On the superposition principle of linear Gaussian estimation - A physical analogy

In this paper a new interpretation of linear estimation in the context of classical mechanics is presented. In this context, Accumulated State Densities can be interpreted as the Lagrange function of a “least action” principle that provides the expectation vectors for filtering and retrodiction as a solution. The superposition principle, which states that the solution of this algorithm is a linear combination of the initial value and the measurements, is a consequence of the fact that the measurements are independent conditioned on the accumulated state and that the “action” functionals are mutually independent. Two example applications are shown, which save some computation when the estimate of the complete trajectory becomes important.