A Linear Algebraic Approach to Kalman Filtering

A new linear algebraic approach is used here to derive the celebrated Kalman filter. The filtering problem is first converted into an equivalent linear algebraic problem by relating the estimate of process state to the vector of measured output via a linear equation. Then we obtain the Kalman recursion equations by using a simple linear algebraic lemma. This derivation is conceptually simple, elegant, and thus very suitable for pedagogical purposes. Another advantage of our approach is that the noise correlated case is dealt with as easily as the noise uncorrelated case.