Nonlinear state space model identification using a regularized basis function expansion

@article{Svensson2015NonlinearSS,
  title={Nonlinear state space model identification using a regularized basis function expansion},
  author={Andreas Svensson and Thomas Bo Sch{\"o}n and A. Solin and Simo S{\"a}rkk{\"a}},
  journal={2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
  year={2015},
  pages={481-484}
}
This paper is concerned with black-box identification of nonlinear state space models. By using a basis function expansion within the state space model, we obtain a flexible structure. The model is identified using an expectation maximization approach, where the states and the parameters are updated iteratively in such a way that a maximum likelihood estimate is obtained. We use recent particle methods with sound theoretical properties to infer the states, whereas the model parameters can be… 
View on IEEE
arxiv.org
6 Citations
Background Citations
3
Methods Citations
2
Results Citations
1

Figures and Tables from this paper

6 Citations

A flexible state space model for learning nonlinear dynamical systems
Online Joint State Inference and Learning of Partially Unknown State-Space Models
TLDR
The method is exemplified via two intelligent vehicle applications where it is shown to have competitive system dynamics estimation performance compared to the globally supported basis function method, and be real-time applicable to problems with a large-scale state-space.
A robust and efficient system identification method for a state-space model with heavy-tailed process and measurement noises
TLDR
A robust and efficient system identification method is proposed for a state-space model with heavy-tailed process and measurement noises by using the maximum likelihood criterion and an expectation maximization algorithm is derived by treating auxiliary random variables as missing data.
Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model
TLDR
The use of the augmented state-space model gives both a reduced estimation error and bias and to facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented.
Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method
TLDR
This paper presents a two-step instrumental variable method to obtain the regularized and consistent parameter estimates of the Hammerstein ARMAX model based on the bilinear parameterized form and shows that in a stochastic environment the proposed IV method produces consistent estimates in the presence of correlated noise disturbances.
Learning probabilistic models of dynamical phenomena using particle filters
TLDR
This thesis studies and develops methods and probabilistic models for statistical learning of dynamical behavior in real-life phenomena, typically as a dependence over time.

References

SHOWING 1-10 OF 27 REFERENCES
Learning Nonlinear Dynamical Systems Using an EM Algorithm
TLDR
A generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems if Gaussian radial basis function (RBF) approximators are used to model the nonlinearities, the integrals become tractable and the maximization step can be solved via systems of linear equations.
Modelling and Identification with Rational Orthogonal Basis Functions
Computationally Efficient Bayesian Learning of Gaussian Process State Space Models
TLDR
A procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure, which allows for a fully Bayesian treatment of the problem.
Regularized system identification using orthonormal basis functions
TLDR
The regularization method is extended from impulse response estimation to the more general orthonormal basis functions estimation and it is shown that the former is a special case of the latter, and more specifically, theFormer is equivalent to ridge regression of the coefficients of the orthonorm basis functions.
Expectation maximization based parameter estimation by sigma-point and particle smoothing
TLDR
A unified view of approximative EM algorithms that use either sigma-point or particle smoothers to evaluate the integrals involved in the expectation step of the EM method is presented, and these methods are compared to direct likelihood maximization.
Robust maximum-likelihood estimation of multivariable dynamic systems
The Recursive Bayesian Estimation Problem via Orthogonal Expansions: an Error Bound
Abstract When solving the non linear non Gaussian filtering problem via orthognal series expansions the involved probability density functions are approximated with truncated series expansions.…
On the estimation of transfer functions, regularizations and Gaussian processes - Revisited
An efficient stochastic approximation EM algorithm using conditional particle filters
  • F. Lindsten
  • Computer Science
    2013 IEEE International Conference on Acoustics, Speech and Signal Processing
  • 2013
TLDR
The proposed method combines the efficient conditional particle filter with ancestor sampling (CPF-AS) with the stochastic approximation EM (SAEM) algorithm, which results in a procedure which does not rely on asymptotics in the number of particles for convergence, meaning that the method is very computationally competitive.
Identification of nonlinear systems using Polynomial Nonlinear State Space models
...
...