Passive trajectory tracking based on angles and other measurements

In the first part of [TE 6 705] , we presented the general principles of passive trajectography and the algorithms for dealing with the basic TPA problem (passive trajectography by angle measurement). In TPA, a single, moving sensor is used to measure the angular direction of a source, which is assumed to be in uniform rectilinear motion (MRU). We have identified the fundamental limitations of TPA techniques and presented typical results based on canonical assumptions. In this second section, we address the problem of providing additional information to angle measurements. The additional measurements considered here are :

• either, those relating to the detection of a possible manoeuvre of the source;

• or the frequencies emitted by the source ;

• or angular measurements from another geographically distant platform.

We'll show that in these three cases, the observer no longer needs to maneuver as in TPA, which represents an unquestionable advantage.

The first paragraph of this dossier deals with the problem of source maneuver detection. One particularity of this problem lies in the fact that this maneuver is not always detectable: indeed, we show that there exists a whole family of kinematics (non-MRU) of the source undetectable by the observer, even in the absence of noise. For other geometries where maneuver detection is potentially possible, we present parametric and non-parametric statistical tests that exploit estimation residuals, i.e. the differences between measurements and their estimates. We give the general performance of these tests and illustrate these theoretical results with a typical example.

When a manoeuvre is detected at time t _M , rather than forgetting all previous measurements and re-estimating the new trajectory followed by the source, we can take into account, as an additional measurement, the kinematic elements relating to the goal acquired before it manoeuvred. This is the subject of the second paragraph, which deals with the usual case where the source's velocity does not change – in modulus – before and after the manoeuvre. We then turn to the case of greatest practical interest, where the observer (carrier) never manoeuvres, either before or after detecting the source manoeuvre. We show that the observer can then estimate the kinematic...