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Dual-comb ranging has emerged as an effective technology for long-distance metrology, providing absolute distance measurements with high speed, precision, and accuracy. Here, we demonstrate a dual-comb ranging method that utilizes a free-space transceiver unit, enabling dead-zone-free measurements and simultaneous ranging with interchanged comb roles to allow for long-distance measurements even when the target is moving. It includes a GPU-accelerated algorithm for real-time signal processing and a free-running single-cavity solid-state dual-comb laser with a carrier wavelength $\lambda_c \approx$ 1055 nm, a pulse repetition rate of 1 GHz and a repetition rate difference of 5.06 kHz. This combination offers a fast update rate and sufficient signal strength to reach a single-shot time-of-flight precision of around 0.1 $\mu$m (i.e. $< \lambda_c/4$) on a cooperative target placed at a distance of more than 40 m. The free-running laser is sufficiently stable to use the phase information for interferometric distance measurements, which improves the single-shot precision to $<$20 nm. To assess the ranging accuracy, we track the motion of the cooperative target when moved over 40 m and compare it to a reference interferometer. The residuals between the two measurements are below 3 $\mu$m. These results highlight the potential of this approach for accurate and dead-zone-free long-distance ranging, supporting real-time tracking with nm-level precision., Comment: Supplementary Information included

We prove an effective closing lemma for unipotent flows on quotients of perfect real groups. This is largely motivated by recent developments in effective unipotent dynamics., Comment: 24 pages

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work with Lindenstrauss, Margulis, Mohammadi, and Shah., Comment: 27 pages. Comments welcome!

The multi-scale transport and exchange processes in the atmosphere over mountains -- programme and experiment (TEAMx) wants to advance the understanding of transport and exchange processes over mountainous terrain as well as to collect unique multi-scale datasets that can be used, e.g., for process studies, model development and model evaluation. The TEAMx Observational Campaign (TOC) is planned to take place between 2024 and 2025. In summer 2022 a TEAMx pre-campaign (TEAMx-PC22) was conducted in the Inn Valley and one of its tributaries, the Weer Valley, to test the suitability and required logistics of measurement sites, to evaluate their value for the main campaign, and to test new observation techniques in complex terrain. Scientifically, this campaign focused on resolving the mountain boundary layer and valley wind systems on multiple scales. Through the combined effort of six institutions the pre-campaign can be deemed successful. A detailed description of the setup at each sub-target area is given. Due to the spatial distribution of instruments and their spatio-temporal resolution, atmospheric processes and phenomena like valley winds have been investigated at different locations and on different scales. Furthermore, scale interactions were detected and are discussed in detail in two example cases. Additionally, observational gaps were determined which should be closed for the TOC. Data of the pre-campaign are publicly available online and can be used for process studies, demonstrating the utility of new observation methods, model verification, and for data assimilation., Comment: This manuscript was submitted on 07. Nov 2023 and is under review at Meteorologische Zeitschrift - Contributions to Atmospheric Sciences, Borntraeger Science Publishers, Germany (ISSN: 0941-2948; ISSN online version: 1610-1227)

We use composition of binary quadratic forms to systematically create pairs of Seifert surfaces that are non-isotopic in the four-ball. Our main topological result employs Gauss composition to classify the pairs of binary quadratic forms that arise as the Seifert forms of pairs of disjoint Seifert surfaces of genus one. The main ingredient of the proof is number-theoretic and of independent interest. It establishes a new connection between the Bhargava cube and the geometric approach to Gauss composition via planes in the space of two-by-two matrices. In particular, we obtain a geometric recipe that given any two binary quadratic forms finds a Bhargava cube that gives rise to their composition., Comment: 29 pages, 2 figures, comments welcome. v4: minor changes

Existing work on scene flow estimation focuses on autonomous driving and mobile robotics, while automated solutions are lacking for motion in nature, such as that exhibited by debris flows. We propose DEFLOW, a model for 3D motion estimation of debris flows, together with a newly captured dataset. We adopt a novel multi-level sensor fusion architecture and self-supervision to incorporate the inductive biases of the scene. We further adopt a multi-frame temporal processing module to enable flow speed estimation over time. Our model achieves state-of-the-art optical flow and depth estimation on our dataset, and fully automates the motion estimation for debris flows. The source code and dataset are available at project page., Comment: Photogrammetric Computer Vision Workshop, CVPRW 2023, camera ready

Let $\{a_t: t \in \mathbb{R}\}< SL_{d}(\mathbb{R})$ be a diagonalizable subgroup whose expanding horospherical subgroup $U < SL_{d}(\mathbb{R})$ is abelian. By the Birkhoff ergodic theorem, for any $x \in SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ and for almost every point $u \in U$ the point $ux$ is Birkhoff generic for $a_t$ when $t \to \infty$. We prove that the same is true when $U$ is replaced by any non-degenerate analytic curve in $U$. This Birkhoff genericity result has various applications in Diophantine approximation. For instance, we obtain density estimates for Dirichlet improvability along typical points on a curve in Euclidean space. Other applications address approximations by algebraic numbers and best approximations (in the sense of Lagarias)., Comment: 38 pages

Multi-beam LiDAR sensors, as used on autonomous vehicles and mobile robots, acquire sequences of 3D range scans ("frames"). Each frame covers the scene sparsely, due to limited angular scanning resolution and occlusion. The sparsity restricts the performance of downstream processes like semantic segmentation or surface reconstruction. Luckily, when the sensor moves, frames are captured from a sequence of different viewpoints. This provides complementary information and, when accumulated in a common scene coordinate frame, yields a denser sampling and a more complete coverage of the underlying 3D scene. However, often the scanned scenes contain moving objects. Points on those objects are not correctly aligned by just undoing the scanner's ego-motion. In the present paper, we explore multi-frame point cloud accumulation as a mid-level representation of 3D scan sequences, and develop a method that exploits inductive biases of outdoor street scenes, including their geometric layout and object-level rigidity. Compared to state-of-the-art scene flow estimators, our proposed approach aims to align all 3D points in a common reference frame correctly accumulating the points on the individual objects. Our approach greatly reduces the alignment errors on several benchmark datasets. Moreover, the accumulated point clouds benefit high-level tasks like surface reconstruction., Comment: ECCV 2022, camera ready

We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(12), 2019). As an application, we establish entropy bounds for limits of invariant measures on homogeneous toral sets in GL(4) of biquadratic, cyclic, or dihedral type., Comment: 44 pages

To any $k$-dimensional subspace of $\mathbb Q^n$ one can naturally associate a point in the Grassmannian ${\rm Gr}_{n,k}(\mathbb R)$ and two shapes of lattices of rank $k$ and $n-k$ respectively. These lattices originate by intersecting the $k$-dimensional subspace with the lattice $\mathbb Z^n$. Using unipotent dynamics we prove simultaneous equidistribution of all of these objects under a congruence conditions when $(k,n) \neq (2,4)$., Comment: 52 pages

We propose a data-driven scene flow estimation algorithm exploiting the observation that many 3D scenes can be explained by a collection of agents moving as rigid bodies. At the core of our method lies a deep architecture able to reason at the \textbf{object-level} by considering 3D scene flow in conjunction with other 3D tasks. This object level abstraction, enables us to relax the requirement for dense scene flow supervision with simpler binary background segmentation mask and ego-motion annotations. Our mild supervision requirements make our method well suited for recently released massive data collections for autonomous driving, which do not contain dense scene flow annotations. As output, our model provides low-level cues like pointwise flow and higher-level cues such as holistic scene understanding at the level of rigid objects. We further propose a test-time optimization refining the predicted rigid scene flow. We showcase the effectiveness and generalization capacity of our method on four different autonomous driving datasets. We release our source code and pre-trained models under \url{github.com/zgojcic/Rigid3DSceneFlow}.

We introduce PREDATOR, a model for pairwise point-cloud registration with deep attention to the overlap region. Different from previous work, our model is specifically designed to handle (also) point-cloud pairs with low overlap. Its key novelty is an overlap-attention block for early information exchange between the latent encodings of the two point clouds. In this way the subsequent decoding of the latent representations into per-point features is conditioned on the respective other point cloud, and thus can predict which points are not only salient, but also lie in the overlap region between the two point clouds. The ability to focus on points that are relevant for matching greatly improves performance: PREDATOR raises the rate of successful registrations by more than 20% in the low-overlap scenario, and also sets a new state of the art for the 3DMatch benchmark with 89% registration recall., Comment: CVPR 2021 (Oral) - Improved performance after fixing GNN bug

We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show -- under additional congruence assumptions on the CM order -- that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large. This variant of the equidistribution theorems of Duke and Cornut-Vatsal is an(other) application of the recent work of Einsiedler and Lindenstrauss on the classification of joinings of higher-rank diagonalizable actions., Comment: 46 pages. Revised according to the referee's comments

We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the reference fingerprint map (RFM). Spatial filtering and kernel smoothing of the kinematically collected raw data allow efficiently estimating the standard deviations during RFM generation. In the positioning stage, the weights control the contribution of each feature to the dissimilarity measure, which in turn quantifies the difference between the set of online measured features and the fingerprints stored in the RFM. Features with little variability contribute more to the estimated position than features with high variability. Iterations are necessary because the variability depends on the location, and the location is initially unknown when estimating the position. Using real WiFi signal strength data from extended test measurements with ground truth in an office building, we show that the standard deviations of these features vary considerably within the region of interest and are neither simple functions of the signal strength nor of the distances from the corresponding access points. This is the motivation to include the empirical standard deviations in the RFM. We then analyze the deviations of the estimated positions with and without the location-dependent weighting. In the present example the maximum radial positioning error from ground truth are reduced by 40% comparing to kNN without the weighted dissimilarity measure., Comment: 18 pages, 9 figures, and 1 table

To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement and the second two essentially arise from the accidental local isomorphism between SO(4) and SO(3)xSO(3). As an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings we prove simultaneous equidistribution of all of these objects under two splitting conditions., Comment: 45 pages, added a section about oriented planes. To appear in Duke Mathematical Journal

We propose an approach for fingerprinting-based positioning which reduces the data requirements and computational complexity of the online positioning stage. It is based on a segmentation of the entire region of interest into subregions, identification of candidate subregions during the online-stage, and position estimation using a preselected subset of relevant features. The subregion selection uses a modified Jaccard index which quantifies the similarity between the features observed by the user and those available within the reference fingerprint map. The adaptive feature selection is achieved using an adaptive forward-backward greedy search which determines a subset of features for each subregion, relevant with respect to a given fingerprinting-based positioning method. In an empirical study using signals of opportunity for fingerprinting the proposed subregion and feature selection reduce the processing time during the online-stage by a factor of about 10 while the positioning accuracy does not deteriorate significantly. In fact, in one of the two study cases the 90th percentile of the circular error increased by 7.5% while in the other study case we even found a reduction of the corresponding circular error by 30%., Comment: 15 pagers, 10 figures, 10 tables, revised version for publishing to TLBS. arXiv admin note: text overlap with arXiv:1711.07812

We propose 3DSmoothNet, a full workflow to match 3D point clouds with a siamese deep learning architecture and fully convolutional layers using a voxelized smoothed density value (SDV) representation. The latter is computed per interest point and aligned to the local reference frame (LRF) to achieve rotation invariance. Our compact, learned, rotation invariant 3D point cloud descriptor achieves 94.9% average recall on the 3DMatch benchmark data set, outperforming the state-of-the-art by more than 20 percent points with only 32 output dimensions. This very low output dimension allows for near realtime correspondence search with 0.1 ms per feature point on a standard PC. Our approach is sensor- and sceneagnostic because of SDV, LRF and learning highly descriptive features with fully convolutional layers. We show that 3DSmoothNet trained only on RGB-D indoor scenes of buildings achieves 79.0% average recall on laser scans of outdoor vegetation, more than double the performance of our closest, learning-based competitors. Code, data and pre-trained models are available online at https://github.com/zgojcic/3DSmoothNet., Comment: CVPR 2019

A non-vector-based dissimilarity measure is proposed by combining vector-based distance metrics and set operations. This proposed compound dissimilarity measure (CDM) is applicable to quantify similarity of collections of attribute/feature pairs where not all attributes are present in all collections. This is a typical challenge in the context of e.g., fingerprinting-based positioning (FbP). Compared to vector-based distance metrics (e.g., Minkowski), the merits of the proposed CDM are i) the data do not need to be converted to vectors of equal dimension, ii) shared and unshared attributes can be weighted differently within the assessment, and iii) additional degrees of freedom within the measure allow to adapt its properties to application needs in a data-driven way. We indicate the validity of the proposed CDM by demonstrating the improvements of the positioning performance of fingerprinting-based WLAN indoor positioning using four different datasets, three of them publicly available. When processing these datasets using CDM instead of conventional distance metrics the accuracy of identifying buildings and floors improves by about 5% on average. The 2d positioning errors in terms of root mean squared error (RMSE) are reduced by a factor of two, and the percentage of position solutions with less than 2m error improves by over 10%., Comment: 7 pages, 5 figures, 3 tables, a paper accepted to be published IPIN 2018, Nantes France

We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011.

We propose an approach to reduce both computational complexity and data storage requirements for the online positioning stage of a fingerprinting-based indoor positioning system (FIPS) by introducing segmentation of the region of interest (RoI) into sub-regions, sub-region selection using a modified Jaccard index, and feature selection based on randomized least absolute shrinkage and selection operator (LASSO). We implement these steps into a Bayesian framework of position estimation using the maximum a posteriori (MAP) principle. An additional benefit of these steps is that the time for estimating the position, and the required data storage are virtually independent of the size of the RoI and of the total number of available features within the RoI. Thus the proposed steps facilitate application of FIPS to large areas. Results of an experimental analysis using real data collected in an office building using a Nexus 6P smart phone as user device and a total station for providing position ground truth corroborate the expected performance of the proposed approach. The positioning accuracy obtained by only processing 10 automatically identified features instead of all available ones and limiting position estimation to 10 automatically identified sub-regions instead of the entire RoI is equivalent to processing all available data. In the chosen example, 50% of the errors are less than 1.8 m and 90% are less than 5 m. However, the computation time using the automatically identified subset of data is only about 1% of that required for processing the entire data set., Comment: 16 pages, 4 figures, and 2 tables. Accepted to publish on LBS 2018, Zurich

Foot-mounted inertial positioning (FMIP) can face problems of inertial drifts and unknown initial states in real applications, which renders the estimated trajectories inaccurate and not obtained in a well defined coordinate system for matching trajectories of different users. In this paper, an approach adopting received signal strength (RSS) measurements for Wifi access points (APs) are proposed to align and calibrate the trajectories estimated from foot mounted inertial measurement units (IMUs). A crowd-sourced radio map (RM) can be built subsequently and can be used for fingerprinting based Wifi indoor positioning (FWIP). The foundation of the proposed approach is graph based simultaneously localization and mapping (SLAM). The nodes in the graph denote users poses and the edges denote the pairwise constrains between the nodes. The constrains are derived from: (1) inertial estimated trajectories; (2) vicinity in the RSS space. With these constrains, an error functions is defined. By minimizing the error function, the graph is optimized and the aligned/calibrated trajectories along with the RM are acquired. The experimental results have corroborated the effectiveness of the approach for trajectory alignment, calibration as well as RM construction., Comment: 9 figures, 6 pages, paper under review of IPIN 2017

Foot-mounted inertial positioning (FMIP) and fingerprinting based WiFi indoor positioning (FWIP) are two promising solutions for indoor positioning. However, FMIP suffers from accumulative positioning errors in the long term while FWIP involves a very labor-intensive offline training phase. A new approach combining the two solutions is proposed in this paper, which can limit the error growth in FMIP and is free of any offline site survey phase. This approach is realized in the framework of a particle filter, where each particle denotes a potential trajectory of the user and is weighted according to its consistency in signal strength space. Compared with the traditional Gaussian process based approaches, the proposed one has less computational cost and is free from any prior information in the position domain, such as the positions of access points, received signal strengths at certain positions and so on. An experiment is carried out to demonstrate the performance of the proposed approach compared to the traditional Gaussian process based approach., Comment: 12 figures. Accepted by European Navigation Conference 2017, Lausanne

We propose a scheme to employ backpropagation neural networks (BPNNs) for both stages of fingerprinting-based indoor positioning using WLAN/WiFi signal strengths (FWIPS): radio map construction during the offline stage, and localization during the online stage. Given a training radio map (TRM), i.e., a set of coordinate vectors and associated WLAN/WiFi signal strengths of the available access points, a BPNN can be trained to output the expected signal strengths for any input position within the region of interest (BPNN-RM). This can be used to provide a continuous representation of the radio map and to filter, densify or decimate a discrete radio map. Correspondingly, the TRM can also be used to train another BPNN to output the expected position within the region of interest for any input vector of recorded signal strengths and thus carry out localization (BPNN-LA).Key aspects of the design of such artificial neural networks for a specific application are the selection of design parameters like the number of hidden layers and nodes within the network, and the training procedure. Summarizing extensive numerical simulations, based on real measurements in a testbed, we analyze the impact of these design choices on the performance of the BPNN and compare the results in particular to those obtained using the $k$ nearest neighbors ($k$NN) and weighted $k$ nearest neighbors approaches to FWIPS., Comment: 11 pages, 11 figures, published in proceedings UPINLBS 2016

The main limitation that constrains the fast and comprehensive application of Wireless Local Area Network (WLAN) based indoor localization systems with Received Signal Strength (RSS) positioning algorithms is the building of the fingerprinting radio map, which is time-consuming especially when the indoor environment is large and/or with high frequent changes. Different approaches have been proposed to reduce workload, including fingerprinting deployment and update efforts, but the performance degrades greatly when the workload is reduced below a certain level. In this paper, we propose an indoor localization scenario that applies metric learning and manifold alignment to realize direct mapping localization (DML) using a low resolution radio map with single sample of RSS that reduces the fingerprinting workload by up to 87\%. Compared to previous work. The proposed two localization approaches, DML and $k$ nearest neighbors based on reconstructed radio map (reKNN), were shown to achieve less than 4.3\ m and 3.7\ m mean localization error respectively in a typical office environment with an area of approximately 170\ m$^2$, while the unsupervised localization with perturbation algorithm was shown to achieve 4.7\ m mean localization error with 8 times more workload than the proposed methods. As for the room level localization application, both DML and reKNN can meet the requirement with at most 9\ m of localization error which is enough to tell apart different rooms with over 99\% accuracy., Comment: more refined analysis required