Probabilistic Analysis of the Auto Tracking Failure by the Mobile Robot Video System

Abstract

The article is devoted to the development of a methodology for estimating the probability of an object auto tracking failure by the mobile robot video system under the influence of external factors caused by random vibrations of the mobile platform. The mathematical formulation of the probabilistic analysis problem is based on the processes representation occurring in the system by a vector stochastic differential equation. The condition for the auto tracking failure is the exit of the tracked object from the of the video system field of view and non-return to it within a specified time. The probability of auto-tracking failure depends on the dynamic tracking system properties and is described by a recurrent formula that accounts the probability of an object being out of the field of view and the probability of its non-return. The method of calculating the failure probability includes the solution of two ordinary differential equations systems for probabilistic moments. One system of equations characterizes the probability density of tracked object location coordinates distribution in an open area of space. Another system of equations characterizes the change in time of the probability density of the tracked object coordinates, which is outside the video system field of view. A simplified example is given that clearly illustrates the evolution of the system probabilistic characteristics under the study in space and time.