Ordered sequential filtering for finite dimensional systems with distributed observations

This short paper treats the topic of suboptimal linear estimation for systems which have a finite dimensional state vector but a distributed set of observations. Such systems are of some practical interest, and are indeed considerably easier to work with than most distributed parameter systems. The method proposed here is that a filter structure of linear form, driven by a statistic which is a weighted integral of the distributed observation, be used to generate estimates of the state of the system. The filter parameters, and the weighting function for the integral are selected so that the estimate is unbiased and results in minimum mean-square error, subject to the structural constraints.