Extended Kalman filter

About: Extended Kalman filter is a research topic. Over the lifetime, 25974 publications have been published within this topic receiving 517984 citations.

Mobile robot localization by tracking geometric beacons

Abstract: The application of the extended Kaman filter to the problem of mobile robot navigation in a known environment is presented. An algorithm for, model-based localization that relies on the concept of a geometric beacon, a naturally occurring environment feature that can be reliably observed in successive sensor measurements and can be accurately described in terms of a concise geometric parameterization, is developed. The algorithm is based on an extended Kalman filter that utilizes matches between observed geometric beacons and an a priori map of beacon locations. Two implementations of this navigation algorithm, both of which use sonar, are described. The first implementation uses a simple vehicle with point kinematics equipped with a single rotating sonar. The second implementation uses a 'Robuter' mobile robot and six static sonar transducers to provide localization information while the vehicle moves at typical speeds of 30 cm/s. >

A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking

Abstract: Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

Gaussian filters for nonlinear filtering problems

Abstract: We develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions. A new update rule of weights for Gaussian sum filters is proposed. Our numerical tests demonstrate that new filters significantly improve the extended Kalman filter with no additional cost, and the new Gaussian sum filter has a nearly optimal performance.

On the identification of variances and adaptive Kalman filtering

Abstract: A Kalman filter requires an exact knowledge of the process noise covariance matrix Q and the measurement noise covariance matrix R . Here we consider the case in which the true values of Q and R are unknown. The system is assumed to be constant, and the random inputs are stationary. First, a correlation test is given which checks whether a particular Kalman filter is working optimally or not. If the filter is suboptimal, a technique is given to obtain asymptotically normal, unbiased, and consistent estimates of Q and R . This technique works only for the case in which the form of Q is known and the number of unknown elements in Q is less than n \times r where n is the dimension of the state vector and r is the dimension of the measurement vector. For other cases, the optimal steady-state gain K op is obtained directly by an iterative procedure without identifying Q . As a corollary, it is shown that the steady-state optimal Kalman filter gain K op depends only on n \times r linear functionals of Q . The results are first derived for discrete systems. They are then extended to continuous systems. A numerical example is given to show the usefulness of the approach.

Kalman Filtering: Theory and Practice

Abstract: 1. General Information. 2. Linear Dynamic Systems. 3. Random Processes and Stochastic Systems. 4. Linear Optimal Filters and Predictors. 5. Nonlinear Applications. 6. Implementation Methods. 7. Practical Considerations. Appendix A: Software. Appendix B: A Matrix Refresher.