Proposal and comparison of an eXogenous Kalman Filter and a Particle Filter for use with ROV thruster models
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- Institutt for marin teknikk 
Robust and accurate observer design is a prerequisite for safe and efficient underwater navigation. Especially with today's increased focus on automation and autonomy. In this thesis two model based observer designs for underwater vehicles are proposed and compared. One is based on the eXogenous Kalman Filter (XKF) and the other is based on the Particle Filter (PF). The designs are also compared to the Extended Kalman Filter (EKF) which is one of the standard observers used today. The drawback of the EKF is the lack of global stability due to a destabilising feedback loop providing linearization points. In the XKF this problem is solved by instead providing linearization points from a globally stable auxiliary state estimator . In the proposed XKF design, a Nonlinear passive Observer (NLO) is implemented for this purpose. The PF however uses the mathematical model directly to generate a number of plausible state hypotheses. Only the most plausible hypotheses makes up the final state estimates. Using the model directly, i.e. without linearization, theoretically makes the PF a more accurate observer than the EKF and the XKF. Albeit global stability cannot be proven for the PF either. A simulator was developed in Matlab/Simulink to evaluate and compare the filters. In simulations it was assumed that noisy measurements of thrust were available for use with a mathematical ROV model. In addition, it was assumed that noisy measurements of position and heading were available from other measurement sources. Experimental data were also gathered from physical experiments using a ROV in the NTNU MC-lab. While the proposed observers were designed with the intention of using measured thrust as input, such measurements were not available with the equipment in the MC-lab. Hence, measurements from an Inertial Measurement Unit (IMU) were used as a replacement of the thruster model. As a consequence only the PF was tested using experimental data. Simulations shows that the EKF and XKF performs relatively similar when both filters are given correct initial values. In the case of inaccurate initial values the differences are larger. As expected, the EKF diverges if the initial values are too erroneous, while the XKF is always able to converge. In cases where both filters are able to converge, the XKF has much faster convergence rates. The XKF gives slightly longer computational times, but its great stability properties makes it the preferable filter compared to the EKF. The PF proves to be the most accurate observer, and it has the fastest convergence rates when the initial values are erroneous. Using the PF with experimental data verifies that the implementation suggested in the thesis works as intended also outside the simulator. The big drawback of the PF is however that it uses approximately 20 times longer time than the Kalman filters. In addition the PF may diverge if not tuned properly. Taken everything into consideration the XKF is considered the best observer for autonomous vehicles.