Menu
I read some works about Kalman filter for CV object tracking but I can't find some reference about the choice of: 1)the process noise covariance Q; 2)Measurement noise covariance R. So far I have realized that the model is equation of motion (someone uses acceleration as state variable, others use position and speed only) but nobody is clear about Q and R choice including this example by mathworks: http://www.mathworks.it/it/help/vision/examples/using-kalman-filter-for-object-tracking.html Recently I found this page: http://blog.cordiner.net/2011/05/03/object-tracking-using-a-kalman-filter-matlab/ but the Q and R assignment is not clear. Does anyone know help me, please ?
571
It is well known that the covariance matrixes of process noise (Q) and measurement noise (R) have a significant impact on the Kalman filter's performance in estimating dynamic states. The conventional ad-hoc approaches for estimating the covariance matrixes are not adequate in achieving the best filtering performance.
It is often used to remove the noise from sensor data or estimate the next sensor values. For example, one can use Kalman filtering in a power measurement process to remove high noise in raw voltage data.
A Kalman filter has been used to estimate the measurement and process noise covariance matrices R and Q respectively. Determination of the suitable values of R and Q plays a crucial role to obtain a converged filter [2, 3].
Kalman filters are used to optimally estimate the variables of interests when they can't be measured directly, but an indirect measurement is available. They are also used to find the best estimate of states by combining measurements from various sensors in the presence of noise.
R is the covariance matrix of the measurement noise, assumed to be Gaussian. In the context of tracking objects in video it means your detection error. Let's say you are using a face detector to detect faces, and then you want to track them using the Kalman filter. You run the detector, you get a bounding box for each face, and then you use the Kalman filter to track the centroid of each box. The R matrix must describe how uncertain you are about the location of the centroid. So in this case for the x,y coordinates the corresponding diagonal values of R should be a few pixels. If your state includes velocity, then you need to guess the uncertainty of the velocity measurement, and take the units into account. If your position is measured in pixels and your velocity in pixels per frame, then the diagonal entries of R must reflect that.
Q is the covariance of the process noise. Simply put, Q specifies how much the actual motion of the object deviates from your assumed motion model. If you are tracking cars on a road, then the constant velocity model should be reasonably good, and the entries of Q should be small. If you are tracking people's faces, they are not likely to move with a constant velocity, so you need to crank up Q. Again, you need to be aware of the units in which your state variables are expressed.
So this is the intuition. In practice you start with some reasonable initial guess for R and Q, and then you tune them experimentally. So setting R and Q is a bit of an art. Also, in most cases using diagonal matrices for R and Q is sufficient.
Here is an example that uses the vision.KalmanFilter in Matalb for tracking multiple people.
98
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
