Asymptotically Optimal Nonparametric Signal Interpolation

The problem of interpolation (smoothing) of a partially observable Markov random sequence is considered. For the dynamic observation models, an equation in the interpolation posterior probability density is derived. This equation has a certain form of the normalized product of the posterior probability densities in forward and backward times and differs from its counterpart for static observation models [3, 1] in an additional equation. The aim of this paper is to consider the problem of smoothing for the case of unknown distributions of the unobservable component of the random Markov sequence. For the strongly stationary Markov processes with mixing and for the conditional density of observation model belonging to the exponent family success was reached. A resultant method is based on the empirical Bayes approach and the kernel non-parametric estimation [5]. The equation of the nonlinear optimal smoothing estimate is derived in a form independent of the unknown distributions of an unobservable process. Such form of equation allows one to use the non-parametric estimates of some conditional statistics given any set of dependent observations. Modeling was carried out to compare the nonparametric estimates with optimal mean-square smoothing estimates in Kalman scheme

Asymptotically Optimal Nonparametric Signal Interpolation

The problem of interpolation (smoothing) of a partially observable Markov random sequence is considered. For the dynamic observation models, an equation in the interpolation posterior probability density is derived. This equation has a certain form of the normalized product of the posterior probability densities in forward and backward times and differs from its counterpart for static observation models [3, 1] in an additional equation. The aim of this paper is to consider the problem of smoothing for the case of unknown distributions of the unobservable component of the random Markov sequence. For the strongly stationary Markov processes with mixing and for the conditional density of observation model belonging to the exponent family success was reached. A resultant method is based on the empirical Bayes approach and the kernel non-parametric estimation [5]. The equation of the nonlinear optimal smoothing estimate is derived in a form independent of the unknown distributions of an unobservable process. Such form of equation allows one to use the non-parametric estimates of some conditional statistics given any set of dependent observations. Modeling was carried out to compare the nonparametric estimates with optimal mean-square smoothing estimates in Kalman scheme

Path Planning in Threat Environment for UUV with Non-Uniform Radiation Pattern

The problem of optimal trajectory planning of the unmanned underwater vehicle (UUV) is considered and analytically solved. The task is to minimize the risk of detection of the moving object by a static sonar while moving between two given points on a plane. The detection is based on the primary acoustic field radiated by the object with a non-uniform radiation pattern. In the first part of the article, the probability of non-detection is derived. Further, it is used as an optimization criterion. The non-uniform radiation pattern of the object differentiates this work from previous research in the area. The optimal trajectory and velocity law of the moving object are found, as well as the criterion value on it