Generalized least-squares method of estimating trajectories from angle measurements (Q1286549)

The problem is to estimate a trajectory of a moving target from angle measurements. The author applies new matrix decomposition techniques, such as the restricted singular-value decomposition, to solve this problem. First, he derives necessary and sufficient conditions for observability and introduces the concept of a nonobservable trajectory subspace. The main reason of possible nonobservability consists in the coincidence of the autoregression equations for the target and for the observer. Then he reduces the nonlinear equations of angle measurements to a high-dimensional linear problem with adaptive and multiplicative errors (some kind of a restricted total least-squares (RTLS) problem). It is demonstrated that a nonobservable trajectory corresponds to degenerate RTLS-problem. In the nonobservable case, the author proposes a modified RTLS-method that permits to estimate all the space that is not observable. A dimension-reduction problem is formulated and solved with the help of a stable total least-square algorithm. Numerical modelling results are presented. The author's method can be applicable to cases when the extended Kalman filters work badly.