I see that, in the correction step of Kalman filter, there is an equation to update the covariance matrix. I have been using it in the form:
P = (I - KH)P'
P is the covariance matrix,
K is the Kalman Gain and
H is the observation model. The
I is the identity matrix. However, I also see a different equation in some literature:
P = P' - KSKT
S = HPHT + Q
Q is the noise matrix for the observation model. Are these two equations same? If so, how to prove it?