221 research outputs found
The adaptive patched cubature filter and its implementation
There are numerous contexts where one wishes to describe the state of a
randomly evolving system. Effective solutions combine models that quantify the
underlying uncertainty with available observational data to form scientifically
reasonable estimates for the uncertainty in the system state. Stochastic
differential equations are often used to mathematically model the underlying
system.
The Kusuoka-Lyons-Victoir (KLV) approach is a higher order particle method
for approximating the weak solution of a stochastic differential equation that
uses a weighted set of scenarios to approximate the evolving probability
distribution to a high order of accuracy. The algorithm can be performed by
integrating along a number of carefully selected bounded variation paths. The
iterated application of the KLV method has a tendency for the number of
particles to increase. This can be addressed and, together with local dynamic
recombination, which simplifies the support of discrete measure without harming
the accuracy of the approximation, the KLV method becomes eligible to solve the
filtering problem in contexts where one desires to maintain an accurate
description of the ever-evolving conditioned measure.
In addition to the alternate application of the KLV method and recombination,
we make use of the smooth nature of the likelihood function and high order
accuracy of the approximations to lead some of the particles immediately to the
next observation time and to build into the algorithm a form of automatic high
order adaptive importance sampling.Comment: to appear in Communications in Mathematical Sciences. arXiv admin
note: substantial text overlap with arXiv:1311.675
Converted Measurement Trackers for Systems with Nonlinear Measurement Functions
Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian, and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics. There are two potential issues that arise when performing converted measurement tracking. The first is conversion bias that occurs when the measurement transformation introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs because the estimate of the converted measurement error covariance is correlated with the measurement noise, leading to a biased Kalman gain. The goal of this research is to develop a new approach to converted measurement tracking that eliminates the conversion bias and mitigates the estimation bias. This new decorrelated unbiased converted measurement (DUCM) approach is developed and applied to numerous tracking problems applicable to sonar and radar systems. The resulting methods are compared to the current state of the art based on their mean square error (MSE) performance, consistency and performance with respect to the posterior Cramer-Rao lower bound
Robust Gaussian Filtering using a Pseudo Measurement
Many sensors, such as range, sonar, radar, GPS and visual devices, produce
measurements which are contaminated by outliers. This problem can be addressed
by using fat-tailed sensor models, which account for the possibility of
outliers. Unfortunately, all estimation algorithms belonging to the family of
Gaussian filters (such as the widely-used extended Kalman filter and unscented
Kalman filter) are inherently incompatible with such fat-tailed sensor models.
The contribution of this paper is to show that any Gaussian filter can be made
compatible with fat-tailed sensor models by applying one simple change: Instead
of filtering with the physical measurement, we propose to filter with a pseudo
measurement obtained by applying a feature function to the physical
measurement. We derive such a feature function which is optimal under some
conditions. Simulation results show that the proposed method can effectively
handle measurement outliers and allows for robust filtering in both linear and
nonlinear systems
Moment Estimation Using a Marginalized Transform
We present a method for estimating mean and covariance of a transformed Gaussian random variable. The method is based on evaluations of the transforming function and resembles the unscented transform and Gauss-Hermite integration in that respect. The information provided by the evaluations is used in a Bayesian framework to form a posterior description of the parameters in a model of the transforming function. Estimates are then derived by marginalizing these parameters from the analytical expression of the mean and covariance. An estimation algorithm, based on the assumption that the transforming function can be described using Hermite polynomials, is presented and applied to the non-linear filtering problem. The resulting marginalized transform (MT) estimator is compared to the cubature rule, the unscented transform and the divided difference estimator. The evaluations show that the presented method performs better than these methods, more specifically in estimating the covariance matrix. Contrary to the unscented transform, the resulting approximation of the covariance matrix is guaranteed to be positive-semidefinite
Denoising MAX6675 reading using Kalman filter and factorial design
This paper aims to tune the Kalman filter (KF) input variables, namely measurement error and process noise, based on two-level factorial design. Kalman filter then was applied in inexpensive temperature-acquisition utilizing MAX6675 and K-type thermocouple with Arduino as its microprocessor. Two levels for each input variable, respectively, 0.1 and 0.9, were selected and applied to four K-type thermocouples mounted on MAX6675. Each sensor with a different combination of input variables was used to measure the temperature of ambient-water, boiling water, and sudden temperature drops in the system. The measurement results which consisted of the original and KF readings were evaluated to determine the optimum combination of input variables. It was found that the optimum combination of input variables was highly dependent on the system's dynamics. For systems with relatively constant dynamics, a large value of measurement error and small value of process noise results in higher precision readings. Nevertheless, for fast dynamic systems, the previous input variables' combination is less optimal because it produced a time-gap, which made the KF reading differ from the original measurement. The selection of the optimum input combination using two-level factorial design eased the KF tuning process, resulting in a more precise yet low-cost sensor
Computational intelligence approaches to robotics, automation, and control [Volume guest editors]
No abstract available
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