87,268 research outputs found
Robust Singular Smoothers For Tracking Using Low-Fidelity Data
Tracking underwater autonomous platforms is often difficult because of noisy,
biased, and discretized input data. Classic filters and smoothers based on
standard assumptions of Gaussian white noise break down when presented with any
of these challenges. Robust models (such as the Huber loss) and constraints
(e.g. maximum velocity) are used to attenuate these issues. Here, we consider
robust smoothing with singular covariance, which covers bias and correlated
noise, as well as many specific model types, such as those used in navigation.
In particular, we show how to combine singular covariance models with robust
losses and state-space constraints in a unified framework that can handle very
low-fidelity data. A noisy, biased, and discretized navigation dataset from a
submerged, low-cost inertial measurement unit (IMU) package, with ultra short
baseline (USBL) data for ground truth, provides an opportunity to stress-test
the proposed framework with promising results. We show how robust modeling
elements improve our ability to analyze the data, and present batch processing
results for 10 minutes of data with three different frequencies of available
USBL position fixes (gaps of 30 seconds, 1 minute, and 2 minutes). The results
suggest that the framework can be extended to real-time tracking using robust
windowed estimation.Comment: 9 pages, 9 figures, to be included in Robotics: Science and Systems
201
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation
In this paper, we present the optimization formulation of the Kalman
filtering and smoothing problems, and use this perspective to develop a variety
of extensions and applications. We first formulate classic Kalman smoothing as
a least squares problem, highlight special structure, and show that the classic
filtering and smoothing algorithms are equivalent to a particular algorithm for
solving this problem. Once this equivalence is established, we present
extensions of Kalman smoothing to systems with nonlinear process and
measurement models, systems with linear and nonlinear inequality constraints,
systems with outliers in the measurements or sudden changes in the state, and
systems where the sparsity of the state sequence must be accounted for. All
extensions preserve the computational efficiency of the classic algorithms, and
most of the extensions are illustrated with numerical examples, which are part
of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure
Estimation, Analysis and Smoothing of Self-Similar Network Induced Delays in Feedback Control of Nuclear Reactors
This paper analyzes a nuclear reactor power signal that suffers from network
induced random delays in the shared data network while being fed-back to the
Reactor Regulating System (RRS). A detailed study is carried out to investigate
the self similarity of random delay dynamics due to the network traffic in
shared medium. The fractionality or selfsimilarity in the network induced delay
that corrupts the measured power signal coming from Self Powered Neutron
Detectors (SPND) is estimated and analyzed. As any fractional order randomness
is intrinsically different from conventional Gaussian kind of randomness, these
delay dynamics need to be handled efficiently, before reaching the controller
within the RRS. An attempt has been made to minimize the effect of the
randomness in the reactor power transient data with few classes of smoothing
filters. The performance measure of the smoothers with fractional order noise
consideration is also investigated into.Comment: 6 pages, 6 figure
Smoothing Dynamic Systems with State-Dependent Covariance Matrices
Kalman filtering and smoothing algorithms are used in many areas, including
tracking and navigation, medical applications, and financial trend filtering.
One of the basic assumptions required to apply the Kalman smoothing framework
is that error covariance matrices are known and given. In this paper, we study
a general class of inference problems where covariance matrices can depend
functionally on unknown parameters. In the Kalman framework, this allows
modeling situations where covariance matrices may depend functionally on the
state sequence being estimated. We present an extended formulation and
generalized Gauss-Newton (GGN) algorithm for inference in this context. When
applied to dynamic systems inference, we show the algorithm can be implemented
to preserve the computational efficiency of the classic Kalman smoother. The
new approach is illustrated with a synthetic numerical example.Comment: 8 pages, 1 figur
Multivariate control charts based on Bayesian state space models
This paper develops a new multivariate control charting method for vector
autocorrelated and serially correlated processes. The main idea is to propose a
Bayesian multivariate local level model, which is a generalization of the
Shewhart-Deming model for autocorrelated processes, in order to provide the
predictive error distribution of the process and then to apply a univariate
modified EWMA control chart to the logarithm of the Bayes' factors of the
predictive error density versus the target error density. The resulting chart
is proposed as capable to deal with both the non-normality and the
autocorrelation structure of the log Bayes' factors. The new control charting
scheme is general in application and it has the advantage to control
simultaneously not only the process mean vector and the dispersion covariance
matrix, but also the entire target distribution of the process. Two examples of
London metal exchange data and of production time series data illustrate the
capabilities of the new control chart.Comment: 19 pages, 6 figure
Robust Control Charts for Time Series Data
This article presents a control chart for time series data, based on the one-step- ahead forecast errors of the Holt-Winters forecasting method. We use robust techniques to prevent that outliers affect the estimation of the control limits of the chart. Moreover, robustness is important to maintain the reliability of the control chart after the occurrence of alarm observations. The properties of the new control chart are examined in a simulation study and on a real data example.Control chart;Holt-Winters;Non-stationary time series;Out- lier detection;Robustness;Statistical process control
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