Proceedings ArticleDOI
Optimal solution of the two-stage Kalman estimator
Chien-Shu Hsieh,Fu-Chuang Chen +1 more
- Vol. 2, pp 1532-1537
TLDR
In this article, the optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed, where the algebraic constraint is removed.Abstract:
The optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed. It is well known that, under an algebraic constraint, the optimal estimate of the system state can be obtained from a two-stage Kalman estimator. Unfortunately, this algebraic constraint is seldom satisfied for practical systems. This paper proposes a general form of the optimal solution of the two-stage estimator, in which the algebraic constraint is removed. Furthermore, it is shown that, by applying the adaptive process noise covariance concept, the optimal solution of the two-stage Kalman estimator is composed of a modified bias-free filter and an bias-compensating filter, which can be viewed as a generalized form of the conventional two-stage Kalman estimator.read more
Citations
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Journal ArticleDOI
Industrial Applications of the Kalman Filter: A Review
François Auger,Mickael Hilairet,Josep M. Guerrero,Eric Monmasson,Teresa Orlowska-Kowalska,Seiichiro Katsura +5 more
TL;DR: The Kalman filter has received a huge interest from the industrial electronics community and has played a key role in many engineering fields since the 1970s, ranging from trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal processing, and so on.
Journal ArticleDOI
Design of a Fault-Tolerant Controller Based on Observers for a PMSM Drive
TL;DR: Two virtual sensors (a two-stage extended Kalman filter and a back-electromotive-force adaptive observer) and a maximum-likelihood voting algorithm are combined with the actual sensor to build a fault-tolerant controller (FTC).
Journal ArticleDOI
Optimal two-stage Kalman filter in the presence of random bias
J. Y. Keller,Mohamed Darouach +1 more
TL;DR: It is shown that the state estimate can be expressed as xkk = xkk + βkkbkk where xkk is a modified bias-free state estimate and bkk the optimal estimate of random bias.
Journal ArticleDOI
Technical communique: Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs
TL;DR: The resulting filter is an extension of the recursive three-step filter (ERTSF) and serves as a unified solution to the addressed unknown input filtering problem.
Journal ArticleDOI
A Two-Stage Augmented Extended Kalman Filter as an Observer for Sensorless Valve Control in Camless Internal Combustion Engines
TL;DR: A proposed observer comprising an augmented extended Kalman filter and another EKF results in a sensorless control, which estimates the inductance of the actuator, which may vary, and achieves a numerically efficient estimation.
References
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Journal ArticleDOI
Treatment of bias in recursive filtering
TL;DR: In this article, the problem of estimating the state x of a linear process in the presence of a constant but unknown bias vector b is considered, and it is shown that the optimum estimate \hat{x} of the state can be expressed as x + V_{x}\hat{b} (1) where x is the bias-free estimate, computed as if no bias were present, and V x is a matrix which can be interpreted as the ratio of the covariance of \tilde{x] and b to the variance of b.
Journal ArticleDOI
Separate bias Kalman estimator with bias state noise
TL;DR: A modified decoupled Kalman estimator suitable for use when the bias vector varies as a random-walk process is defined and demonstrated in a practical application consisting of the calibration of a strapdown inertial navigation system.
Journal ArticleDOI
An alternate derivation and extension of Friendland's two-stage Kalman estimator
TL;DR: An alternate simplified derivation of Friedland's two-stage Kalman estimator for a somewhat more general class of problems than considered by Friedland is given in this article, which is also extended to encompass two variations on the basic idea which are of practical interest.
Journal ArticleDOI
On the optimality of two-stage state estimation in the presence of random bias
TL;DR: Sufficient conditions for the optimality of a two-stage state estimator in the presence of random bias are derived and it is indicated that for most practical systems the proposed solution to the two- stage estimation problem will be suboptimal.
Journal ArticleDOI
Extension of Friedland's separate-bias estimation to randomly time-varying bias of nonlinear systems
TL;DR: A pseudo-separate-bias estimation algorithm for randomly time-Varying bias of a class of nonlinear time-varying stochastic systems is obtained and a simulation example is presented to illustrate the effectiveness of the algorithm.