A GPS receiver capable of supporting multiple antennas can be used to determine a general vehicle's attitude as well as its position. The general principle in vehicle’s attitude determination lies in the differential carrier phase measurements of the line-of-sight GPS signal. One problem with using this technique on-board a satellite is that the GPS antennas generally are sited on a non-optimal location on the space-facing facet of the spacecraft, which provides a poor multipath environment for the GPS antennas. Therefore, it is important to find a method to calibrate the multipath error, in order to obtain higher vehicle’s attitude accuracy. In addition to the error caused by multipath, there are also arbitrary measurement biases. Furthermore, the GPS phase difference measurements are sampled randomly across the hemisphere and there is substantial thermal noise present in the GPS carrier phase difference measurements. This research investigates the problems faced in GPS attitude determination, mainly with respect to multipath, arbitrary measurement biases and thermal noise. The spherical harmonic template and weighted least square estimation methods are used to construct the multipath map, in order to mitigate the above-mentioned problems. Additionally, a novel technique based on Analysis of Variance (suggested by Dr. Stephen Hodgart) is used to analyse the error of the multipath mapping. This technique is able to separate these error sources and predict the rms error of the multipath map. It is also able to automatically interpolate to every point in the attitude hemisphere even when the data do not evenly cover the hemisphere. The multipath maps constructed in this thesis are based on experimental test data, downloaded from SSTL’s satellite (UoSat 12) on January 2000 and 13 July 2000. The 13 July 2000 data are noisy with distinct periodic fluctuation. Its noise variance is estimated to be 152.8 mm2 and the constructed map is in error by 41.3 mm2. As for the January 2000 data, they are of a much higher quality than the 13 July 2000 data with the noise variance of 14.6mm2 and the constructed map is in error by 0.69 mm2. In order to reduce the error in the constructed multipath map, weighted least square estimation is used to estimate the coefficient of spherical harmonic functions as a function of co-elevation and F-test is used to remove the insignificant spherical harmonic functions whose coefficients have samll amplitude. As a result, the 22nd order spherical harmonic multipath map constructed with January 2000 data is in error by 0.51mm2 rms, which translate to 0.06° for a baseline with a length of 648.7mm. After the multipath mitigation, the GPS attitude determination with accuracy of 0.10 rms is possible. As a result, the multipath mitigation method describe in this thesis have achieved a signal processing gain of 14.6dB.