Probability density update for a distributed system based on unnormalized local densities in the continuous-discrete case

Results have been published that give the conditional probability density update for a distributed nonlinear stochastic system that is based on the conditional density updates for the local estimators. However, the local densities are required to be solutions to nonlinear equations, which are unsolvable in the general case. A formulation that uses unnormalized local densities, which are more tractable, and yet produces the same normalized density for the global system as the previous method is given. This new result is applicable to a much wider variety of problems than the former due to the larger body of problems for which unnormalized densities are available.<>