Browsing by Subject "maximum likelihood estimation"

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Open Access
Deterministic and stochastic error modeling of inertial sensors and magnetometers
(2012) Seçer, Görkem
This thesis focuses on the deterministic and stochastic modeling and model parameter estimation of two commonly employed inertial measurement units. Each unit comprises a tri-axial accelerometer, a tri-axial gyroscope, and a tri-axial magnetometer. In the first part of the thesis, deterministic modeling and calibration of the units are performed, based on real test data acquired from a flight motion simulator. The deterministic modeling and identification of accelerometers is performed based on a traditional model. A novel technique is proposed for the deterministic modeling of the gyroscopes, relaxing the test bed requirement and enabling their in-use calibration. This is followed by the presentation of a new sensor measurement model for magnetometers that improves the calibration error by modeling the orientation-dependent magnetic disturbances in a gimbaled angular position control machine. Model-based Levenberg-Marquardt and modelfree evolutionary optimization algorithms are adopted to estimate the calibration parameters of sensors. In the second part of the thesis, stochastic error modeling of the two inertial sensor units is addressed. Maximum likelihood estimation is employed for estimating the parameters of the different noise components of the sensors, after the dominant noise components are identified. Evolutionary and gradient-based optimization algorithms are implemented to maximize the likelihood function, namely particle swarm optimization and gradient-ascent optimization. The performance of the proposed algorithm is verified through experiments and the results are compared to the classical Allan variance technique. The results obtained with the proposed approach have higher accuracy and require a smaller sample data size, resulting in calibration experiments of shorter duration. Finally, the two sensor units are compared in terms of repeatability, present measurement noise, and unaided navigation performance.
Open Access
Robust minimax estimation applied to kalman filtering
(2008) Aybar, Bahadır
Kalman filtering is one of the most essential tools in estimating an unknown state of a dynamic system from measured data, where the measurements and the previous states have a known relation with the present state. It has generally two steps, prediction and update. This filtering method yields the minimum mean-square error when the noise in the system is Gaussian and the best linear estimate when the noise is arbitrary. But, Kalman filtering performance degrades significantly with the model uncertainty in the state dynamics or observations. In this thesis, we consider the problem of estimating an unknown vector x in a statespace model that may be subject to uncertainties. We assume that the model uncertainty has a known bound and we seek a robust linear estimator for x that minimizes the worst case mean-square error across all possible values of x and all possible values of the model matrix. Robust minimax estimation technique is derived and analyzed in this thesis, then applied to the state-space model and simulation results with different noise perturbation models are presented. Also, a radar tracking application assuming a linear state dynamics is also investigated. Modifications to the James-Stein estimator are made according to the scheme we develop in this thesis, so that some of its limitations are dealt with. In our scheme, James-Stein estimation can be applied even if the observation equation is perturbed and the number of observations are less than the number of states, still yielding robust estimations.