Kalman Filtering for a Quadratic Form State Equality Constraint

Wang, Dayi; Li, Maodeng; Huang, Xiang‐Yu; Li, Ji

doi:10.2514/1.62890

Cited by 10 publications

(15 citation statements)

References 19 publications

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“…Section IV presents two applications of the proposed method. The first application in Section IV.A is quadratically constrained Kalman filtering of the form in [4,5]. It is shown here that for such a filter with a quadratic state estimate constraint, the constrained Kalman filter reduces to an orthogonal projection of the unconstrained Kalman estimate onto the constraint surface, analogous to the norm-constrained case in [4] -another contribution of this paper.…”

Section: Introductionmentioning

confidence: 92%

“…Aerospace problems such as finding an optimal sun vector from coarse sun sensor measurements [1,2], or converting a vehicle's cartesian coordinates to geodetic coordinates [3] involve solving least squares problems with quadratic constraints. Least squares problems with quadratic constraints also arise in aerospace vehicle state estimation problems [4,5]. Therefore, this paper treats the quadratically constrained least squares problem with positive semi-definite weight matrix.…”

Section: Introductionmentioning

confidence: 99%

“…However, as demonstrated in Section II, this places a restriction on the quadratically constrained least squares problems that can be solved in this way. Recently, it was demonstrated in [5] that the finding the roots of the rational equation is equivalent to finding the eigenvalues of an associated companion matrix. This is accomplished by writing the rational function in terms of a common denominator, and then setting the numerator, which is a polynomial, equal to zero.…”

Section: Introductionmentioning

confidence: 99%

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Quadratically Constrained Least Squares with Aerospace Applications

Ruiter

2016

Journal of Guidance, Control, and Dynamics

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This paper treats the problem of quadratically constrained least squares, with positive semi-definite weight matrices. A new method of solution is presented that searches directly over the constraint set, and does not require the determination of Lagrange multipliers. Global convergence of the algorithm is rigorously proven. In addition, a covariance analysis is performed for the constrained optimal solution. Two aerospace applications are presented: 1) quadratically constrained Kalman filtering similar in form to the norm-constrained Kalman filter from the literature-it is shown that the optimal quadratically constrained update is simply an orthogonal projection of the optimal unconstrained update onto the constraint set, 2) a new quadratically constrained Kalman filter using the covariance expression developed in this paper, yielding a statistically more consistent constrained filter. The new filter is demonstrated numerically with a spacecraft attitude estimation example.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quadratically Constrained Least Squares with Aerospace Applications

Ruiter

2016

Journal of Guidance, Control, and Dynamics

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“…Solving (16) results in the optimal gain M k of (14), which yields the MVU estimatex c k under the equality constraint (10). QED Note that the constrained Kalman filter (CKF) (12) with optimal gain (14) is the same as the CKF which is obtained by solving (11) and setting W = P −1 k|k .…”

Section: Estimate Projection With the Kalman Fil-ter Estimatementioning

confidence: 99%

“…Although many constrained filters have been proposed, estimate projection is the most commonly used approach for constraint enforcement [9]. In [10] Kalman filtering with quadratic equality state constraints is developed using Lagrangian multipliers. The most recent developments in constrained Kalman filtering are evaluated in [11], where a constrained Kalman-like filter for continuous-time constrained systems is considered with respect to a group of orthonormal matrices.…”

Section: Introductionmentioning

confidence: 99%

Maximum Correntropy Criterion Constrained Kalman Filter

Fakoorian

Moosavi

Izanloo

et al. 2017

Volume 2: Mechatronics; Estimation and Identification; Uncertain Systems and Robustness; Path Planning and Motion Control; Trac

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Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

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