I am working on the code to trace mouse location on screen using the Kalman filter. But I wanted to know which parameters (with values) I should consider? What values should be taken in the transition matrix? And most important what range of values to consider for the X position of the mouse, the Y position of the mouse, the velocity change along the X axis, and the velocity change along the Y axis (these are rows of transition matrix).
help.
This is an interesting problem. I assume you would need a position-velocity-acceleration model which gives you a target tracking model.
[dotx \\ ddot x \\ dddotx] = [1 DT DT^2\2 \\ 0 1 DT \\ 0 0 1] [[x \\ dotx \\ ddotx] + noise
y = [1 0 0] [x \\ dotx \\ ddotx] + measurement noise
I hope you understand the notation (latex).
I agree with mr. Ramos, first you should model your problem, e.g. consider the problem with constant velocity or with acceleration. Then your parameters will appear!!
I also agree with mr. Ramos. Let's elaborate this answer: A position,velocity acceleration model.
Such a model has the following states (x, x_vel, x_acc, y, y_vel, y_acc). Regarding the measurement noise, you can specify it as a noise on the acceleration. Paper [1] applies such a model, and you'll find the description of the noise in this paper.
The transitionmodel can be as Mr. Ramos describes for the both coordinates.
The measurement is 2 dimensional [1 0 0 0 0 0;0 0 0 1 0 0]
[1] Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis. F De Groote et al. Journal of Biomechanics (Impact Factor: 2.5). 12/2008; 41(16):3390-8. DOI: 10.1016/j.jbiomech.2008.09.035
I forgot to mention that DT is the sampling interval, because you have a continuous equation (i.e., Newton's 2nd law of motion) but your data is sampled (discrete). The A matrix is
A = [1 DT (DT^2)/2
0 1 DT
0 0 1 ]
C depends on what you measure, i.e., position, velocity, or acceleration.
You need to determine what your state and measurement variables are first of all. What measurements does the mouse provide? What are you trying to estimate? If you are trying to estimate the position of the cursor arrow on the screen, then cartesian x, y coordinates are OK for the state space. You will also need to model the first and possibly second derivative terms i.e. velocity and acceleration, depending on the sampling time of the measurements. Ask yourself how much can the trajectory of the mouse deviate from a straight constant velocity line in the time between samples. The bit I can't help you with is what the mouse actually measures. At a guess, I would think it's integrated voltage on orthogonal (x, y) axes, but there could be slippage and other tricky things to consider. Hopefully a resdident mouse expert can help here.
As far as tracking goes, this should be fairly straightforward once you establish your state space and measurement model. Basic tracking techniques are covered in a number of books, e.g. Bar-Shalom & Fortmann 1988 and subsequent updates. You may need manoeuvring target tracking techniques also as the mouse can accelerate appreciably. A constant turn rate model might even apply - for instance if the user tries to draw a circle with the mouse. Here is a link to a survey paper on this subject that I wrote some time ago. (This paper was submitted for publication but did not appear due to a conflict of interest with the associate editor at the time.)
Technical Report A Survey of Manoeuvring Target Tracking Methods
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