Evaluation of mathematical models for gyrocompass behaviour:: Error modelling and applications

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Heading information is a fundamental parameter in ship’s navigation. Traditionally a gyrocompass is used as the primary sensors to provide heading reference on board ship. However, gyrocompass indicated headings are subject to a number of errors, which are functions of the ship’s motion and of the latitude of operation. The objective of this thesis is to investigate the gyrocompass behavior, study its deviations under different conditions of operation and develop suitable algorithms for the software compensation of these deviations. To meet this objective, mathematical models describing the gyrocompass behaviour are developed using different dynamic considerations. In particular, the gyrocompass equations of motion and their solutions are developed for the cases of a stationary, uniformly moving, and maneuvering ship. A general discrete-time model as well as a special model to represent a maneuvering ship are developed. Specific attention is drawn to the problem of high latitude behaviour of the gyrocompass. Simulation studies of the gyrocompass dynamic response are carried out using the mathematical models developed in this study. The simulation results indicate that transient errors of 1° are expected at latitudes of 30°, while errors in excess of 10° are likely to occur at latitudes of 70°. These errors may degrade considerable not only the gyrocompass performance, but also the performance of a multi-sensor integrated navigation system (e.g. introducing as much as 0.5 nautical miles error in a satellite fix), or they may introduce an error of as much as 2 mgals in real-time Eötvös correction calculations in precise sea gravimetry. An open-loop software compensation procedure of gyrocompass errors is proposed as an alternative to manual mechanical compensation traditionally used, to improve the gyroscope performance. The algorithm developed in this thesis is a function of the gyrocompass design parameters and of the particular dynamics of the ship’s motion. Finally, recommendations for future work include sea-trials of the developed software compensation algorithm, extension of the mathematical models to incorporate random disturbing forces, and evaluation of the dynamic response of modern marine gyrocompasses, such as, the Sperry MK 37 Gyrocompass Equipment.