1985
DOI: 10.6028/jres.090.032
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Adaptive Kalman Filtering

Abstract: The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimation with erroneous models.Modifications to the filter involve allowing the filter to adapt the measurement model to the… Show more

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Cited by 31 publications
(15 citation statements)
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“…Therefore, the estimate of the optimal weight vectorŵ c would be able to follow the variations in the optimal weight vector due to the nonlinear, nonstationary, and heterogeneous noise environment. A typical choice of Ψ p 2 ¼10 À 4 can be considered for the nonstationary case [7,25,27], but for a stationary environment the value of Ψ 2 p ¼ 0, since a time-invariant system weight vector does not change with time [7,8,24,25,29].…”
Section: Sequential Subspace Estimatormentioning
confidence: 99%
See 1 more Smart Citation
“…Therefore, the estimate of the optimal weight vectorŵ c would be able to follow the variations in the optimal weight vector due to the nonlinear, nonstationary, and heterogeneous noise environment. A typical choice of Ψ p 2 ¼10 À 4 can be considered for the nonstationary case [7,25,27], but for a stationary environment the value of Ψ 2 p ¼ 0, since a time-invariant system weight vector does not change with time [7,8,24,25,29].…”
Section: Sequential Subspace Estimatormentioning
confidence: 99%
“…Starting from Eq. (29), the SSE's computational complexity for Jacobian evaluation is OðN 2 Þ. The complexity for Eq.…”
Section: Computational Complexitymentioning
confidence: 99%
“…Linear KF (LKF) is utilized for SF in most cases because there is no accurate knowledge available for the state-space model [15]. In this paper, a covariance-matching technique is utilized in the state-space model of SF because this intuitive technique can be implemented easily with low computational costs [13,15,27,33].…”
Section: Dual Adaptive Filtering For Measurement Noise Estimationmentioning
confidence: 99%
“…The noise covariance matrices are defined as time-varying matrices, but it is difficult to define how these matrices evolve over time. Some stochastic filters define mathematical expressions for these two noise covariance matrices, obtaining new matrices for each discrete time instant k ∈ N. They are the Adaptive Kalman Filter (AKF) (Brown and Rutan, 1985), the Adaptive Extended Kalman Filter (AEKF) (Nayak et al, 2016) and the Optimal Adaptive Kalman Filter (OAKF) (Yang and Gao, 2006) . Some of these filters are applied to target tracking problems as in Kumar et al (2017); Tripathi et al (2016); Dang (2008).…”
Section: Introductionmentioning
confidence: 99%