|Institution:||University of Oslo|
|Full text PDF:||https://www.duo.uio.no/handle/10852/11095
The goal of this thesis is to find a method to get a correct estimate of the parameters/constants within the Kalman filter equations to get a higher accuracy in the state estimates of the Kalman filter. The maximum likelihood estimator (MLE) is chosen due to its adventitious attributes, such as easy implementation in the given system, good statistical properties and optimal minimization of the estimated error minus the real measurement. A short introduction in the Kalman filter and maximum likelihood estimator is given. It is established that we can use the maximum likelihood function in cooperation with the Kalman filter to compute the maximum likelihood parameter estimates. The mathematical background for the 3 and 5 state 1 dimensional mathematical system of the navigation system is derived and simulated data is acquired. We find a potential high identifiability on the simulated data with respect to the noise parameters, both for the system noise and measurement noise, which holds even when irregular sampling is introduced. The hessian eigenvalues and multiple start-guess “method” are verified to be sufficient to verify the found parameters. When we use real data collected from a ROV and a tow fish the high identifiability disappears and the results become highly inconsistent. Different reasoning’s to why this happens are discussed and we conclude that the best course of action is to move on and use the full 3 dimensional set of equations implemented in NavLab. Even though the inconsistence partly disappears can high enough reliability not be established both for the ROV and tow fish data. The found parameters are analysed with subject to improved estimation accuracy, bias estimation and error, also this cannot be established. Due to the reliability issues and only marginal improvement of the bias and error estimation we conclude that the MLE is not sufficient to identify the parameters in the given navigation system.