Tracking multiple dynamic targets in LoS-NLoS condition with multidimensional scaling

We consider the problem of tracking multiple targets in the presence of noise and a mixture of line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. The targets are assumed to describe independent trajectories with non-stationary (dynamic) statistics, i.e., with variable velocities and accelerations (limited in absolute value). These moving targets are observed by fixed anchors, which measure the distance between themselves and each target periodically. LoS and NLoS conditions are modeled by a first order time-homogeneous Markov chain, such that the occurrence, the intensity and the persistence (duration) of transitions between LoS and NLoS states are random but according to the steady state distribution of the process. The challenge, therefore, is that such variations are difficult to detect in the presence of noise and target mobility, and if not corrected, may result in severe degradation of tracking accuracy. In order to mitigate this problem we introduce a wavelet-based technique to simultaneously attenuate the noise effect on ranging and detect the LoS-NLoS transitions, allowing for their subsequent correction. The technique is non-parametric, in which no knowledge of the statistics of the LoS/NLoS transition process is assumed. The impact of such pre-filtering on the performance of the Multidimensional Scaling (MDS) tracking algorithm (proposed in an earlier work) is studied, and for the LoS case compared against the error performance for classic Extended Kalman Filter (EKF). It is shown that the MDS-based tracking algorithm with Jacobian eigenspace updating together with wavelet pre-filtering is superior (at the region of interest) to the EKF approach, and can well cope with mixed LoS-NLoS scenarios.