Abstract
This paper describes a sequential square root method which is aimed at solving the numerical problems affecting the conventional Kalman filter. Simple square root algorithms are derived for the Kalman covariance and information filters and for the smoothing equations. A comparison with other square root methods is also provided.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, B. D. and Moore, J. B. (1979) Optimal Filtering, Prentice-Hall, Englewood Cliffs, NJ.
Bellantoni, J. F. and Dodge, K. W. (1967) A square root formulation of the Kalman-Schmidt filter, AIAA J. 5, 1309–1314.
Bierman, G. J. (1982) Factorization Methods for Discrete Sequential Estimation, Academic Press, New York.
Carraro, C. (1984) Identification and estimation of regression models with structural variability of the parameters, in T. Basar and L. F. Pau (eds) Dynamic Modelling and Control of National Economies, Pergamon Press, Oxford.
Carraro, C. (1985) Regression and Kalman filter methods for time-varying econometric models, Econometric Research Program, Research Memorandum n.320, Princeton University and Ch. I of New Methods for Macroeconomic Policy Analysis, Ph.D. Dissertation, Princeton University.
Carraro, C. and Sartore, D. (1987) Square root iterative filter: Theory and applications to econometric models, Ann. Economic et Statistique, 6–7, 435–459.
Chow, G. C. (1983) Econometrics, McGraw-Hill, New York.
Engle, R. F. and Watson, M. W. (1984) Alternative algorithms for the estimation of dynamic factor, MIMIC and varying coefficient regression models, J. Econometrics 23, 385–400.
Engle, R. F. and Watson, M. W. (1985) Applications of Kalman filtering in econometrics, Harward Institute of Economic Research, Discussion Paper No. 1187.
Harvey, A. (1981). The Kalman filter and its applications in econometrics and time series analysis. Presented at the 6th Symposium on Operation Research, Augsburg.
Kalman, R. E. (1960) A new approach to linear filtering and prediction problems, J. Basic Enging., 82D, 33–45.
Kalman, R. E. and Bucy, R. S. (1961) New results in linear filtering and prediction theory, Trans. ASME, Series D 83, 95–103.
Kaminski, P. G., Bryson, A. E. and Schmidt, S. F. (1971) Discrete square root filtering: A survey of current techniques, IEEE Trans. Automatic Control, 727–736.
Jazwinski, A. H. (1971) Stochastic Processes and Filtering Theory, Academic Press, New York.
Schmidt, S. F. (1972) Precision navigation for approach and landing operation, Proc. J. Automatic Control Conference, Stanford University, 455–463.
Schmidt, S. F., Weinberg, J. P., and Lukesh, J. S. (1963) Case study of Kalman filtering in the C-5 aircraft navigation system Jt. Automatic Control Conference, University of Michigan, 59–109.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Carraro, C. Square root kalman algorithms in econometrics. Computer Science in Economics and Management 1, 41–51 (1988). https://doi.org/10.1007/BF00435202
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00435202