Particle filters on Lie Groups represent a cutting-edge approach in nonlinear filtering and control. By generating randomly distributed particles from proposed densities, while accurately preserving rotation matrices, they offer a promising solution to nonlinear systems. However, particle filters grapple with numerous challenges such as high computational costs due to the large number of particles needed, vulnerability to particle degeneracy as well as the curse of dimensionality. To address these issues, Sequential Markov Chain Monte Carlo (SMCMC) methods aim to mitigate sensitivity to high-dimensional systems by iteratively sampling from the posterior density of the system state, gradually refining the estimation. In this paper we extend SMCMC techniques to matrix Lie groups, resulting in the Lie Groups Sequential Markov Chain Monte Carlo (LG-SMCMC) filter that circumvent the major drawbacks of particle filters. The proposed approach incorporates enhancements based on the Metropolis-Hastings algorithm, further improving the algorithms efficiency and robustness. To validate the effectiveness of these methods, the algorithms are tested on an Unmanned Aerial Vehicle (UAV) navigation scenario with challenging discrepancies in the noise tuning.

The paper deals with the detection performance of a moving target in multispectral IR image sequences with lowSNR. In this context, track-before-detect (TBD) is the generally used method, which consists in accumulating raw images over time to track before detect. For each target hypothesis (position, velocity, amplitude), the signal is integrated over time. In this way, the potential target with the best spatio-temporal correlation will be a candidate for a detection test. In this paper, we develop a minimum detection bound regardless of the TBD method used. Specifically, this bound gives the minimum average number of multispectral images required to detect the target.

Passive target estimation is a widely investigated problem of practical interest. We are concerned specifically with an autonomous flight system developed onboard the ONERA ReSSAC unmanned helicopter. This helicopter is equipped with a (visible or infrared) camera and so is able to measure azimuths and elevation angles of a target. The latter is supposed to follow a constant velocity motion. It is well known that observer must maneuver in order to insure the observability of the target state. We are interested in tracking partly the target state when both the observer and the target have a constant velocity model in a three-dimensional space. We describe the set of all the trajectories compatible with the angle measurements and we propose a quick method to estimate these trajectories.

In this paper, we consider different approaches in reducing the amount of data transfer in a distributed Kalman filtering based on noisy linear observations. The observations are either compressed using equivalent measurements, or transmitted only if their values change more than a specified value. The objective is to reduce sensor data traffic with relatively small estimation performance degradation. Through simulations, we evaluate the performances of a distributed Kalman filter using three techniques for data transfer.

Cold atom interferometer is a promising technology to obtain a highly sensitive and accurate absolute gravimeter. With the help of an anomalies gravity map, local measurements of gravity allow a terrain-based navigation. We describe the model of the absolute gravity measurement. We develop a Laplace-based particle filter adapted to this context. This non-linear filter is able to estimate the positions and velocities of a carrier (vessel). Some results on realistic simulated data are presented.