A partially linearized sigma point filter for latent state estimation in nonlinear time series models

A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment-matching algorithm and then a linear programming based procedure is used in the update step of the state estimation. The effectiveness of the new filtering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process.

[1]  Alois Geyer,et al.  A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure , 1999 .

[2]  Aurora Hermoso-Carazo,et al.  Different approaches for state filtering in nonlinear systems with uncertain observations , 2007, Appl. Math. Comput..

[3]  H. Kushner.  Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

[4]  Bjarne A. Foss,et al.  Constrained nonlinear state estimation based on the UKF approach , 2009, Comput. Chem. Eng..

[5]  Nilanjan Saha,et al.  Extended Kalman filters using explicit and derivative-free local linearizations , 2009 .

[6]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[7]  Dennis S. Bernstein,et al.  Data assimilation for magnetohydrodynamics systems , 2006 .

[8]  Guiming Wang,et al.  On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models , 2007 .

[9]  P. Houtekamer,et al.  Data Assimilation Using an Ensemble Kalman Filter Technique , 1998 .

[10]  Paresh Date,et al.  A new algorithm for latent state estimation in non-linear time series models , 2008, Appl. Math. Comput..

[11]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[12]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[13]  G. Grimmett,et al.  Probability and random processes , 2002 .

[14]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[15]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[16]  Paresh Date,et al.  A new moment matching algorithm for sampling from partially specified symmetric distributions , 2008, Oper. Res. Lett..

[17]  A. Farina,et al.  Tracking a ballistic target: comparison of several nonlinear filters , 2002 .

[18]  Hisashi Tanizaki,et al.  Prediction, filtering and smoothing in non-linear and non-normal cases using Monte Carlo integration , 1994 .

[19]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[20]  L. A. Bauer.  Inauguration of the magnetic survey of the North Pacific Ocean , 1905 .

[21]  J. C. Jimenez,et al.  Local linearization filters for non-linear continuous-discrete state space models with multiplicative noise , 2003 .

[22]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[23]  Gregory L. Plett,et al.  Sigma-point Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 1: Introduction and state estimation , 2006 .

[24]  Ali Esmaili,et al.  Probability and Random Processes , 2005, Technometrics.

[25]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[26]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[27]  Yingmin Li,et al.  Unscented Kalman filter for time varying spectral analysis of earthquake ground motions , 2009 .

[28]  R. Saigal.  Linear Programming: A Modern Integrated Analysis , 1995 .

[29]  Yin Zhang,et al.  Linear Programming: A Modern Integrated Analysis (Romesh Saigal) , 1996, SIAM Rev..