An Introduction to the Kalman Filter

3 A deterministic construction of the Kalman filter 7 3.1 The quadratic criterion to be minimized in the absence of process control noise and the corresponding solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Iterative expression of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 Recursion on the matrix P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.2 Modification of the expression of the solution . . . . . . . . . . . . . . . . . . . . 10 3.3 Final expression of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Summary of the computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.5 Introduction of the penalty term in the criterion . . . . . . . . . . . . . . . . . . . . . . . 11