Analysis of continuous-time Kalman filtering under incorrect noise covariances

Sangsuk-Iam, S.; Bullock, T. E.

doi:10.1016/0005-1098(88)90113-6

Cited by 12 publications

(3 citation statements)

References 23 publications

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“…. Before presenting Student's t-filter, we note that the effect of (partial) model misspecification as above to behaviour and stability of the Kalman filter has been studied for discrete-time systems in [26]- [30] and for continuous-time systems in [31].…”

Section: B the (Misspecified) Kalman Filtermentioning

confidence: 99%

Student's <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula>-Filters for Noise Scale Estimation

Tronarp

Karvonen

Särkkä

2019

IEEE Signal Process. Lett.

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We analyse certain Student's t-filters for linear Gaussian systems with misspecified noise covariances. It is shown that the under appropriate conditions the filter both estimates the state and re-scales the noise covariance matrices in a Kullback-Leibler optimal fashion. If the noise covariances are misscaled by a common scalar, then the re-scaling is asymptotically exact. We also compare the Student's t-filter scale estimates to the maximum likelihood estimates. Simulations demonstrating the results on the Wiener velocity model are provided.

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Section: B the (Misspecified) Kalman Filtermentioning

confidence: 99%

Student's <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula>-Filters for Noise Scale Estimation

Tronarp

Karvonen

Särkkä

2019

IEEE Signal Process. Lett.

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“…Traditionally, the CMs are either predetermined through extensive experimentation or are artificially inflated to adopt a conservative strategy. The case when inaccurate noise covariances are used is known to cause filter divergence [3,4,5,6,7,8]. These challenges motivate adaptive algorithms for state estimation while simultaneously estimating the noise CMs.…”

Section: Introductionmentioning

confidence: 99%

Riemannian Trust-Region based Adaptive Kalman filter with unknown noise Covariance matrices

Moghe,

Akella,

Zanetti

2021

Preprint

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The problem of adaptive Kalman filtering for a discrete observable linear time-varying system with unknown noise covariance matrices is addressed in this paper. The measurement difference autocovariance method is used to formulate a linear least squares cost function containing the measurements and the process and measurement noise covariance matrices. Subsequently, a Riemannian trust-region optimization approach is designed to minimize the least squares cost function and ensure symmetry and positive definiteness for the estimates of the noise covariance matrices. The noise covariance matrix estimates, under sufficient excitation of the system, are shown to converge to their unknown true values. Saliently, the exponential stability and convergence guarantees for the proposed adaptive Kalman filter to the optimal Kalman filter with known noise covariance matrices is shown to be achieved under the relatively mild assumptions of uniform observability and uniform controllability. Numerical simulations on a linear time-varying system demonstrate the effectiveness of the proposed adaptive filtering algorithm.

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“…Instead of these ad hoc inflation techniques, more sophisticated algorithms have also been developed [7][8][9]. The case when the noise covariance matrices are unknown has been shown to cause filter divergence [10][11][12][13][14][15]. These challenges associated with filter divergence provided motivation for the development of adaptive filtering algorithms that simultaneously estimate the system states along with the covariance matrices.…”

mentioning

confidence: 99%

Adaptive Kalman Filter for Detectable Linear Time-Invariant Systems

Moghe

Zanetti

Akella

2019

Journal of Guidance, Control, and Dynamics

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A novel covariance matching technique is proposed for estimating the states and unknown entries of the process and measurement noise covariance matrices for additive white Gaussian noise elements in a linear Kalman filter. Under this assumption of detectability (i.e., unobservable modes remain stable), the stability and convergence properties of the covariance matching Kalman filter are established. It is shown that the measurement covariance matrix cannot be unambiguously estimated if the measurement model contains linearly dependent measurements. Monte Carlo simulations evaluate the numerical properties of the proposed algorithm.

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Analysis of continuous-time Kalman filtering under incorrect noise covariances

Cited by 12 publications

References 23 publications

Student's <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula>-Filters for Noise Scale Estimation

Student's <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula>-Filters for Noise Scale Estimation

Riemannian Trust-Region based Adaptive Kalman filter with unknown noise Covariance matrices

Adaptive Kalman Filter for Detectable Linear Time-Invariant Systems

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