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.

Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation

Abstract: Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor's angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process noise (Q) and measurement noise (R) have a significant impact on the Kalman filter's performance in estimating dynamic states. The conventional ad-hoc approaches for estimating the covariance matrixes are not adequate in achieving the best filtering performance. To address this problem, this paper proposes an adaptive filtering approach to adaptively estimate Q and R based on innovation and residual to improve the dynamic state estimation accuracy of the extended Kalman filter (EKF). It is shown through the simulation on the two-area model that the proposed estimation method is more robust against the initial errors in Q and R than the conventional method in estimating the dynamic states of a synchronous machine.

Observability, Eigenvalues, and Kalman Filtering

Abstract: In higher order Kalman filtering applications the analyst often has very little insight into the nature of the observability of the system. For example, there are situations where the filter may be estimating certain linear combinations of state variables quite well, but this is not apparent from a glance at the error covariance matrix. It is shown here that the eigenvalues and eigenvectors of the error covariance matrix, when properly normalized, can provide useful information about the observability of the system.

The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

Abstract: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.

Invariant Extended Kalman Filter: theory and application to a velocity-aided attitude estimation problem

Abstract: A new version of the Extended Kalman Filter (EKF) is proposed for nonlinear systems possessing symmetries. Instead of using a linear correction term based on a linear output error, it uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from of a linear state error, but from an invariant state error. The benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as is the case for the EKF, which should result in a better convergence of the estimation. This filter is applied to the practically relevant problem of estimating the velocity and attitude of a moving rigid body, e.g. an aircraft, from GPS velocity, inertial and magnetic measurements. In this context it can be seen as an extension of the “Multiplicative EKF” often used for quaternion estimation.

Kalman filtering in two dimensions: Further results

Abstract: The two-dimensional reduced update Kalman filter was recently introduced. The corresponding scalar filtering equations were derived for the case of estimating a Gaussian signal in white Gaussian noise and were shown to constitute a general nonsymmetric half-plane recursive filter. This paper extends the method to the deconvolution problem of image restoration. This paper also provides a more thorough treatment of the uniquely two-dimensional boundary condition problems. Numerical and subjective examples are presented.