A blogger named Lalas produced on Quantitative Thoughts a very comprehensive and compact tutorial on the R package dlm by Petris. I use dlm a lot.

Unfortunately, Lalas does not give details on how the SVD is used. They do report that their tutorial is based in part on slides by Petris, and on slides by Zivot and Yollin. Petris himself acknowledges the SVD approach as originating with:

• L. Wang, G. Libert, P. Manneback, “Kalman Filter Algorithm Based on Singular Value Decomposition,” Proceedings of the 31st Conference on Decision and Control, 1992, pp. 1224–1229.
• Y. Zhang, R. Li, “Fixed-Interval Smoothing Algorithm Based on Singular Value Decomposition,” Proceedings of the 1996 IEEE International Conference on Control Applications, 1996, pp. 916–921.

Update, 1^st August 2015

While reading a review by Tusell, my attention was drawn to the very recent (2015) KFAS package, developed and described by Helske, which I’m intending to try as a competitor to dlm. The detailed references are:

• F. Tusell, “Kalman filtering in R“, Journal of Statistical Software, 39(2), March 2011
• J. Helske, “KFAS: Exponential family state space models in R“, https://cran.r-project.org/web/packages/KFAS/vignettes/KFAS.pdf
• J. Helske,KFAS: Kalman Filter and Smoother for Exponential Family State Space Models. R package version 1.1.2, http://cran.r-project.org/package=KFAS