In GNSS-denied and poorly-known environments, reliable autonomous navigation is a major challenge, as conventional data fusion algorithms require an extensive knowledge of their surroundings to accurately estimate the vehicle state. To address this issue, we propose to use an adaptive Gaussian process regression to model an approximation of the environment solely based on scarce and noisy samples. This paper takes advantage of the flexibility of Gaussian processes to dynamically model the underlying terrain by adapting the process to the relevant data at each step. To this end, we propose to locally fit the Gaussian process and perform regression by using only a subset of data points selected according to a proximity criterion. The developed method employs a regularised particle filter to effectively estimate the system state using the output of the regression. By integrating Gaussian process-based terrain predictions, the particle filter can effectively compensate for the lack of precise terrain information, thus enhancing navigation performance in GNSS-denied scenarios. To evaluate the effectiveness of the proposed approach, simulations were performed in terrain-aided navigation of an unmanned aerial vehicle. Comparative analysis with existing navigation methods illustrates the superiority of the proposed approach in terms of accuracy and robustness.

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.

Kalman-Particle Kernel Filter (KPKF) is a sub-class of Particle Filter (PF) that uses Gaussian kernels as particles, which enables a local Kalman update for each measurement in addition to the usual weight update. Besides, recent research about filtering on Lie groups brought powerful theoretical results, and showed the superiority of this approach. Hence, this paper extends the Euclidean KPKF to a new formulation on Lie groups and introduces substantial improvements based on Lie groups Kalman filters theory and Laplace Particle Filters on Lie groups (LG-LPF) for improved resampling. The proposed algorithm is tested on an angles-only UAV navigation scenario with challenging initial errors. It shows superior robustness and accuracy compared to Lie group Extended Kalman Filter (LG-EKF), with near-to optimal performance, even with a limited amount of particles.

Particle filters are suited to solve nonlinear and non-Gaussian estimation problems which find numerous applications in autonomous systems navigation. Previous works on Laplace Particle Filter on Lie groups (LG-LPF) demonstrated its robustness and accuracy on challenging navigation scenarios compared to classic particle filters. Nevertheless, LG-LPF is applicable when the prior probability density and the likelihood have a predominant mode, which narrows the scope of applications of this method. Thus, this paper proposes a generalized strategy to use LG-LPF while keeping its benefits. The core idea is to compute an accurate multimodal importance function based on local optimizations and resample the particles accordingly. This approach is compared to a Laplace Particle Filter (LPF) designed in the Euclidean space, on a UAV navigation scenario with ambiguous Doppler measurements. The Lie group approach shows improved accuracy and robustness in every case, even with a reduced number of particles.

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.