Optimal importance density for position location problem with non-Gaussian noise

Semidefinite programming‐based localisation and tracking algorithm using Gaussian mixture modelling

“…In (2), the prediction by the inertial sensing data is modelled as the estimation of the latent state variable in SSM. Since different states of motion can be modelled in a multimodal prior density, in which each cluster accounts for one type of velocity increase (zero, positive and negative) [22]. To capture different states (e.g.…”

“…Thus, the collected inertial sensing data is needed to be post-processed, and the influence caused by drift errors constantly accumulating over the time must be eliminated periodically. In [22], the velocity in the motion model is modelled as a Gaussian mixture random variable. In this paper, to calibrate the cumulative inertial sensing errors, the step length estimation in the motion model is also modelled as a GMM, which provides proper approximation for experimental measurements.…”

Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics

“…However, in many scenarios, neither the process, nor the measurement noise are Gaussian. For instance, in [9], a non-Gaussian trimodal process noise The authors are with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0E9, Canada (e-mail: leila.pishdad@mail.mcgill.ca; fabrice.labeau@mcgill.ca) distribution is used, corresponding to the three different states of motion: constant velocity, accelerating, and decelerating. Additionally, mutipath fading effects could result in multimodal non-Gaussian measurement noise distributions [9]- [11].…”

“…However, in many scenarios, neither the process, nor the measurement noise are Gaussian. For instance, in [9], a non-Gaussian trimodal process noise…”

“…Moreover, since GMs can be viewed as conditionally Gaussian distributions, they enable the analytic evaluation of the posterior. Consequently, they have been used for modeling the non-Gaussian noise distributions [5], [9], [10], [13]- [24], [31], prior [8], [14], [15], [23], [25]- [28], likelihood [29], and also the posterior [16], [21], [22], [30]- [36].…”