. This demonstrates the similarity of these spectra and the dif culty in differentiating the samples by simple inspection. However, there are characteristic differences in the band positions of each spectrum which may be exploited by using PCR; the wavenumbers of the C H stretching and C H bending bands and bands in the ngerprint region can be used as variables. The process of analysis involves a series of steps. Replicate spectra should rst be obtained for the oils to be analysed and for the unknown samples. The mean of each wavenumber for each class of oil should be calculated. The absolute difference between the unknown wavenumber and the means for each class and each band are then determined. Then, the sum of the differences for each class across all bands employed is determined and the assignment of the unknown to the class with the smallest sum of differences can be made. The results of the analysis of a mixture of unknown vegetable oils, with seven peaks being used, are shown in Figure 3.16. Different symbols are used here to represent each type of

Before getting into the details of the GPS signal, observation models, and position computations, we rst provide more information on the Space Segment and the Control Segment Orbit Design The satellite constellation is designed to have at least four satellites in view anywhere, anytime, to a user on the ground For this purpose, there are nominally 24 GPS satellites distributed in six orbital planes So that we may discuss the orbit design and the implications of that design, we must digress brie y to explain the geometry of the GPS constellation According to Kepler s laws of orbital motion, each orbit takes the approximate shape of an ellipse, with the Earth s centre of mass at the focus of the ellipse For a GPS orbit, the eccentricity of the ellipse is so small (002) that it is almost circular.

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The semi-major axis (largest radius) of the ellipse is approximately 26,600 km, or approximately four Earth radii The six orbital planes rise over the equator at an inclination angle of 55 The point at which they rise from the Southern to Northern Hemisphere across the equator is called the Right Ascension of the ascending node Since the orbital planes are evenly distributed, the angle between the six ascending nodes is 60 Each orbital plane nominally contains four satellites, which are generally not spaced evenly around the ellipse Therefore, the angle of the satellite within its own orbital plane, the true anomaly , is only approximately spaced by 90 The true anomaly is measured from the point of closest approach to the Earth (the perigee).

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(We note here that there are other types of anomaly in GPS terminology, which are angles that are useful for calculating the satellite coordinates within its orbital plane) Note that instead of specifying the satellite s anomaly at every relevant time, we could equivalently specify the time that the satellite had passed the perigee, and then compute the satellite s future position based on the known laws of motion of the satellite around an ellipse Finally, the argument of perigee is the angle between the equator and perigee Since the orbit is nearly circular, this orbital parameter is not well de ned, and alternative parameterization schemes are often used Taken together (the eccentricity, semi-major axis, inclination, Right Ascension of the ascending node, the time of perigee passing, and the argument of perigee), these six parameters de ne the satellite orbit These parameters are known as Keplerian elements.

The RRF map-matching algorithm has been further improved by the addition of a road network tracing routine and the use of intelligent road network data, which contains drive restriction information A comparison between the existing RRF vehicle tracking algorithm performance and the algorithms performance enhanced with new routines is now given The improvement in map matching is achieved by the addition of two subroutines to the existing algorithm A route network analysis routine, provided with ArcView s Network Analyst Extension, was incorporated into the existing softwareThis analysis software calculated the distance through the road network from a vehicle s previous position to each potential present position, offered by the map-matching algorithm Potential positions requiring an impossible network travel distance are instantly rejected using the newly incorporated network analysis software.

This improved the reliability of the route tracking system at locations such as roundabouts or dual carriageways, and immediately after the loss of GPS point positions A further algorithm was developed so that the RRF could interrogate Ordnance Survey (OS) OSCAR Traf c Manager with Drive Restriction Information (DRI), DRI is provided by ETAK on licence to the OS This routine will allow the algorithm to make decisions on road selection using road direction and access information For example, on a dual carriageway, each carriageway is coded as a separate one-way road A roundabout is also coded as a one-way road, as of course is a conventional one-way road A simple comparison between a vehicle s direction of travel (its bearing) and the bearing of permitted travel along a road segment is used for this test.

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