1,984 research outputs found
Efficient Derivative Computation for Cumulative B-Splines on Lie Groups
Continuous-time trajectory representation has recently gained popularity for
tasks where the fusion of high-frame-rate sensors and multiple unsynchronized
devices is required. Lie group cumulative B-splines are a popular way of
representing continuous trajectories without singularities. They have been used
in near real-time SLAM and odometry systems with IMU, LiDAR, regular, RGB-D and
event cameras, as well as for offline calibration. These applications require
efficient computation of time derivatives (velocity, acceleration), but all
prior works rely on a computationally suboptimal formulation. In this work we
present an alternative derivation of time derivatives based on recurrence
relations that needs instead of matrix
operations (for a spline of order ) and results in simple and elegant
expressions. While producing the same result, the proposed approach
significantly speeds up the trajectory optimization and allows for computing
simple analytic derivatives with respect to spline knots. The results presented
in this paper pave the way for incorporating continuous-time trajectory
representations into more applications where real-time performance is required.Comment: First two authors contributed equall
Continuous-Time Ultra-Wideband-Inertial Fusion
We present a novel continuous-time online state estimation framework using
ultra-wideband and inertial sensors. For representing motion states
continuously over time, quaternion-based cubic B-splines are exploited with
efficient solutions to kinematic interpolations and spatial differentiations.
Based thereon, a sliding-window spline fitting scheme is established for
asynchronous multi-sensor fusion and online calibration. We evaluate the
proposed system, SFUISE (spline fusion-based ultra-wideband-inertial state
estimation), in real-world scenarios based on public data set and experiments.
The proposed spline fusion scheme is real-time capable and delivers superior
performance over state-of-the-art discrete-time schemes. We release the source
code and own experimental data set at https://github.com/KIT-ISAS/SFUISE.Comment: 8 pages, submitted to IEEE Robotics and Automation Letters (RA-L
Spline-based self-controlled case series method
The self-controlled case series (SCCS) method is an alternative to study designs such as cohort and case control methods and is used to investigate potential associations between the timing of vaccine or other drug exposures and adverse events. It requires information only on cases, individuals who have experienced the adverse event at least once, and automatically controls all fixed confounding variables that could modify the true association between exposure and adverse event. Time-varying confounders such as age, on the other hand, are not automatically controlled and must be allowed for explicitly. The original SCCS method used step functions to represent risk periods (windows of exposed time) and age effects. Hence, exposure risk periods and/or age groups have to be prespecified a priori, but a poor choice of group boundaries may lead to biased estimates. In this paper, we propose a nonparametric SCCS method in which both age and exposure effects are represented by spline functions at the same time. To avoid a numerical integration of the product of these two spline functions in the likelihood function of the SCCS method, we defined the first, second, and third integrals of I-splines based on the definition of integrals of M-splines. Simulation studies showed that the new method performs well. This new method is applied to data on pediatric vaccines
Jacobian Computation for Cumulative B-Splines on SE(3) and Application to Continuous-Time Object Tracking
In this paper we propose a method that estimates the SE(3) continuous trajectories (orientation and translation) of the dynamic rigid objects present in a scene, from multiple RGB-D views. Specifically, we fit the object trajectories to cumulative B-Splines curves, which allow us to interpolate, at any intermediate time stamp, not only their poses but also their linear and angular velocities and accelerations. Additionally, we derive in this work the analytical SE(3) Jacobians needed by the optimization, being applicable to any other approach that uses this type of curves. To the best of our knowledge this is the first work that proposes 6-DoF continuous-time object tracking, which we endorse with significant computational cost reduction thanks to our analytical derivations. We evaluate our proposal in synthetic data and in a public benchmark, showing competitive results in localization and significant improvements in velocity estimation in comparison to discrete-time approaches. © 2016 IEEE
Reliable Single Chip Genotyping with Semi-Parametric Log-Concave Mixtures
The common approach to SNP genotyping is to use (model-based) clustering per individual SNP, on a set of arrays. Genotyping all SNPs on a single array is much more attractive, in terms of flexibility, stability and applicability, when developing new chips. A new semi-parametric method, named SCALA, is proposed. It is based on a mixture model using semi-parametric log-concave densities. Instead of using the raw data, the mixture is fitted on a two-dimensional histogram, thereby making computation time almost independent of the number of SNPs. Furthermore, the algorithm is effective in low-MAF situations. Comparisons between SCALA and CRLMM on HapMap genotypes show very reliable calling of single arrays. Some heterozygous genotypes from HapMap are called homozygous by SCALA and to lesser extent by CRLMM too. Furthermore, HapMap's NoCalls (NN) could be genotyped by SCALA, mostly with high probability. The software is available as R scripts from the website www.math.leidenuniv.nl/~rrippe
Continuous-Time Fixed-Lag Smoothing for LiDAR-Inertial-Camera SLAM
Localization and mapping with heterogeneous multi-sensor fusion have been
prevalent in recent years. To adequately fuse multi-modal sensor measurements
received at different time instants and different frequencies, we estimate the
continuous-time trajectory by fixed-lag smoothing within a factor-graph
optimization framework. With the continuous-time formulation, we can query
poses at any time instants corresponding to the sensor measurements. To bound
the computation complexity of the continuous-time fixed-lag smoother, we
maintain temporal and keyframe sliding windows with constant size, and
probabilistically marginalize out control points of the trajectory and other
states, which allows preserving prior information for future sliding-window
optimization. Based on continuous-time fixed-lag smoothing, we design
tightly-coupled multi-modal SLAM algorithms with a variety of sensor
combinations, like the LiDAR-inertial and LiDAR-inertial-camera SLAM systems,
in which online timeoffset calibration is also naturally supported. More
importantly, benefiting from the marginalization and our derived analytical
Jacobians for optimization, the proposed continuous-time SLAM systems can
achieve real-time performance regardless of the high complexity of
continuous-time formulation. The proposed multi-modal SLAM systems have been
widely evaluated on three public datasets and self-collect datasets. The
results demonstrate that the proposed continuous-time SLAM systems can achieve
high-accuracy pose estimations and outperform existing state-of-the-art
methods. To benefit the research community, we will open source our code at
~\url{https://github.com/APRIL-ZJU/clic}
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