1,129 research outputs found
On the exponential convergence of the Kaczmarz algorithm
The Kaczmarz algorithm (KA) is a popular method for solving a system of
linear equations. In this note we derive a new exponential convergence result
for the KA. The key allowing us to establish the new result is to rewrite the
KA in such a way that its solution path can be interpreted as the output from a
particular dynamical system. The asymptotic stability results of the
corresponding dynamical system can then be leveraged to prove exponential
convergence of the KA. The new bound is also compared to existing bounds
Foreword
Magnetometers and inertial sensors (accelerometers and gyroscopes) are widely used to estimate 3D orientation. For the orientation estimates to be accurate, the sensor axes need to be aligned and the magnetometer needs to be calibrated for sensor errors and for the presence of magnetic disturbances. In this work we use a grey-box system identification approach to compute maximum likelihood estimates of the calibration parameters. An experiment where the magnetometer data is highly disturbed shows that the algorithm works well on real data, providing good calibration results and improved heading estimates. We also provide an identifiability analysis to understand how much rotation is needed to be able to solve the calibration problem.MC ImpulseCADIC
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
Magnetometer calibration using inertial sensors
In this work we present a practical algorithm for calibrating a magnetometer
for the presence of magnetic disturbances and for magnetometer sensor errors.
To allow for combining the magnetometer measurements with inertial measurements
for orientation estimation, the algorithm also corrects for misalignment
between the magnetometer and the inertial sensor axes. The calibration
algorithm is formulated as the solution to a maximum likelihood problem and the
computations are performed offline. The algorithm is shown to give good results
using data from two different commercially available sensor units. Using the
calibrated magnetometer measurements in combination with the inertial sensors
to determine the sensor's orientation is shown to lead to significantly
improved heading estimates.Comment: 19 pages, 8 figure
Optimal controller/observer gains of discounted-cost LQG systems
The linear-quadratic-Gaussian (LQG) control paradigm is well-known in
literature. The strategy of minimizing the cost function is available, both for
the case where the state is known and where it is estimated through an
observer. The situation is different when the cost function has an exponential
discount factor, also known as a prescribed degree of stability. In this case,
the optimal control strategy is only available when the state is known. This
paper builds on from that result, deriving an optimal control strategy when
working with an estimated state. Expressions for the resulting optimal expected
cost are also given
Developments Under the Freedom of Information Act
This article reviews authors' recently developed algorithm for identification of nonlinear state-space models under missing observations and extends it to the case of unknown model structure. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. If the model structure is unknown, an approximation of it is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is illustrated through a real application
Habitual Criminal Statutes: Shield or Sword
An essential part of future collision avoidance systems is to be able to predict road curvature. This can be based on vision data, but the lateral movement of leading vehicles can also be used to support road geometry estimation. This paper presents a method for detecting lane departures, including lane changes, of leading vehicles. This information is used to adapt the dynamic models used in the estimation algorithm in order to accommodate for the fact that a lane departure is in progress. The goal is to improve the accuracy of the road geometry estimates, which is affected by the motion of leading vehicles. The significantly improved performance is demonstrated using sensor data from authentic traffic environments
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