Probability density update for a distributed system based on unnormalized local densities

A method for producing a normalized probability density for a global system state constructed from the unnormalized densities of the local models is given and proved. The local densities are required to be solutions to Kushner´s equation, which is unsolvable in the general case. The formulation uses unnormalized local densities, which are solutions of the more tractable Zakai equation, and yet produces the same normalized density for the global system as the previous method. It is applicable to a much wider variety of problems for which the Zakai equation is solvable and Kushner´s equation is not