This paper deals with the optimization of the observer trajectory for target motion analysis. The observations are made of estimated bearings. The problem consists in determining the sequence of controls (e.g. the observer headings) which maximizes a cost functional. This cost functional is generally a functional of the FIM matrix associated with the estimation of the source trajectory parameters. Further, note that these parameters are only partially observed. The determinant of the Fisher information matrix (FIM) has all the desirable properties, the monotonicity property excepted. This is a fundamental difference with "classical" optimal control. The analysis is thus greatly complicated. So, a large part of this paper is centered around a direct analysis of the FIM determinants. Using them, it is shown that, under the long-range and bounded controls hypotheses, the sequence of controls lies in the general class of bang-bang ones. These results demonstrate the interest of maneuver diversity. More generally, they provide a general framework for devising a strategy for optimizing the observer trajectory, only based on the observations (i.e. the bearing rates).