**Publications**(53)

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How to avoid normalization of particle flow for nonlinear filters, Bayesian decisions, and transport

^{3}) the Unscented Kalman Filter usually performs well, whereas for even nonlinearities (e.g., x

^{2}), the Extended Kalman Filter is sometimes much better than the Unscented Kalman Filter. This is contrary to the usual engineering folklore, and therefore we have checked our results very thoroughly. In particular, the Unscented Kalman Filter correctly approximates the conditional mean using a 4th order Gauss-Hermite quadrature, in contrast to the Extended Kalman Filter which uses a simple 0th order approximation, but the conditional mean is not the desired estimate in practical applications for strongly bimodal conditional probability densities, which are induced by even nonlinearities, owing to a sign ambiguity. On the other hand, even nonlinearities do not always induce multimodal densities that persist for a significant amount of time, and thus the Unscented Kalman Filter sometimes performs well for such problems. We study the effects of initial uncertainty of the state vector and nonlinearity in measurements.

^{3}, whereas for poor proposal densities c(d) grows exponentially with d. In contrast, for certain problems, QMC converges much faster than MC with N. In particular, QMC converges as k(d)/N, in which k(d) is logarithmic in N and its dependence on d is an interesting story.

_{R}) and the probability of correct data association (P

_{DA}) are computed as a function of: (1) average object separation, (2) sensor resolution, and (3) one-sigma prediction error, for sensor measurements with dimensions n equals 1, 2, 3, ... . The values of P

_{R}and P

_{DA}are plotted versus the average object separation normalized by the sensor resolution, parameterized by the one-sigma prediction error, for values of n equals 1, 2, 3, ... . By inspection of these curves, it is obvious that P

_{R}is less than P

_{DA}for n equals 1, 2, 3, ... for any values of average object separation and sensor resolution, for almost any practical value of one-sigma prediction error of interest. This means that sensor resolution is a more important issue than data association in most practical applications. Nevertheless, 99 percent of the literature on multiple target tracking has ignored the issue of resolution.

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