I have a basic doubt in statistics.(I am working with kalman filter)
Lets say i get a state variable 'Xt' for each time instance t as the kalman filter output.And for each time step, i also have a ground truth 'Yt' from an expensive sensor.
So,
Yt=Xt+ Nt , where Nt is the noise with covariance P.
I have the complete csv data of Yt and Xt measured for every time stamp. How can i evaluate the covariance P from the data?
The covariance of the random variable (Yt-Xt) can be calculated in the usual way: https://en.wikipedia.org/wiki/Covariance_matrix.
This variable is the "residual" of your prediction. It is a combination of bias in your model and variance in measurement. Calling it "noise" seems to express an assumption that the bias is small.
Chris Morris Thank you for the answer! But I think we cannot calculate it using usual way. And the method I found to estimate the covariance from the given equation is through reduced chi-suquared stastics which is used for OLS Estimation: https://en.wikipedia.org/wiki/Ordinary_least_squares#Estimation
Ahmed K. Jameil Thank you Sir.
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