Kalman filters are a powerful tool for reducing the effects of noise in measurements. This paper gives a no-nonsense introduction to the subject for people with A-level maths. The basic ideas of getting better estimates from many measurements are simply introduced. Thereafter, the basics are gradually developed, using worked examples, to a full Kalman filter. Wherever possible, variations, simplifications, and applications are given in the hope that the reader will be encouraged to use Kalman filter techniques
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References
1.
Lastly, for those that may have been encouraged to look for more information, a short bibliography.
2.
Practical Computing. April 1983. This is a very simple introduction, but worth reading. It also gives a BASIC Kalman filter program.
3.
Technical Memo AW48. Royal Aircraft Establishment, Farnborough, Hants. This has an excellent exposition of the Kalman filter and clearly derives and shows how to use an alpha beta tracker.
4.
Optimal Filtering by Anderson and Moore. This is a university mathematician's guide to Kalman filters, and therefore gives far more detail than many may want. A good reference book.
5.
‘New Results in Linear Filtering and Prediction’ by Kalman and Bucy (1961). Journal of Basic Engineering (ASME) Vol 83-D pp 95–108. This is the original (intractable?) mathematics and is best avoided.
6.
‘Performance Analysis of a Particularly Simple Kalman Filter’ by MaybeckPeter. Journal of Guidance and ControlVol 1, No 6, Nov–Dec 1978. A reasonable introduction to real applications of Kalman Filters.
7.
‘The tracking index’ by KalataP R. IEEE Transactions on Aerospace and Electronic SystemsVol AES20, No 2, March 1984. Although a little tricky to follow, this introduces some cunning advice to help with an α-β tracker.
