On robust Kalman filtering

Kovačevíc, Branko; Đurović, Željko; Glavaski, S.

doi:10.1080/00207179208934328

Cited by 43 publications

(32 citation statements)

References 19 publications

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“…Another approach to the state estimation under unknown noise CMs is robust estimation, which respects uncertainty of the CMs and other model parameters and provides “conservative estimates” …”

Section: Discussion and Comparison Of Noise CM Estimation Methodsmentioning

confidence: 99%

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

111

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This paper deals with the estimation of the noise covariance matrices of systems described by state-space models. Stress is laid on the systematic survey and classification of both the recursive and batch processing methods proposed in the literature with a special focus on the correlation methods. Besides the correlation methods, representatives of other groups are introduced also with respect to their basic idea, estimate properties, assumptions and possible extensions, and user-defined parameters. Common and dual properties of the methods are highlighted, and a simulation comparison using exemplary MATLAB implementations of the methods is provided. KEYWORDSadaptive systems, noise covariance matrix, state estimation, state-space model, system identification INTRODUCTIONKnowledge of a system model is a key prerequisite for many state estimation, signal processing, fault detection, and optimal control problems. The model is often designed to be consistent with random behaviour of the system quantities and properties of the measurements. While the deterministic part of the model often arises from mathematical modelling on the basis of physical, chemical, or biological laws governing the behaviour of the system, the statistics of the stochastic part are often difficult to find by the modelling and have to be identified using the measured data. Incorrect description of the noise statistics may result in significant worsening of estimation, signal processing, detection, or control quality or even in a failure of the underlying algorithms.In the last 5 decades, therefore, a significant research interest has been focused on a design of the methods for the estimation of the properties of the stochastic part of the model. The attention has been devoted to both the input-output models 1-5 and the state-space (SS) models 6-14 and both recursive and batch processing methods. This paper focuses on the methods estimating the properties of the stochastic part of the system described by an SS model discrete in time. In particular, the methods estimating the covariance matrices (CMs) † of noises in the state and measurement equation from a sequence of measured data are of interest. The methods are further denoted as the noise CM estimation methods.

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Section: Discussion and Comparison Of Noise CM Estimation Methodsmentioning

confidence: 99%

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

111

View full text Add to dashboard Cite

show abstract

“…It was shown in [5,10] that Eqs. 16-18 form an equivalent Kalman filtering algorithm based on LS criterion witĥ bðtÞ ¼xðt=tÞ and Pðt=tÞ ¼ covðbðtÞÞ: As seen in Eq.…”

Section: Kalman Filter With Variable Number Of Measurements-based Psdmentioning

confidence: 97%

“…This generalization is intended to achieve a better bias-variance tradeoff in the state tracking and hence representing a clearer time-frequency content of the signal to be analyzed. The proposed KFVNM algorithm is motivated from the work in [5,10], where a new Kalman filter recursion using the equivalence between the Kalman filter and a particular least-squares (LS) regression problem was proposed. First, we rewrite the linear state-space model in Eqs.…”

Section: Kalman Filter With Variable Number Of Measurements-based Psdmentioning

confidence: 99%

“…On the other hand, parametric methods assume the signals under analysis can be modeled as the output of a linear system where the input is white noise. In general, nonparametric methods have lower computational complexity than parametric methods, while parametric methods can provide higher frequency resolutions if the observations can be adequately explained by the model and the SNR is sufficiently high [10].…”

Section: Introductionmentioning

confidence: 99%

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A novel method for nonstationary power spectral density estimation of cardiovascular pressure signals based on a Kalman filter with variable number of measurements

Zhang

Tsui

Chan

et al. 2008

Med Biol Eng Comput

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We present a novel parametric power spectral density (PSD) estimation algorithm for nonstationary signals based on a Kalman filter with variable number of measurements (KFVNM). The nonstationary signals under consideration are modeled as time-varying autoregressive (AR) processes. The proposed algorithm uses a block of measurements to estimate the time-varying AR coefficients and obtains high-resolution PSD estimates. The intersection of confidence intervals (ICI) rule is incorporated into the algorithm to generate a PSD with adaptive window size from a series of PSDs with different number of measurements. We report the results of a quantitative assessment study and show an illustrative example involving the application of the algorithm to intracranial pressure signals (ICP) from patients with traumatic brain injury (TBI).

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“…measurement update (Kovacevic et al 1992;Durgaprasad and Thakur, 1998). The Huber M-estimation methodology is essentially based on modifying the quadratic cost function in the filter framework, and works between smooth ℓ 2 -norm properties for small residuals and robust ℓ 1 -norm properties for large residuals (Petrus, 1999).…”

mentioning

confidence: 99%

Robust Huber-Based Cubature Kalman Filter for GPS Navigation Processing

2016

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A robust state estimation technique based on the Huber-based Cubature Kalman Filter (HCKF) is proposed for Global Positioning System (GPS) navigation processing. The Cubature Kalman Filter (CKF) employs a third-degree spherical-radial cubature rule to compute the Gaussian weighted integration, such that the numerical instability induced by round-off errors can be avoided. In GPS navigation, the filter-based estimation of the position and velocity states can be severely degraded due to contaminated measurements caused by outliers or deviation from a Gaussian distribution assumption. For the signals contaminated with non-Gaussian noise or outliers, a robust scheme combining the Huber M-estimation methodology and the CKF framework is beneficial where the Huber M-estimation methodology is used to reformulate the measurement information of the CKF. GPS navigation processing using the HCKF algorithm has been carried out and the performance has been compared to those based on the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and CKF approaches. Simulation and experimental results presented in this paper confirm the effectiveness of the method. K E Y WO R D S 1. GPS navigation.2. Unscented Kalman filter. 3. Cubature Kalman filter 4. Huber M-estimation.

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On robust Kalman filtering

Cited by 43 publications

References 19 publications

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

A novel method for nonstationary power spectral density estimation of cardiovascular pressure signals based on a Kalman filter with variable number of measurements

Robust Huber-Based Cubature Kalman Filter for GPS Navigation Processing

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