Browsing by Subject "particle swarm optimization"

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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
Maximum likelihood estimation of robust constrained Gaussian mixture models
(2013) Arı, Çağlar
Density estimation using Gaussian mixture models presents a fundamental trade off between the flexibility of the model and its sensitivity to the unwanted/unmodeled data points in the data set. The expectation maximization (EM) algorithm used to estimate the parameters of Gaussian mixture models is prone to local optima due to nonconvexity of the problem and the improper selection of parameterization. We propose a novel modeling framework, three different parameterizations and novel algorithms for the constrained Gaussian mixture density estimation problem based on the expectation maximization algorithm, convex duality theory and the stochastic search algorithms. We propose a new modeling framework called Constrained Gaussian Mixture Models (CGMM) that incorporates prior information into the density estimation problem in the form of convex constraints on the model parameters. In this context, we consider two different parameterizations where the first set of parameters are referred to as the information parameters and the second set of parameters are referred to as the source parameters. To estimate the parameters, we use the EM algorithm where we solve two optimization problems alternatingly in the E-step and the M-step. We show that the M-step corresponds to a convex optimization problem in the information parameters. We form a dual problem for the M-step and show that the dual problem corresponds to a convex optimization problem in the source parameters. We apply the CGMM framework to two different problems: Robust density estimation and compound object detection problems. In the robust density estimation problem, we incorporate the inlier/outlier information available for small number of data points as convex constraints on the parameters using the information parameters. In the compound object detection problem, we incorporate the relative size, spectral distribution structure and relative location relations of primitive objects as convex constraints on the parameters using the source parameters. Even with the propoper selection of the parameterization, density estimation problem for Gaussian mixture models is not jointly convex in both the E-step variables and the M-step variables. We propose a third parameterization based on eigenvalue decomposition of covariance matrices which is suitable for stochastic search algorithms in general and particle swarm optimization (PSO) algorithm in particular. We develop a new algorithm where global search skills of the PSO algorithm is incorporated into the EM algorithm to do global parameter estimation. In addition to the mathematical derivations, experimental results on synthetic and real-life data sets verifying the performance of the proposed algorithms are provided.