This thesis describes the studies carried out to investigate the effect on the ship's coordinates and their errors of using a diagonal covariance matrix instead of full covariance matrix for correlated observations. A comparison of the results of computation with and without correlation can indicate wehwhether or not the correlation can be ignored. tests using both a diagonal covariance matrix and a full covariance matrix for the observations are hence proposed. For this purpose two test were carried out using observations thought to have correlation in practice. These are hyperbolic systems and GPS pseudo-range observables. The computation method investigated for position fixing in this research is known as Kalman filtering. A program developed by Hashim (1989) is available for this investigation. However, an initial study showed that some corrections were required before further developments and tests could be made. The corretions made to the program, which then required the program to be tested again, are also presented.