This paper presents a general formulation for a minimum cost data association problem which associates data features via one-to-one, m-to-one and one-to-n links with minimum total cost of the links. A motivating example is a problem of tracking multiple interacting nanoparticles imaged on video frames, where particles can aggregate into one particle or a particle can be split into multiple particles. Many existing multitarget tracking methods are capable of tracking non-interacting targets or tracking interacting targets of restricted degrees of interactions. The proposed formulation solves a multitarget tracking problem for general degrees of inter-object interactions. The formulation is in the form of a binary integer programming problem. We propose a polynomial time solution approach that can obtain a good relaxation solution of the binary integer programming, so the approach can be applied for multitarget tracking problems of a moderate size (for hundreds of targets over tens of time frames). The resulting solution is always integral and obtains a better duality gap than the simple linear relaxation solution of the corresponding problem. The proposed method was validated through applications to simulated multitarget tracking problems and a real multitarget tracking problem.

This paper describes the design of a candidate noise processor for the Sanguine receiver based on communication theory considerations and detailed experiments using wide-band recordings of extremely low-frequency (ELF) (3-300 Hz) atmospheric noise. This processor consists of the following elements: 1) a compensating (or whitening) filter; 2) nonlinear notch filtering at frequencies of manmade interference; 3) a post-notch filter nonlinearity; and 4) a phase coherent linear matched filter. Due to the impulsive non-Gaussian nature of the noise, nonlinear processing with a bandwidth considerably greater than the 40-80-Hz signal bandwidth is significantly better than a linear receiver (consisting only of a matched filter and appropriate whitening filters). Simulations using noise recordings from a number of widely separated locations in the world have shown improvements of 7 dB to 20 dB at times of high ELF atmospheric noise levels at the receiver input.

Chernoff bounds on the error probability for the detection of non-Gaussian stochastic signals in additive white Gaussian noise are computed. By the use of Fokker-Planck (F-P) equations and a certain conditional expectation, the quasi-transition function, an equation for time evolution of the Chernoff bound is obtained. This time evolution equation is solved exactly to give all previously known results. Although the general non-Gaussian case cannot be conveniently solved for short time duratio ns, in the important special case of stationary processes and long integration times, bounding the error probability reduces to solving for the largest eigenvalue\lambda_0of a differential operator. In particular,P(error) \leq \exp (\lambda_0T), whereTis the observation period. By iteratively determining\lambda_0via the Galerkin variational procedure, we compare the performance of different receiver forms for a specific problem involving the detection of non-Gaussian random signal processes.