This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version of STFT by making the window length a continuous parameter. The resulting differentiable adaptive STFT possesses commendable properties, such as the ability to adapt in the same time-frequency representation to both transient and stationary components, while being easily optimized by gradient descent. We validate the performance of our method in vibration analysis.

Collaboratively estimating the state of two robots under communication constraints is challenging regarding computational complexity and statistical optimality. Previous work only achieves practical solutions by either disregarding parts of the measurements or imposing a communication overhead, being non-optimal or not entirely distributed, respectively. In this work, we present a centralized-equivalent but dis-tributed approach for pairwise state estimation where two agents only communicate when they meet. Our approach utilizes elements from wave scattering theory to efficiently and consistently summarize (pre-compute) past estimator information (i.e., state evolution and uncertainty) between encounters of two agents. This summarized information is then used in a joint correction step taking into account all past information of each agent in a statistically correct way. This novel approach enables us to distribute the pre-computations of both state evolution and uncertainties on the agents and reconstruct the centralized-equivalent system estimate with very few computations once the agents meet again while still applying all measurements from both agents on both estimates upon encounter. We compare our approach on a real-world dataset against a state of the art collaborative state estimation approach.

The recently introduced matrix group$\mathbf {SE_2(3)}$provides a 5$\mathbf {\times }$5 matrix representation for the orientation, velocity, and position of an object in the 3-D space, a triplet we call “extended pose.” In this article, we build on this group to develop a theory to associate uncertainty with extended poses represented by 5$\mathbf {\times }$5 matrices. Our approach is particularly suited to describe how uncertainty propagates when the extended pose represents the state of an inertial measurement unit (IMU). In particular, it allows revisiting the theory of IMU preintegration on manifold and reaching a further theoretic level in this field. Exact preintegration formulas that account for rotating earth, that is, centrifugal force and Coriolis force, are derived as a byproduct, and the factors are shown to be more accurate. The approach is validated through extensive simulations and applied to sensor fusion where a loosely coupled fixed-lag smoother fuses IMU and LiDAR on 1-h-long experiments using our experimental car. It shows how handling rotating earth may be beneficial for long-term navigation within incremental smoothing algorithms.

To fuse information from inertial measurement units (IMU) with other sensors one needs an accurate model for IMU error propagation in terms of position, velocity and orientation, a triplet we call extended pose. In this paper we leverage a nontrivial result, namely log-linearity of inertial navigation equations based on the recently introduced Lie group SE2(3), to transpose the recent methodology of Barfoot and Furgale for associating uncertainty with poses (position, orientation) of SE(3) when using noisy wheel speeds, to the case of extended poses (position, velocity, orientation) of SE2(3) when using noisy IMUs. Besides, our approach to extended poses combined with log-linearity property allows revisiting the theory of preintegration on manifolds and reaching a further theoretic level in this field. We show exact preintegration formulas that account for rotating Earth, that is, centrifugal force and Coriolis effect, may be derived as a byproduct.

The present paper introduces a novel methodology for Unscented Kalman Filtering (UKF) on manifolds that extends previous work by the authors on UKF on Lie groups. Beyond filtering performance, the main interests of the approach are its versatility, as the method applies to numerous state estimation problems, and its simplicity of implementation for practitioners not being necessarily familiar with manifolds and Lie groups. We have developed the method on two independent open-source Python and Matlab frameworks we call UKF-M, for quickly implementing and testing the approach. The online repositories contain tutorials, documentation, and various relevant robotics examples that the user can readily reproduce and then adapt, for fast prototyping and benchmarking. The code is available at https://github.com/CAOR-MINES-ParisTech/ukfm.

This paper proposes a real-time approach for long-term inertial navigation based only on an Inertial Measurement Unit (IMU) for self-localizing wheeled robots. The approach builds upon two components: 1) a robust detector that uses recurrent deep neural networks to dynamically detect a variety of situations of interest, such as zero velocity or no lateral slip; and 2) a state-of-the-art Kalman filter which incorporates this knowledge as pseudo-measurements for localization. Evaluations on a publicly available car dataset demonstrates that the proposed scheme may achieve a final distance error of 20 m for a 21 km long trajectory of a vehicle driving for over an hour, equipped with an IMU of moderate precision (the gyro drift rate is 10 deg/h). To our knowledge, this is the first paper which combines sophisticated deep learning techniques with state-of the-art filtering methods for pure inertial navigation on wheeled vehicles and as such opens up for novel data-driven inertial navigation techniques. Moreover, albeit taylored for IMU-only based localization, our method may be used as a component for self-localization of wheeled robots equipped with a more complete sensor suite.

Combining visual information with inertial measurements is a popular approach to achieve robust and autonomous navigation in robotics, specifically in GPS-denied environments. In this paper, building upon both the recent theory of Unscented Kalman Filtering on Lie Groups (UKF-LG) and more generally the theory of invariant Kalman filtering (IEKF), an innovative UKF is derived for the monocular visual simultaneous localization and mapping (SLAM) problem. The body pose, velocity, and the 3D landmarks' positions are viewed as a single element of a (high dimensional) Lie group SE2+p(3), which constitutes the state, and where the accelerometers' and gyrometers' biases are appended to the state and estimated as well. The efficiency of the approach is validated both on simulations and on five real datasets.

Demodulation consists in factorizing a signal as a product of a high-frequency component (carrier) and a low-frequency component (modulation). Most of the classical demodulation methods developed for telecommunications cannot be transposed directly on mechanical problems. In gearbox vibration monitoring the assumption that the carrier energy is concentrated on a single harmonic is not verified. This paper shows the limits of this assumption and proposes a new approach based on optimization, more adapted to line spectrum signals.

Fusing visual information with inertial measurements for state estimation has aroused major interests in recent years. However, combining a robust estimation with computational efficiency remains challenging, specifically for low-cost aerial vehicles in which the quality of the sensors and the processor power are constrained by size, weight and cost. In this paper, we present an innovative filter for stereo visual inertial odometry building on: (i) the recently introduced stereo multistate constraint Kalman filter; (ii) the invariant filtering theory; and (iii) the unscented Kalman filter (UKF) on Lie groups. Our solution combines accuracy, robustness and versatility of the UKF. We then compare our approach to state-of-art solutions in terms of accuracy, robustness and computational complexity on the EuRoC dataset and a challenging MAV outdoor dataset.

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the proposed algorithm is based on a maximum a posteriori estimator, determined by optimization. But owing to the specific properties of the considered class of problems, the involved linearizations are proved to have a form of independence with respect to the current estimates, leveraged to avoid (partially or sometimes totally) the need to relinearize. The method is validated on a robot localization example, both in simulations and on real experimental data.