Track initialization from incomplete measurements

Abstract

Target tracking from incomplete measurements using Extended Kalman filtering suffers from unstable behavior due to difficult initialization. Instead of using numerical batch-estimators, we offer an analytical approach to initialize the filter from a minimum number of observations. Additionally, we provide the possibility to estimate only sub-sets of parameters, and to reliably model resulting added uncertainties by the covariance matrix. In a practical example with 3D bearings-only measurements, we implement our approach using geometrical considerations and give numerical results. The Monte-Carlo simulations show that the estimation accuracy is close to the Cramer-Rao lower bound and that the initialization is consistent according to the chi-square 95% acceptance region within a 40km by 40km area, which is four times the distance between the two sensors.