Abstract
We present a new method for the state estimation, based on uncertainty quantification (UQ), which allows efficient numerical determination of probability distributions. We adapt these methods in order to allow the representation of the probability distribution of the state. By assuming that the mean corresponds to real state (i.e; that there is no bias in measurements), the state is estimated. UQ determines expansions of an unknown random variable as functions of given ones. The distributions may be quite general—namely, Gaussian/normality assumptions are not necessary. In the framework of state estimation, the natural given variables are the measurement errors, which may be partially or totally unknown. We examine these situations and we show that an artificial variable may be used instead the real one. We examine three approaches for the determination of the probability distribution of the state: moment matching (MM), collocation (COL) and variational (VAR). We show that the method is effective to calculate by using two significant examples: a classical discrete linear system containing difficulties and the Influenza in a boarding school. In all these examples, the proposed approach was able to accurately estimate the values of the state variables. The approach may also be used for non-additive noise and for the determination of the distribution of the noise.
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References
Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME J Basic Eng 82(D):35–45
Evensen G (2009) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res 99:10143–10162
Estumano D, Orlande H, Colaco M, Dulikravich G (2013) State estimation problem for Hodgkin-Huxley’s model: a comparison of particle filter algorithms. In: Proceedings of the 4th inverse problems, design and optimization symposium (IPDO-2013)
Madankan R, Singla P, Singh T, Scott PD (2013) Polynomial-chaos-based bayesian approach for state and parameter estimations. J Guid Contl Dyn 36(4):1058–1074
Wiener N (1938) The homogeneous chaos. Amer J Math 60(23–26):897–936
Xiu D, Karniadakis GE (2002) The wiener-askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644
Lopez RH, de Cursi ES, Lemosse D (2011) Approximating the probability density function of the optimal point of an optimization problem. Eng Optim 43(3):281–303
Lopez RH, Miguel LFF, de Cursi ES (2013) Uncertainty quantification for algebraic systems of equations. Comput Struct 128:89–202
de Cursi ES (2015) Uncertainty quantification and stochastic modelling with matlab. ISTE Press, London and Elsevier, Oxford
de Cursi ES, Lopez RH, Carlon AC (2016) A new filter for state estimation. In: 18th scientific convention on engineering and architecture, La Havana, Cuba, Nov 2016
Lopez RH, de Cursi ES, Carlon AG (2017) A state estimation approach based on stochastic expansions. Comput Appl Math. https://doi.org/10.1007/s40314-017-0515-0
Bassi M, de Cursi ES, Ellaia R (2016) Generalized fourier series for representing random variables and application for quantifying uncertainties in optimization. In: Proceedings of the 3rd international symposium on stochastic modelling and uncertainty quantification (Uncertainties 2016). http://www.swge.inf.br/PDF/USM-2016-0037_027656.PDF
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This work is partially financed by the European Union with the European regional development fund (ERDF) and by the Normandie Regional Council.
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de Cursi, E.S., Lopez, R.H., Carlon, A.G. (2019). A New Approach for State Estimation. In: Canavero, F. (eds) Uncertainty Modeling for Engineering Applications. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-030-04870-9_3
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DOI: https://doi.org/10.1007/978-3-030-04870-9_3
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