One question, will the Kalman filter get more accurate as more variables are input into it? ie. if you have 1 unknown variable and 3 known variables can you use the filter with all 3 known variables to give a better prediction of the unknown variable and can you keep increasing the known inputs as long as you have accurate measurements of the data.

Mostly thinking of applying this to IMUs, where I know they already use magnetometer readings in the Kalman filter to remove error/drift, but could you also use temperature/gyroscope/other readings as well? Or do IMUs already do the this?

]]>Can you please explain:

1. How do we initialize the estimator ?

2. How does the assumption of noise correlation affects the equations ?

3. How can we see this system is linear (a simple explanation with an example like you did above would be great!) ? ]]>

Pd. I’m sorry for my pretty horrible English :(

]]>Xk=FkXk-1 (equation 3)

You then use the co-variance identity to get equation 4.

Cov(AX) = AEA^t

For Cov(X)= E, are you saying that Cov(X-1) = Pk-1?

Is this the reason why you get Pk=Fk*Pk-1*Fk^T? because Fk*Xk-1 is just Xk therefore you get Pk rather than Pk-1? in equation 5 as F is the prediction matrix?

]]>I have truly enjoyed the Kalman Filter explanation.

Cool you ]]>