The covariance correction equation of the MBP algorithm is seldom used directly. Numerically, the covariance matrix P (t |t) must be positive semidefinite, but in the correction equation we are...

The covariance correction equation of the MBP algorithm is seldom used directly. Numerically, the covariance matrix P (t ˜ |t) must be positive semidefinite, but in the correction equation we are subtracting a matrix from a positive semidefinite matrix and cannot guarantee that the result will remain positive semidefinite (as it should be) because of roundoff and truncation errors. A solution to this problem is to replace the standard correction equation with the stabilized Joseph form, that is,

(a) Derive the Joseph stabilized form.

(b) Demonstrate that it is equivalent to the standard correction equation.