Extending the Kalman filter for structured identification of linear and nonlinear systems

Best, Matt C.; Bogdanski, Karol

doi:10.1504/ijmic.2017.082952

Cited by 12 publications

(13 citation statements)

References 13 publications

(14 reference statements)

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“…An initialisation of all the parameters is needed; these can be nominally set to zero, or alternatively a simple linear identification can be performed on the data using the structure represented in eq.10 with constant elements in A, B, C and D. For further information on the linear identification see [14]. In this case, each of the parameters in the linear state space model initialises the relative nonlinear function: all the ( )…”

Section: Methodsmentioning

confidence: 99%

A new structure for non-linear black-box system identification using the extended Kalman filter

Bogdanski

Best

2017

Proceedings of the Institution of Mechanical Engineers, Part D:

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The method works iteratively in the time domain using an Extended Kalman Filter. The model retains a state space structure in modal canonical form, which ensures that a minimal number of parameters need to be identified and also produces additional information in terms of system eigenvalues and dominant modes. This structure is completely black-box, requiring no physical understanding of the process for successful identification, and it is possible to easily expand the order and complexity of nonlinearities, whilst ensuring good parameter conditioning. A simple nonlinear example illustrates the method, and identification of a highly nonlinear brake model is also presented. These examples show the method can be applied as a mechanism for model order reduction; it is equally well suited as a tool for nonlinear plant system identification. In both capacities this new method is valuable, particularly as the generation of simplified models for the whole vehicle and its subsystems is an increasingly important aspect of modern vehicle design.

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Section: Methodsmentioning

confidence: 99%

A new structure for non-linear black-box system identification using the extended Kalman filter

Bogdanski

Best

2017

Proceedings of the Institution of Mechanical Engineers, Part D:

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“…Both filters require covariance estimates and here Q is fixed throughout as Q = ρI, with ρ =1e-7 (see [3] for more detail). For any given estimate θ of the identified parameters, R can be obtained numerically from the covariance of υ using eqn (2).…”

Section: Methodsmentioning

confidence: 99%

“…This is achievable, given recent findings that Kalman filter methods can be applied to identify all parameters in any wellconditioned model structure [3].…”

Section: Introductionmentioning

confidence: 98%

Full vehicle and tyre identification using unscented and extended identifying Kalman filters

Best¹,

Bogdanski²

2016

Advanced Vehicle Control AVEC’16

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• This is an Accepted Manuscript of a book chapter published by [1,2]. The validity of these (necessarily simplified) models also depends on many other fixed, estimated parameters. Usually, even if these other values are physically accurately set, the simplified model can be made to perform better if they are tuned or also identified.Here we embark on an ambitious attempt to identify all the independent parameters in a simplified whole vehicle handling model, including yaw and roll freedoms, independent combined-slip load dependent tyres and appropriate drivetrain lags. This is achievable, given recent findings that Kalman filter methods can be applied to identify all parameters in any wellconditioned model structure [3].In the extended abstract we demonstrated the principle by simulated identification of longitudinal tyre dynamics, including wheel-spin and lock, using an Extended Kalman Filter. In this final paper we consider data collected from a test vehicle carrying out medium to high magnitude manoeuvres including wheel-spin and terminal understeer, in order to build a model which is valid over the whole range of the tyres. We also consider the relative advantages over EKF of using the more computationally efficient, Unscented Kalman Filter for the identification process.

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“…Both Kalman filters require covariance estimates and here Q is fixed throughout as Q = ρI. ρ is the only tuning parameter in both Kalman filters; it weighs the expectation of accuracy of the model f, and particularly the assumptionθ = 0, so it controls the variation rate of the parameters (see [9] for more detail). For any given estimateθ of the identified parameters, R can be obtained numerically from the covariance of υ using Equation (2); here, R is recomputed after each iteration.…”

Section: Implementation In a Simplified Case -Identification Of A Linmentioning

confidence: 99%

“…Several authors have successfully employed EKF to identify a limited number of model parameters, which are concatenated to the state vector and estimated simultaneously with the true states [6,7]. This approach has later been extended to wholly concentrate on parameter estimation [8] and recent findings suggest that Kalman filter methods can be applied to identify all the parameters of any well-conditioned model structure [9]. The Unscented Kalman filter (UKF) has emerged in the last two decades as the main alternative to EKF.…”

Section: Introductionmentioning

confidence: 99%

Kalman and particle filtering methods for full vehicle and tyre identification

Bogdanski

Best

2017

Vehicle System Dynamics

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This paper considers identification of all significant vehicle handling dynamics of a test vehicle, including identification of a combinedslip tyre model, using only those sensors currently available on most vehicle controller area network buses. Using an appropriately simple but efficient model structure, all of the independent parameters are found from test vehicle data, with the resulting model accuracy demonstrated on independent validation data. The paper extends previous work on augmented Kalman Filter state estimators to concentrate wholly on parameter identification. It also serves as a review of three alternative filtering methods; identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are proposed and compared for effectiveness, complexity and computational efficiency. All three filters are suited to applications of system identification and the Kalman Filters can also operate in real-time in on-line model predictive controllers or estimators. ARTICLE HISTORY

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Extending the Kalman filter for structured identification of linear and nonlinear systems

Cited by 12 publications

References 13 publications

A new structure for non-linear black-box system identification using the extended Kalman filter

A new structure for non-linear black-box system identification using the extended Kalman filter

Full vehicle and tyre identification using unscented and extended identifying Kalman filters

Kalman and particle filtering methods for full vehicle and tyre identification

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