Switching Kalman filter
The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy, but related switching state-space models have been in use.
Applications of the switching Kalman filter include: brain-computer interfaces and neural decoding, real-time decoding for continuous neural-prosthetic control, and sensorimotor learning in humans. It also has application in econometrics, signal processing, tracking, computer vision, etc. It is an alternative to the Kalman filter when the system's state has a discrete component. For example, when an industrial plant has "multiple discrete modes of behaviour, each of which having a linear (Gaussian) dynamics".
There are several variants of SKF discussed in.
In the simpler case, switching state-space models are defined based on a switching variable which evolves independent of the hidden variable. The probabilistic model of such variant of SKF is as the following:
[This section is badly written: It does not explain the notation used below.]
The hidden variables include not only the continuous , but also a discrete *switch* (or switching) variable . The dynamics of the switch variable are defined by the term . The probability model of and can depend on .
The switch variable can take its values from a set . This changes the joint distribution which is a separate multivariate Gaussian distribution in case of each value of .
- K. P. Murphy, "Switching Kalman Filters", Compaq Cambridge Research Lab Tech. Report 98-10, 1998
- K. Murphy. Switching Kalman filters. Technical report, U. C. Berkeley, 1998.
- K. Murphy. Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, University of California, Berkeley, Computer Science Division, 2002.
- Kalman Filtering and Neural Networks. Edited by Simon Haykin. ISBN 0-471-22154-6
- Wu, Wei, Michael J. Black, David Bryant Mumford, Yun Gao, Elie Bienenstock, and John P. Donoghue. 2004. Modelling and decoding motor cortical activity using a switching Kalman filter. IEEE Transactions on Biomedical Engineering 51(6): 933-942. doi:10.1109/TBME.2004.826666
- Heald JB, Ingram JN, Flanagan JR, Wolpert DM. Multiple motor memories are learned to control different points on a tool. Nature Human Behaviour. 2, 300–311, (2018).
- Kim, C.-J. (1994). Dynamic linear models with Markov-switching. J. Econometrics, 60:1–22.
- Bar-Shalom, Y. and Li, X.-R. (1993). Estimation and Tracking. Artech House, Boston, MA.
- Zoubin Ghahramani, Geoffrey E. Hinton. Variational Learning for Switching State-Space Models. Neural Computation, 12(4):963–996.