Kalman filter .... linear dynamic filtering

Kalman filter

what is kalman filter ?
Kalman is recursive Linear dynamic filter, based on markov chain perturbed or modelled based on Gaussian noise. The primary applications of kalman filter include Computer vision, Financial Engineering wherever there is involvement of predictive analysis. In practical applications Discerete Kalman filter is applied it works on the basic principle as shown in the figure below[1]

time update <-----------> Measurement update


Time update
i.e.Prediction

* to predict the next state
* to update the probability distribution based on current prediction


Measurement
i.e. correction
* determine vairance of measurement noise
* intialization of noise covariance

A detailed explaination is given in this kalman paper  

 


for example...
Time update
Predict next possible location of target in a 2D environment, to implement this practical task we first intialize the current pixel location (say A(20,30)) of the target to generate a possible probability distribution, ( generate priori) measurement update Predict next possible position the kalman filter will randomly choose particles from the region surrounding say radius r (say r = 10pixels) which will be the new vairance and evaluate the covariance with respect to possible target feature( i.e. small cut out from the image of the target) can be used. and define the particle within the gaussian boundry which minimizes the error, ending up generating posteriori . go back to time update.

Applications
Predictions of relatively linear dynamic stock prices
Prediction of target in target in Automatic Target tracking video survelliance
Embedded system applications include Vehicle stability, vehicle control , camera stability and control
weather prediction
speech analysis
Radar tracking


References and cool Stuff
-----------------------------
Basic intro to kalman
[1]http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf

Excellent resource of kalaman research papers and implemenntation 
[2]http://www.cs.unc.edu/~welch/kalman/

MATLAB implementation book 
[3]http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470173661.html  

MATLAB TOOLBOX

[4]http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html  
[5]http://www.mathworks.com/matlabcentral/fileexchange/5377  

2D Target Tracking using MATLAB
[6]http://www.mathworks.com/matlabcentral/fileexchange/14243  
[7]http://en.pudn.com/downloads50/sourcecode/math/detail173459_en.html  

Wikipedia page for reference

[8]http://en.wikipedia.org/wiki/Kalman_filter