Dynamic mode decomposition for multiscale nonlinear physics

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed subsets of the data, and dominant time scales are discovered using spectral clustering on their eigenvalues. This approach produces time series data for each identified component, which sum to a faithful reconstruction of the input signal. It differs from most other methods in the field of multiresolution analysis (MRA) in that it 1) accounts for spatial and temporal coherencies simultaneously, making it more robust to scale overlap between components, and 2) yields a closed-form expression for local dynamics at each scale, which can be used for short-term prediction of any or all components. Our technique is an extension of multi-resolution dynamic mode decomposition (mrDMD), generalized to treat a broader variety of multiscale systems and more faithfully reconstruct their isolated components. In this paper we present an overview of our algorithm and its results on two example physical systems, and briefly discuss some advantages and potential forecasting applications for the technique

Robot-assisted Backscatter Localization for IoT Applications

Recent years have witnessed the rapid proliferation of backscatter technologies that realize the ubiquitous and long-term connectivity to empower smart cities and smart homes. Localizing such backscatter tags is crucial for IoT-based smart applications. However, current backscatter localization systems require prior knowledge of the site, either a map or landmarks with known positions, which is laborious for deployment. To empower universal localization service, this paper presents Rover, an indoor localization system that localizes multiple backscatter tags without any start-up cost using a robot equipped with inertial sensors. Rover runs in a joint optimization framework, fusing measurements from backscattered WiFi signals and inertial sensors to simultaneously estimate the locations of both the robot and the connected tags. Our design addresses practical issues including interference among multiple tags, real-time processing, as well as the data marginalization problem in dealing with degenerated motions. We prototype Rover using off-the-shelf WiFi chips and customized backscatter tags. Our experiments show that Rover achieves localization accuracies of 39.3 cm for the robot and 74.6 cm for the tags.Comment: To appear in IEEE Transactions on Wireless Communications. arXiv admin note: substantial text overlap with arXiv:1908.0329

Machine Learning Methods for Data Association in Multi-Object Tracking

Data association is a key step within the multi-object tracking pipeline that is notoriously challenging due to its combinatorial nature. A popular and general way to formulate data association is as the NP-hard multidimensional assignment problem (MDAP). Over the last few years, data-driven approaches to assignment have become increasingly prevalent as these techniques have started to mature. We focus this survey solely on learning algorithms for the assignment step of multi-object tracking, and we attempt to unify various methods by highlighting their connections to linear assignment as well as to the MDAP. First, we review probabilistic and end-to-end optimization approaches to data association, followed by methods that learn association affinities from data. We then compare the performance of the methods presented in this survey, and conclude by discussing future research directions.Comment: Accepted for publication in ACM Computing Survey

Scene Invariant Crowd Segmentation and Counting Using Scale-Normalized Histogram of Moving Gradients (HoMG)

The problem of automated crowd segmentation and counting has garnered significant interest in the field of video surveillance. This paper proposes a novel scene invariant crowd segmentation and counting algorithm designed with high accuracy yet low computational complexity in mind, which is key for widespread industrial adoption. A novel low-complexity, scale-normalized feature called Histogram of Moving Gradients (HoMG) is introduced for highly effective spatiotemporal representation of individuals and crowds within a video. Real-time crowd segmentation is achieved via boosted cascade of weak classifiers based on sliding-window HoMG features, while linear SVM regression of crowd-region HoMG features is employed for real-time crowd counting. Experimental results using multi-camera crowd datasets show that the proposed algorithm significantly outperform state-of-the-art crowd counting algorithms, as well as achieve very promising crowd segmentation results, thus demonstrating the efficacy of the proposed method for highly-accurate, real-time video-driven crowd analysis.Comment: 9 page

MFDL: A Multicarrier Fresnel Penetration Model based Device-Free Localization System leveraging Commodity Wi-Fi Cards

Device-free localization plays an important role in many ubiquitous applications. Among the different technologies proposed, Wi-Fi based technology using commercial devices has attracted much attention due to its low cost, ease of deployment, and high potential for accurate localization. Existing solutions use either fingerprints that require labor-intensive radio-map survey and updates, or models constructed from empirical studies with dense deployment of Wi-Fi transceivers. In this work, we explore the Fresnel Zone Theory in physics and propose a generic Fresnel Penetration Model (FPM), which reveals the linear relationship between specific Fresnel zones and multicarrier Fresnel phase difference, along with the Fresnel phase offset caused by static multipath environments. We validate FPM in both outdoor and complex indoor environments. Furthermore, we design a multicarrier FPM based device-free localization system (MFDL), which overcomes a number of practical challenges, particularly the Fresnel phase difference estimation and phase offset calibration in multipath-rich indoor environments. Extensive experimental results show that compared with the state-of-the-art work (LiFS), our MFDL system achieves better localization accuracy with much fewer number of Wi-Fi transceivers. Specifically, using only three transceivers, the median localization error of MFDL is as low as 45$cm$ in an outdoor environment of 36$m^2$, and 55$cm$ in indoor settings of 25$m^2$. Increasing the number of transceivers to four allows us to achieve 75$cm$ median localization error in a 72$m^2$ indoor area, compared with the 1.1$m$ median localization error achieved by LiFS using 11 transceivers in a 70$m^2$ area.Comment: 14 pages, 13 figure

An Efficient Schmidt-EKF for 3D Visual-Inertial SLAM

It holds great implications for practical applications to enable centimeter-accuracy positioning for mobile and wearable sensor systems. In this paper, we propose a novel, high-precision, efficient visual-inertial (VI)-SLAM algorithm, termed Schmidt-EKF VI-SLAM (SEVIS), which optimally fuses IMU measurements and monocular images in a tightly-coupled manner to provide 3D motion tracking with bounded error. In particular, we adapt the Schmidt Kalman filter formulation to selectively include informative features in the state vector while treating them as nuisance parameters (or Schmidt states) once they become matured. This change in modeling allows for significant computational savings by no longer needing to constantly update the Schmidt states (or their covariance), while still allowing the EKF to correctly account for their cross-correlations with the active states. As a result, we achieve linear computational complexity in terms of map size, instead of quadratic as in the standard SLAM systems. In order to fully exploit the map information to bound navigation drifts, we advocate efficient keyframe-aided 2D-to-2D feature matching to find reliable correspondences between current 2D visual measurements and 3D map features. The proposed SEVIS is extensively validated in both simulations and experiments.Comment: Accepted to the 2019 Conference on Computer Vision and Pattern Recognition (CVPR

Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting

We present a continuous time state estimation framework that unifies traditionally individual tasks of smoothing, tracking, and forecasting (STF), for a class of targets subject to smooth motion processes, e.g., the target moves with nearly constant acceleration or affected by insignificant noises. Fundamentally different from the conventional Markov transition formulation, the state process is modeled by a continuous trajectory function of time (FoT) and the STF problem is formulated as an online data fitting problem with the goal of finding the trajectory FoT that best fits the observations in a sliding time-window. Then, the state of the target, whether the past (namely, smoothing), the current (filtering) or the near-future (forecasting), can be inferred from the FoT. Our framework releases stringent statistical modeling of the target motion in real time, and is applicable to a broad range of real world targets of significance such as passenger aircraft and ships which move on scheduled, (segmented) smooth paths but little statistical knowledge is given about their real time movement and even about the sensors. In addition, the proposed STF framework inherits the advantages of data fitting for accommodating arbitrary sensor revisit time, target maneuvering and missed detection. The proposed method is compared with state of the art estimators in scenarios of either maneuvering or non-maneuvering target.Comment: 16 pages, 8 figures, 5 tables, 80 references; Codes availabl

DenseNet: Implementing Efficient ConvNet Descriptor Pyramids

Convolutional Neural Networks (CNNs) can provide accurate object classification. They can be extended to perform object detection by iterating over dense or selected proposed object regions. However, the runtime of such detectors scales as the total number and/or area of regions to examine per image, and training such detectors may be prohibitively slow. However, for some CNN classifier topologies, it is possible to share significant work among overlapping regions to be classified. This paper presents DenseNet, an open source system that computes dense, multiscale features from the convolutional layers of a CNN based object classifier. Future work will involve training efficient object detectors with DenseNet feature descriptors

A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point', or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point' also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point'. Our statistical methods detect this `tipping point' and its time of onset.Comment: 33 pages with 15 figure; accepted for publication in the Cryosphere (2013

Topological Data Analysis of Financial Time Series: Landscapes of Crashes

We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a 'persistence landscapes'. We quantify the temporal changes in persistence landscapes via their $L^p$-norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the $L^p$-norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of $L^p$-norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which goes beyond the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here