Discrete-time observability and estimability analysis for bearings-only target motion analysis

On the convergence of iterative methods for bearings-only tracking

“…Therefore a local minimum of the likelihood functional cannot exist on all the correspondingX domain. Note that observability is generally ensured for a leg-by-leg observer trajectory [14,15]. Further, from (24) we note that the speed of convergence of an iterative algorithm is proportional to P p k=1 r k =r k (ˆk ¡¯k) sin(ˆk ¡¯k).…”

“…Consider, first, a two-leg path of the source. Opposite to the case of a nonmaneuvering source, two transition matrices (F 1 and F 2 ) are now required [15]. The state equations then take the following general form: …”

“…To overcome this problem, 15 an approximate localization of the source maneuvers can be obtained by sequential detection [20] based, for instance, on the following type of test [28] which may be viewed as an approximation 16 of a likelihood ratio around the parameter µ 0 2 £ 0 : 14 Approximating the asymptotic performance of this test is a difficult task, since the sequence of observations is not identically distributed. 15 Computation cost of an exhaustive search for ¿ .…”

“…The second condition is guaranteed if the observability conditions [1,6,15] 11Ã is the matrix A where¯k is replaced by˜k. 12 The symbol P here denotes the probability.…”

“…15 Computation cost of an exhaustive search for ¿ . 16 More precisely, denotingμ the MLE over £ and µ ¤ the MLE over £ 0 we consider the following expansion of the likelihood:…”