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KalmanFilterTechNote.lyx
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A Kalman Filter
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to Improve Measurements of Wind
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from NSF/NCAR Research Aircraft
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\begin_layout Author
William A.
Cooper
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DRAFT
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6/30/2017
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National Center for Atmospheric Research
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Earth Observing Laboratory
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Research Aviation Facility
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begin{abstract}
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To improve the measurements of wind made from NSF/NCAR aircraft, a Kalman
filter is developed and applied to archived data files from research projects.
The filter is an error-state Kalman filter, and the emphasis is on improving
the measurements of pitch and heading because they are usually the dominating
source of uncertainty in measured wind.
The NSF/NCAR Gulfstream V research aircraft is emphasized in the development,
but the filter as developed can be applied to data from other present and
past NCAR aircraft as well.
So that the resulting filter can be applied in cases where the primary
measurements from the inertial reference system were not recorded in the
data file, a method is developed for retrieving those measurements by different
iating the recorded variables representing attitude angles and aircraft-velocity
components.
In addition, some new algorithms are introduced for estimating the rate
of climb of the aircraft from the measured accelerations and for estimating
the angle of attack from pressures measured at ports on the radome.
In addition, simplified methods for estimating the errors in pitch and
heading without the full complexity and processing requirements of the
Kalman filter are documented.
The result is that standard uncertainties in pitch and heading are reduced
to about 0.01
\begin_inset Formula $^{\circ}$
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, so that they no longer dominate the uncertainty in the wind measurements.
Some examples illustrate the effects of the Kalman filter on measured wind
and on variance spectra.
The processing technique is incorporated into an R script that can add
the improved variables to a standard netCDF data archive so that they can
be made available for community use.
Documents that are accessible via links in this technical document provide
information on the workflow that generated the document, the details of
the processing algorithms, and instructions for use and modification of
the processing script.
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Acknowledgments
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The research aircraft discussed in this technical note, the NSF/NCAR
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aircraft!NSF/NCAR GV
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Gulfstream V often called "HIAPER", was the result of an extensive effort
both within and outside of NCAR and at the National Science Foundation.
Chris Webster's development and maintenance of the software used for data
processing was a very important contribution to this effort.
The technical staff of the NCAR Earth Observing Laboratory were involved
in all stages of the development and operation of this research platform,
and the project management staff, operations staff, and computing and data
management groups of that Laboratory conducted the projects that produced
the data used in this document.
Without all these contributions, the measurements characterized in this
document would not have been available to the community.
NCAR is sponsored by the National Science Foundation (NSF), and the NSF
also supported the experiments that collected the data used in this technical
note.
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Two reviewers, Donald Lenschow and Matthew Hayman, made many suggestions
that improved this document.
In many other ways, Don Lenschow established the basis for this work and,
over many years, provided the author with valued guidance regarding the
measurement of wind.
The suggestions of Matt Hayman were particularly helpful in regard to the
mathematical equations and associated descriptions.
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The data used in the examples presented are from the
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DEEPWAVE=Deep Propagating Gravity Wave Experiment
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DEEPWAVE
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DEEPWAVE research project
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project (Deep Propagating Gravity Wave Experiment over New Zealand), described
at
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.
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[NEED A DATA CITATION HERE]
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Measurements (
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Substantial use also was made of the
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ggplot2
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ggplot2 package (
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The code used for the Kalman filter relies on the Jacobian function
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function!Jacobian
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in the R
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Introduction
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Overview
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overview!this document
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A recent technical note (
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key "Cooper2016ncartn"
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) discussed the uncertainty
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uncertainty!wind
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associated with
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wind!measurement
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measurements of wind from the NSF/NCAR Gulfstream V
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aircraft!NSF/NCAR GV
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GV=NSF/NCAR Gulfstream V
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research aircraft, hereafter called the GV.
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GV|see
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{
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aircraft!NSF/NCAR GV
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}
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NSF/NCAF GV|see
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{
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aircraft!NSF/NCAR GV
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}
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The aircraft is owned by the
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NSF=National Science Foundation
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National Science Foundation (NSF) and operated by the Research Aviation
Facility
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RAF=Research Aviation Facility
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(RAF), Earth Observing Laboratory (EOL), National Center for Atmospheric
Research
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NCAR=National Center for Atmospheric Research
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(NCAR).
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aircraft!NSF/NCAR GV
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The components and algorithms
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algorithm!wind
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that comprise the
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wind!**
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wind-measuring system on the GV
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uncertainty!wind!technical note
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were documented in that reference, so that information will not be repeated
here.
The central content of that technical note was a detailed analysis of uncertain
ty
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uncertainty!analysis for wind
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for the wind measurements.
The
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uncertainty!standard
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standard uncertainty was estimated to be about 0.1
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m