Abstract :
This paper deals with the estimation of the trajectory parameters for a target moving within a sensor network. We are especially interested by fusing binary information at the network level. This binary information is related to the local target behavior; i.e. its distance from a given sensor is increasing (-) or decreasing (+). In this domain, seminal contributions include . However, in this rich framework we choose to focus on even simpler observations so as to put in evidence the limits and the difficulties of the decentralized binary framework. More specifically, the binary sequences {-,+} can be (locally) summarized by the times of closest point approach (cpa). So, we consider that the available observations, at the network level, are the estimated values of the cpa times. The analysis is also greatly simplified if we assume that the target motion is rectilinear and uniform or a leg-by-leg one. First, we examine the observability requirements for the trajectory parameters. Though the observations do not permit a complete observability, this study allows us to determine the observable part of the state vector. Moreover, we show that observable and unobservable parts are separated. Thus, it is possible to develop simple and efficient methods for estimating the observable parameters. In the case of a single-leg trajectory, we resort to a simple maximum-likelihood estimator, while for the case of multiple-leg trajectories other methods are presented. It is then possible to give confidence intervals for the unobservable components of the state vector. Finally, the constant velocity assumption is relaxed through diffusion process, whether continuous or discrete-time.
