Kalman filtering with state equality constraints

Simon, Daniel J.; Chia, Tien Li

doi:10.1109/7.993234

Cited by 512 publications

(463 citation statements)

References 18 publications

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“…Another approach to constrained filtering is to project the unconstrained estimate xt of the Kalman filter onto the constraint surface [13,16]. The constrained estimate can therefore be written as (23) such that Dx= d, (24) where Wis a positive-definite weighting matrix.…”

Section: Estimate Projectionmentioning

confidence: 99%

“…Section 2 considers linear systems and linear constraints. The various ways of enforcing linear constraints in the linear Kalman filter include model reduction [15], perfect measurements [8 -10], estimate projection [13,16], gain projection [17, 1S], probability density function (PDF) truncation [2,19,20], and system projection [21]. Under certain conditions, all these approaches result in the same state estimate.…”

Section: Introductionmentioning

confidence: 99%

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Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Simon

2010

IET Control Theory Appl.

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778

468

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The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.

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Section: Estimate Projectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Simon

2010

IET Control Theory Appl.

Self Cite

778

468

View full text Add to dashboard Cite

show abstract

“…This study uses a pseudo-measurement method, one of the constrained Kalman filtering algorithms, which treats the equality constraints as additional fictitious or pseudo-measurement [20]. Unlike the other approaches such as maximum probability method and projection method [21], this has the advantage which allows us to consider the degree of constraint adherence by the magnitude of the additional pseudo-measurement noise variance.…”

Section: B Road-constrained Estimationmentioning

confidence: 99%

Airborne behaviour monitoring using Gaussian processes with map information

Shin

Kim

et al. 2013

IET Radar, Sonar & Navigation

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“…Such relationships can be treated as additional constraints or penalty functions to improve tracking performance [6,15]. In this paper, however, we simply augment the Doppler estimates,…”

Section: Instantaneous Target Altitude Estimationmentioning

confidence: 99%

Instantaneous altitude estimation of maneuvering target in over-the-horizon radar exploiting multipath Doppler signatures

Zhang

Amin

et al. 2013

EURASIP J. Adv. Signal Process.

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Over-the-horizon radar systems are capable of localizing targets in range and azimuth but are unable to achieve reliable altitude estimation. Past work has shown that the time-varying Doppler signatures of micro-multipath signals provide rich information for reliable estimation of altitude changes. In this paper, we develop a new technique for the estimation of instantaneous altitude of maneuvering targets by exploiting the estimated multicomponent Doppler signatures. A key contribution of this paper is to apply effective non-stationary signal analysis techniques for estimating the time-varying Doppler signature of each individual multipath. This enables reliable target altitude estimation in an extended Kalman filter setup. The maximum a-posteriori criterion is used for the estimation of initial target states.

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Kalman filtering with state equality constraints

Cited by 512 publications

References 18 publications

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Airborne behaviour monitoring using Gaussian processes with map information

Instantaneous altitude estimation of maneuvering target in over-the-horizon radar exploiting multipath Doppler signatures

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