Grid Based Solution of Zakai Equation with Adaptive Local Refinement for Bearings-only Tracking

International audienceThe solution of the Zakai equation provides the complete conditional probability density of the state, given the observations. Numerical solution of this equation by the finite difference method usually leads to large systems of equations which have to be solved at each time step, especially when the dimension of state space is more than two. We propose in this paper, for the first time to our best knowledge, a grid-based four dimensional algorithm to solve the Zakai equation. Our approach is based on an adaptive local grid refinement method and is illustrated with a bearings-only target motion analysis example

Adaptive Approximate Bayesian Computational Particle Filters for Underwater Terrain Aided Navigation

International audienceTo perform long-term and long-range missions, underwater vehicles need reliable navigation algorithms. This paper considers multi-beam Terrain Aided Navigation which can provide a drift-free navigation tool. This leads to an estimation problem with implicit observation equation and unknown likelihood. Indeed, the measurement sensor is considered to be a numerical black box model that introduces some unknown stochastic noise. We introduce a measurement updating procedure based on an adaptive kernel derived from Approximate Bayesian Computational filters. The proposed method is based on two well-known particle filters: Regularized Particle Filter and Rao-Blackwellized Particle Filter. Numerical results are presented and the robustness is demonstrated with respect to the original filters, yielding to twice as less non-convergence cases. The proposed method increases the robustness of particle-like filters while remaining computationally efficient

Adaptive Approximate Bayesian Computational Particle Filters for Underwater Terrain Aided Navigation

International audienceTo perform long-term and long-range missions, underwater vehicles need reliable navigation algorithms. This paper considers multi-beam Terrain Aided Navigation which can provide a drift-free navigation tool. This leads to an estimation problem with implicit observation equation and unknown likelihood. Indeed, the measurement sensor is considered to be a numerical black box model that introduces some unknown stochastic noise. We introduce a measurement updating procedure based on an adaptive kernel derived from Approximate Bayesian Computational filters. The proposed method is based on two well-known particle filters: Regularized Particle Filter and Rao-Blackwellized Particle Filter. Numerical results are presented and the robustness is demonstrated with respect to the original filters, yielding to twice as less non-convergence cases. The proposed method increases the robustness of particle-like filters while remaining computationally efficient

Grid Based Solution of Zakai Equation with Adaptive Local Refinement for Bearings-only Tracking

The solution of the Zakai equation provides the complete conditional probability density of the state, given the observations. Numerical solution of this equation by the finite difference method usually leads to large systems of equations which have to be solved at each time step, especially when the dimension of state space is more than two. We propose in this paper, for the first time to our best knowledge, a grid-based four dimensional algorithm to solve the Zakai equation. Our approach is based on an adaptive local grid refinement method and is illustrated with a bearings-only target motion analysis example

TMA from Cosines of Conical Angles Acquired by a Towed Array

International audienceThis paper deals with the estimation of the trajectory of a target in constant velocity motion at an unknown constant depth, from measurements of conical angles supplied by a linear array. Sound emitted by the target does not necessarily navigate along a direct path toward the antenna, but can bounce off the sea bottom and/or off the surface. Observability is thoroughly analyzed to identify the ghost targets before proposing an efficient way to estimate the trajectory of the target of interest and of the ghost targets when they exist

Bearings-Only TMA from Electromagnetic and Acoustic Waves

International audienceThis paper presents a novel BOTMA based upon two types of bearing measurements: the angles of arrival of electromagnetic waves and the angles of arrival of acoustic waves. The difference of the propagation delays makes the problem observable even when the observer is motionless or nonmaneuvering. We construct a recursive estimator (using the extended Kalman filter) and a batch estimator (the maximum likelihood estimator) whose respective performances are evaluated by Monte-Carlo simulations, and compared to the Cramér-Rao lower bound

Bearings-only TMA from electromagnetic and acoustic waves

International audienceThis paper presents a novel BOTMA based upon two types of bearing measurements: the angles of arrival of electromagnetic waves and the angles of arrival of acoustic waves. The difference of the propagation delays makes the problem observable even when the observer is motionless or non-maneuvering. We construct a recursive estimator (using the extended Kalman filter) and a batch estimator (the maximum likelihood estimator) whose respective performances are evaluated by Monte-Carlo simulations, and compared to the Cramér-Rao lower bound

Bearings-only TMA from electromagnetic and acoustic waves

International audienceThis paper presents a novel BOTMA based upon two types of bearing measurements: the angles of arrival of electromagnetic waves and the angles of arrival of acoustic waves. The difference of the propagation delays makes the problem observable even when the observer is motionless or non-maneuvering. We construct a recursive estimator (using the extended Kalman filter) and a batch estimator (the maximum likelihood estimator) whose respective performances are evaluated by Monte-Carlo simulations, and compared to the Cramér-Rao lower bound