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In Bayesian peer-to-peer decentralized data fusion for static and dynamic systems, the underlying estimated or communicated distributions are frequently assumed to be homogeneous between agents. This requires each agent to process and communicate the full global joint distribution, and thus leads to high computation and communication costs irrespective of relevancy to specific local objectives. This work considers a family of heterogeneous decentralized fusion problems, where we consider the set of problems in which either the communicated or the estimated distributions describe different, but overlapping, states of interest that are subsets of a larger full global joint state. We exploit the conditional independence structure of such problems and provide a rigorous derivation for a family of exact and approximate heterogeneous conditionally factorized channel filter methods. We further extend existing methods for approximate conservative filtering and decentralized fusion in heterogeneous dynamic problems. Numerical examples show more than 99.5% potential communication reduction for heterogeneous channel filter fusion, and a multi-target tracking simulation shows that these methods provide consistent estimates.

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We present the development, formulation, validation, and demonstration of a fast, generic, and open source simulation tool, which integrates nonlinear electromigration with multispecies nonequilibrium kinetic reactions. The code is particularly useful for the design and optimization of new electrophoresis-based bioanlaytical assays, in which electrophoretic transport, separation, or focusing control analyte spatial concentration and subsequent reactions. By decoupling the kinetics solver from the electric field solver, we demonstrate an order of magnitude improvement in total simulation time for a series of 100 reaction simulations using a shared background electric field. The code can efficiently handle complex electrophoretic setups coupling sharp electric field gradients with bulk reactions, surface reactions, and competing reactions. For example, we demonstrate the use of the code for investigating accelerated reactions using isotachophoresis (ITP), revealing new regimes of operation which in turn enable significant improvement of the signal-to-noise ratio of ITP-based genotypic assays. The user can define arbitrary initial conditions and reaction rules, and we believe it will be a valuable tool for the design of novel bioanalytical assays. We will offer the code as open source, and it will be available for free download at http://microfluidics.technion.ac.il.

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