Target Tracking Based on Bearing Only Measurements

Abstract

ACKNOWLEDGMENTSThis report represents the results of a six-month (part-time) effort to apply different approximai-ive nonlinear filtering techniques on target tracking problem based on bearing only measurements.The work was performed during the Academical Year 1979-80 Michael Athans, who admitted the author to LIDS, and was his overall supervisor during his stay at LIDS. we could show that given a target range, the target velocity components could be calculated from three consecutive bearings, with no constraints on the observer's trajectory over the observation interval. We could alsoshow, that if the observer's velocity was zero, we could calculate the target's heading exact, even if the assumed range was false.By including a fourth bearing, and introducing the constraint that the observer should be maneuvering during the observation interval, we also derived the equation for calculation of range to target.In order to take into account the fact that the observations are noisy, a procedure for smoothing of initial range and velocity data calculated fron a batch of bearing observations was proposed.In order to adapt the straight trajectory filters to the curved trajectory case, which results from a maneuvering target, we derived the iv structure for a likelihood ratio test based oa the principle of comparing the innovation sequence with its expected statistics, based on the "no maneuvre" hypothesis. When the actual variance of the innovation sequence becomes consistently larger than its expected variance over the most recent L samples, the "target maneuvre" hypothesis is accepted.The proposed action scheme following the maneuvre detection included two main features: at the time when the maneuvre was detected, will be the result.The purpose of this report is to be a mathematical basis for an extensive simulation study where the performance of the different filtering approaches to bearing only tracking can be compared.When this simulation study has been performed, we will be in the position to give an answer to the question: To what extent is it possible to overcome the three main problems with bearing only tracking:1) The poor degree of observability, 2) The nonlinearity of the problem, v claiming for the best possible linearization trajectory, and 3)The target maneuvre detection and handling problem.We have not made any efforr to analyze and compare the computational complexity nor the memory capacity requirements of the different filters.The reason for this is that we didn't want these aspects of the problemn to constraint our choice of filtering a,?proaches at this stage.vi CONTENTS