Alpha beta filter

About: Alpha beta filter is a research topic. Over the lifetime, 5653 publications have been published within this topic receiving 128415 citations.

Adaptive Kalman Filtering for Low-cost INS/GPS

Abstract: GPS and low-cost INS sensors are widely used for positioning and attitude determination applications. Low-cost inertial sensors exhibit large errors that can be compensated using position and velocity updates from GPS. Combining both sensors using a Kalman filter provides high-accuracy, real-time navigation. A conventional Kalman filter relies on the correct definition of the measurement and process noise matrices, which are generally defined a priori and remain fixed throughout the processing run. Adaptive Kalman filtering techniques use the residual sequences to adapt the stochastic properties of the filter on line to correspond to the temporal dependence of the errors involved. This paper examines the use of three adaptive filtering techniques. These are artificially scaling the predicted Kalman filter covariance, the Adaptive Kalman Filter and Multiple Model Adaptive Estimation. The algorithms are tested with the GPS and inertial data simulation software. A trajectory taken from a real marine trial is used to test the dynamic alignment of the inertial sensor errors. Results show that on line estimation of the stochastic properties of the inertial system can significantly improve the speed of the dynamic alignment and potentially improve the overall navigation accuracy and integrity.

Robust observer-based control of systems with state perturbations via LMI approach

Abstract: In this note, the observer-based control for a class of uncertain, linear systems is considered. Exponential stabilizability for the systems is studied and the convergence rate of the system is estimated. A linear matrix inequality (LMI) approach is used to design the observer-based control. The control and observer gains are given from LMI feasible solution. A numerical example is given to illustrate our results.

Nonlinear observer design using Lyapunov's auxiliary theorem

Abstract: The work proposes an approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of first-order linear singular PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov's auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Within the proposed design framework, both full-order and reduced-order observers are studied.

Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition

Abstract: OPTIMAL ESTIMATION Classical Estimation Theory Mean-Square Estimation Maximum-Likelihood Estimation The Cramer-Rao Bound Recursive Estimation Wiener Filtering Problems Discrete-Time Kalman Filter Deterministic State Observer Linear Stochastic Systems The Discrete-Time Kalman Filter Discrete Measurements of Continuous-Time Systems Error Dynamics and Statistical Steady State Frequency Domain Results Correlated Noise and Shaping Filters Optimal Smoothing Problems Continuous-Time Kalman Filter Derivation from Discrete Kalman Filter Some Examples Derivation from Wiener-Hopf Equation Error Dynamics and Statistical Steady State Frequency Domain Results Correlated Noise and Shaping Filters Discrete Measurements of Continuous-Time Systems Optimal Smoothing Problems Kalman Filter Design and Implementation Modeling Errors, Divergence, and Exponential Data Weighting Reduced-Order Filters and Decoupling Using Suboptimal Gains Scalar Measurement Updating Problems Estimation for Nonlinear Systems Update of the Hyperstate General Update of Mean and Covariance Extended Kalman Filter Application to Robotics and Adaptive Sampling Problems ROBUST ESTIMATION Robust Kalman Filter Systems with Modeling Uncertainties Robust Finite Horizon Kalman A Priori Filter Robust Stationary Kalman A Priori Filter Convergence Analysis Linear Matrix Inequality Approach Robust Kalman Filtering for Continuous-Time Systems Problems H-Infinity Filtering of Continuous-Time Systems H-Infinity Filtering Problem Finite Horizon H-Infinity Linear Filter Characterization of All Finite Horizon H-Infinity Linear Filters Stationary H-Infinity Filter-Riccati Equation Approach Relationship with the Kalman Filter Convergence Analysis H-Infinity Filtering for a Special Class of Signal Models Stationary H-Infinity Filter-Linear Matrix Inequality Approach Problems H-Infinity Filtering of Discrete-Time Systems Discrete-Time H-Infinity Filtering Problem H-Infinity A Priori Filter H-Infinity A Posteriori Filter Polynomial Approach to H-Infinity Estimation J-Spectral Factorization Applications in Channel Equalization Problems OPTIMAL STOCHASTIC CONTROL Stochastic Control for State Variable Systems Dynamic Programming Approach Continuous-Time Linear Quadratic Gaussian Problem Discrete-Time Linear Quadratic Gaussian Problem Problems Stochastic Control for Polynomial Systems Polynomial Representation of Stochastic Systems Optimal Prediction Minimum Variance Control Polynomial Linear Quadratic Gaussian Regulator Problems Appendix A: Review of Matrix Algebra Basic Definitions and Facts Partitioned Matrices Quadratic Forms and Definiteness Matrix Calculus References Index