Estimation of general nonlinear state-space systems

Ninness, Brett; Wills, Adrian; Schön, Thomas B.

doi:10.1109/cdc.2010.5717378

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…It is interesting to visually observe the effect of using the global GP model offered by Algorithm 2 in terms of smoothing the cost function. The current example is known to exhibit erratic likelihood behaviour at extreme points in the parameter space [29]. This is perhaps best visualised by restricting to just one parameter, in this case the b parameter.…”

Section: Simple Linear Examplementioning

confidence: 95%

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On the construction of probabilistic Newton-type algorithms

Wills

Schön

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closedform expressions available.

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Section: Simple Linear Examplementioning

confidence: 95%

“…The likelihood and its gradient cannot be calculated exactly in this case and we therefore employed sequential Monte Carlo methods and Fisher's identity [28,29] to provide noisy estimates of both. The number of particles used to calculate these terms was 500 in all cases.…”

Section: More Challenging Nonlinear Examplementioning

confidence: 99%

On the construction of probabilistic Newton-type algorithms

Wills

Schön

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…Other examples of techniques that employ the EM algorithm in a maximum likelihood framework, and that use particle smoothing are presented in [19] and [20]. The same authors propose in [21] a different approach that makes use of Fisher's identity and particle smoothing for gradient computation.…”

Section: A Related Workmentioning

confidence: 99%

Improved Initialization for Nonlinear State-Space Modeling

Marconato

Sjöberg

Suykens

et al. 2014

IEEE Trans. Instrum. Meas.

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This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the model. In particular, the nonlinear dynamic problem is transformed into an approximate static formulation, and simple regression methods are applied to obtain the solution in a fast and efficient way. The proposed method is validated by means of two measurement examples: the Wiener-Hammerstein benchmark problem, and the identification of a crystal detector.A. Marconato and J. Schoukens are with

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“…particle smoother). A PEM estimator based on the optimal Mean-Square Error (MSE) one-step ahead predictor was suggested in [48]. In [67], a MCEM algorithm, in the same spirit of [54], was used; but this time a rejection sampling based particle smoother [14] was employed.…”

Section: Introductionmentioning

confidence: 99%

Linear prediction error methods for stochastic nonlinear models

Abdalmoaty

Hjalmarsson

2019

Automatica

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The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.

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Estimation of general nonlinear state-space systems

Cited by 11 publications

References 26 publications

On the construction of probabilistic Newton-type algorithms

On the construction of probabilistic Newton-type algorithms

Improved Initialization for Nonlinear State-Space Modeling

Linear prediction error methods for stochastic nonlinear models

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