Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

The simultaneous on-line estimation of parameters and states in linear systems

Abstract: The practical implementation of adaptive controllers using minicomputers requires algorithms which are both numerically economical and robust. The problem of combined state and parameter estimation for adaptive controllers was originally posed as a nonlinear filtering problem. The only known nonlinear filter which can be practically implemented on a small computer is the extended Kalman filter. The extended Kalman filter, however, often diverges, thus, there is a need for economical, robust parameter-state estimators. A simple suboptimal parameter and state estimator is presented which fills this need. The filter is based on a particular canonical form for the state-space equations of a linear system which allows the parameters and states to be estimated separately using two linear estimators. If an innovations model is used, the steady-state Kalman filter gains can be estimated and thus, during steady-state operation, the estimates of the states can be easily obtained. Numerical exampies are presented which demonstrate the increased robustness and speed of the proposed linear estimator over the extended Kalman filter.

A Linear Kalman Filter for MARG Orientation Estimation Using the Algebraic Quaternion Algorithm

Abstract: Real-time orientation estimation using low-cost inertial sensors is essential for all the applications where size and power consumption are critical constraints. Such applications include robotics, human motion analysis, and mobile devices. This paper presents a linear Kalman filter for magnetic angular rate and gravity sensors that processes angular rate, acceleration, and magnetic field data to obtain an estimation of the orientation in quaternion representation. Acceleration and magnetic field observations are preprocessed through a novel external algorithm, which computes the quaternion orientation as the composition of two algebraic quaternions. The decoupled nature of the two quaternions makes the roll and pitch components of the orientation immune to magnetic disturbances. The external algorithm reduces the complexity of the filter, making the measurement equations linear. Real-time implementation and the test results of the Kalman filter are presented and compared against a typical quaternion-based extended Kalman filter and a constant gain filter based on the gradient-descent algorithm.

Dynamic ship positioning using a self-tuning Kalman filter

Abstract: A novel adaptive filtering technique is described for a class of systems with unknown disturbances. The estimator includes both a self-tuning filter and a Kalman filter. The state estimates are employed in a closed-loop feedback control scheme which is designed via the usual linear quadratic approach. The approach was developed for application to the dynamic ship positioning control problem and has the advantage that existing nonadaptive Kalman filtering systems may be easily modified to include the self-tuning feature.

The Kalman filter in finance

Abstract: Preface. 1. Introduction. 2. Test for parameter stability. 3. Flexible Least Squares. 4. The Kalman filter. 5. Parameter estimation. 6. The estimates, reconsidered. 7. Modeling with the Kalman filter. A. Tables of references. B. The programs and the data. Bibliography. Index.