Open AccessThe article deals with solving a problem of the passive angle track on target from a spacecraft (SC) via measuring one angle. A main idea of the passive track is to use the angle data to estimate the unknown position of a target. For estimation, methods based on the Kalman filter and its modifications are often used. However, here there is a problem that the linearized filters can easily diverge, when maneuvering. Therefore, in this paper, we propose to solve the problem of passive one angle track on target using a nonlinear particle filter (PF).
The problem under consideration is represented as a Bayesian one of the recursive estimation that is aimed at estimating a state dynamics of the observed angle. It is described through defining the transient and conditional probability densities, and its general solution is represented as a procedure "prediction-correction". The PF algorithm allows solving such a problem by representing a posteriori probability density of the estimated value by a set of generated points with weights generated according to the algorithm of sequential importance sampling and regenerated according to the algorithm of regeneration with systematic residual resampling. In such an algorithm at each subsequent time iteration there is a recursively updated set of weighted points according to which the posterior distribution of the state vector is approximated.
The article in detail describes a developed algorithm of passive tracking and gives its diagrammatic representation. The flowchart diagram can be divided into the following steps: initialization, regeneration, filtering, and extrapolation. The first provides initial generation of a set of points and weights, regeneration allows avoiding the degeneracy of the set, and filtering enables direct estimates. Extrapolation, however, plays a separate important role in correcting the given functional laws. Further, the class hierarchy software implementation is shown as one combined flexible, portable module.
The developed module has been simulated using the real experimental data for the cases of linear and nonlinear variation of the true angle. The accuracy of tracking a target was evaluated by a criterion of the squared estimation error of the measured angle against the true one. Based on the results of the simulation, a conclusion can be drawn that the proposed algorithm is sufficiently fast convergent, which indicates that its using is expedient.