Multiple sparse-grid Gauss-Hermite filtering. (English) Zbl 1459.62178
Summary: A new method for nonlinear estimation, based on sparse-grid Gauss-Hermite filter (SGHF) and state-space partitioning, termed as Multiple sparse-grid Gauss-Hermite filter (MSGHF) is proposed in this work. Gauss-Hermite filter is a widely acclaimed filtering technique for its high accuracy. But the computational load associated with it is so high, that it becomes difficult to apply it on-board for higher dimensional problems. SGHF showcased comparable performance with the GHF, with less computational burden. The proposed technique, MSGHF, further reduces the computational burden considerably, with the filter accuracy remaining almost the same. Simulation results illustrate the performance of the proposed filter with respect to GHF and SGHF.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 93E11 | Filtering in stochastic control theory |
Keywords:
nonlinear filtering; Gauss-Hermite quadrature; sparse-grid; state-space partitioning; Bayesian estimation; complexity reductionReferences:
| [1] | Cho, S. Y.; Kim, B. D., Adaptive IIIR/FIR fusion filter and its application to the INS/GPS integrated system, Automatica, 44, 8, 2040-2047 (2008) · Zbl 1283.93276 |
| [2] | Leong, P. H.; Arulampalam, S.; Lamahewa, T. A.; Abhayapala, T. D., A Gaussian-sum based cubature kalman filter for bearings-only tracking, IEEE Trans. Aerosp. Electron. Syst., 49, 2, 1161-1174 (2013) |
| [3] | Leutbecher, M.; Palmer, T. N., Ensemble forecasting, J. Comput. Phys., 227, 7, 3515-3539 (2008) · Zbl 1132.86308 |
| [4] | Inder, B., Estimating long-run relationships in economics: a comparison of different approaches, J. Econ., 57, 53-68 (1993) · Zbl 0775.62331 |
| [5] | Gordon, N.; Salmond, D. J.; Smith, A. F.M., Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proc. F, 140, 2, 107-113 (1993) |
| [6] | Wu, X.; Wang, Y., Extended and unscented kalman filtering based feedforward neural networks for time series prediction, Appl. Math. Model., 36, 1123-1131 (2012) · Zbl 1243.93115 |
| [7] | Alspach, D. L.; Sorenson, H. W., Nonlinear Bayesian estimation using Gaussian sum approximations, IEEE Trans. Autom. Control, AC-17, 4, 439-448 (1972) · Zbl 0264.93023 |
| [8] | Adiala, V. J.; Hammel, S. E., Utilization of modified polar coordinates for bearings-only tracking, IEEE Trans. Autom. Control, AC-28, 3, 283-294 (1983) · Zbl 0502.93068 |
| [9] | Julier, S.; Uhlmann, J.; Durrant-Whyte, H. F., A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Autom. Control, 45, 3, 477-482 (2000) · Zbl 0973.93053 |
| [10] | Julier, S.; Uhlmann, J., Unscented filtering and nonlinear estimation, Proc. IEEE, 92, 3, 401-422 (2004) |
| [11] | Hermoso-Carazo, A.; Linares-Perez, J., Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems, Appl. Math. Model., 33, 3705-3717 (2009) · Zbl 1185.93133 |
| [12] | Yinfeng, D.; Yingmin, L.; Mingkui, X.; Ming, L., Unscented Kalman filter for time varying spectral analysis of earthquake ground motions, Appl. Math. Model., 33, 398-412 (2009) · Zbl 1167.86306 |
| [13] | Arasaratnam, I.; Haykin, S., Cubature Kalman filters, IEEE Trans. Autom. Control, 54, 6, 1254-1269 (2009) · Zbl 1367.93637 |
| [14] | Arasaratnam, I.; Haykin, S.; Hurd, T., Cubature Kalman filters for continuous-discrete systems: theory and simulations, IEEE Trans. Signal Process., 58, 10, 4977-4993 (2010) · Zbl 1391.93223 |
| [15] | Wang, X.; Liang, Y.; Pan, Q.; Zhao, C.; Yang, F., Design and implementation of Gaussian filter for nonlinear system with randomly delayed measurements and correlated noises, Appl. Math. Comput., 232, 1011-1024 (2014) · Zbl 1410.93131 |
| [16] | Bhaumik, S.; Swati, Cubature quadrature Kalman filter, IET Signal Process., 7, 7, 533-541 (2013) |
| [17] | Singh, A. K.; Bhaumik, S., Higher degree cubature quadrature Kalman filter, Int. J. Control Autom. syst., 13, 5, 1097-1105 (2015) |
| [18] | Ito, K.; Xiong, K., Gaussian filters for nonlinear filtering problems, IEEE Trans. Autom. Control, 45, 5, 910-927 (2000) · Zbl 0976.93079 |
| [19] | Arasaratnam, I.; Haykin, S.; Elliott, R., Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature, Proc. IEEE, 95, 5, 953-977 (2007) |
| [20] | Jia, B.; Xin, M.; Chen, Y., Sparse-grid quadrature nonlinear filtering, Automatica, 48, 2, 327-341 (2012) · Zbl 1260.93161 |
| [21] | Smolyak, S. A., Quadrature and interpolation formulas for tensor products of certain classes of functions, Sov. Math. Dokl., 4, 240-243 (1963) · Zbl 0202.39901 |
| [22] | Closas, P.; Prades, C. F.; Valls, J. V., Multiple quadrature Kalman filtering, IEEE Trans. Signal Process., 60, 12, 6125-6137 (2012) · Zbl 1393.94198 |
| [23] | Golub, G. H.; Welsch, J. H., Calculation of Gauss quadrature rule, Math. Comput., 23, 106, 221-230 (1969) · Zbl 0179.21901 |
| [24] | Niedzwiecki, M.; Kaczmarek, P., Estimation and tracking of complex-valued quasi-periodically varying systems, Automatica, 41, 9, 1503-1516 (2005) · Zbl 1086.93037 |
| [25] | Dash, P. K.; Mallick, R. K., Accurate tracking of harmonic signals in vsc-hvdc systems using pso based unscented transformation, Int. J. Electr. Power Energy Syst., 33, 7, 1315-1325 (2011) |
| [26] | Li, X. R.; Jilkov, V. P., Survey of maneuvering target tracking. part i: dynamic models, IEEE Trans. Aerosp. Electron. Syst., 39, 4, 1333-1364 (2003) |
| [27] | Li, X. R.; Jilkov, V. P., A survey of maneuvering target tracking-part iii: measurement models, Proc. SPIE Conf. Signal Data process. small targets, 1-24 (2001) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
