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Kalman Filtering Toolbox List of Modules and Programs
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Matrix
Storage and Allocation
matc2r
rectangular matrix storage transformation from
one-dimensional
column-wise to one-dimensional
row-wise
matr2c rectangular
matrix storage transformation from
one-dimensional row-wise
to
row-wise to one-dimensional
column-wise
mr1to2 rectangular
matrix storage transformation from
one-dimensional column-wisearray
to two-dimensional
array
mr2to1 rectangular
matrix storage transformation from
two-dimensional array to
one-dimensional column-wise
array
msc2f symmetric
matrix storage transformation from
one-dimensional array
column-wise - only the upper
triangular part stored,
to two-dimensional array
msf2c symmetric
matrix storage transformation from
two-dimensional array to
one- dimensional array -
column-wise, only the
upper triangular part is stored
msre reconstruct
a full symmetric matrix from its stored
upper triangular part; both
input and output
matrices are
stored column-wise into one dimmensional arrays
mstr extract
the upper triangular part from a symmetric
matrix; both input and
output matrices are stored
column-wise into
one-dimensional arrays
mudc2f restore full U
and D matrices stored as two-
dimensional arrays from
its compact upper triangular
part stored column-wise
as one-dimensional array
mudf2c store the full U
and D matrices stored as two-
dimensional arrays to its
compact upper triangular
part stored column-wise
as one-dimensional array
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Specialized Matrix Operations
maat
post-multiplication of a rectangular matrix by its
transposed matrix; the
input matrix is stored column-
wise, one-dimensional,
and the resultant symmetric
matrix is stored
column-wise - only the upper
triangular part
mmab multiplication
of two rectangular matrices when the
resultant matrix is
known to be a symmetric
matrix; the input
matrices are stored one-
dimensional, column-wise,
and the resultant matrix
is stored column-wise -
only the upper triangular
part
mmrt multiplication
of a rectangular matrix and an upper
triangular matrix; the
rectangular matrix is stored
into two-dimensional
array, the upper triangular
matrix is stored into
one-dimensional array column-
wise - only the
upper triangular part, and the
resultant matrix is
stored into two- dimensional array
mphiu multiplication
of a square matrix stored into two-
dimensional array and a
unit upper triangular matrix
stored into
one-dimensional array column-wise -
only
the upper triangular
part; the resultant matrix is
stored into
two-dimensional array
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Specialized
Statistics Functions and Utilities
cep
circular error probable (CEP) computation
convcon setting of most used
conversion constants
gauss_1 probability density
function of the normal Gaussian
distribution
genrn generation
of random numbers with normal (Gaussian)
distribution
gmp1 generation
of first order Gauss-Markov sequence
gmp2 generation
of second order Gauss-Markov sequence
rms root
mean square (RMS) of a sample
rms2 modified
root mean square (modified RMS) of a
sample
rss root
sum square (RSS) of a three component vector
sample
rssxy root sum
square (RSS) of a two component vector
sample
rwalk generation
of a random walk process
statup computation of
the running mean, standard deviation
and root mean square
for a sample
vep vertical
error probable (VEP) computation
xcepvep main program used to
compute CEP or VEP
xgenrn main program
generating random numbers with normal
(Gaussian) distribution
xgmp1 main program
generating first order Gauss-Markov
sequence
xgmp2 main program
generating second order Gauss-Markov
sequence
xrwalk main program
generating random walk process
sequence
xstat main program
testing the following modules: rms,
rss, rssxy, and statup
xstatc main program
determining mean, standard deviation,
and root mean square (rms)
of the elements of a
specified column of the
input array
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Specialized Plotting Programs
xpbar bar graph for a selected column
xyp1 x-y graph for a selected
column
xyp1s x-y graph for a selected column,
with statistics
xyp2w x-y
graph for two selected columns in two
different
windows/subplots, with statistics
xyp3w x-y
graph for three selected columns in three
different
windows/subplots, with statistics
xypc2 x-y
graph of the difference between columns (from
different
files), with statistics
xypc2rss x-y graph for
RSS (root sum square) of the
difference of
three columns from two files, with
statistics
xypm x-y graph for the selected
multiple columns
xyprss
x-y graph for RSS (root sum square) of three
selected
columns, with statistics
xyprss2w x-y graph for
RSS (root sum square) of three
selected
columns corresponding to position and
velocity
errors, in two windows/subplots, with
statistics
xypvstd x-y graph
for a selected column and the associated
envelope
(standard deviation), with statistics
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General Purpose and Conventional
Kalman Filter Functions
gobsd
generation of observed data (measurements) for a
linear time-invariant
model; general form including
control vector term is
included
gobsd generation
of observed data (measurements) for a
linear time-invariant
model; the control term and
process noise multiplier
matrix are not included
kfcov covariance
matrix analysis for a time-invariant
model by using the
conventional formulation
kfcov1 covariance matrix
analysis for a time-invariant
model by using the
conventional formulation (variant
of kfcov, time
propagation and measurement
incorporation steps are
inverted)
kfcov1a covariance matrix
analysis for a time-invariant
model by using the
alternate conventional formulation
mdric1 steady state
solution of the discrete matrix Riccati
equation; covariance
matrix before measurement
incorporation is
determined
meas1cov covariance matrix
measurement updating for one
measurement by using
conventional Kalman formulation
(with symmetrization)
meas1jcov covariance matrix
measurement updating for
one measurement by using
Joseph
classical Kalman formulation
(with symmetrization)
measjcov covariance matrix
measurement updating for all
measurements by using
Joseph stabilized Kalman
formulation
mndec decorrelation
of the measurement noise
sdkf suboptimal
(constant gain) discrete Kalman filter
by using conventional
formulation
smcov determination
of smoothed covariance matrix based
on Rautch-Tung-Striebel
algorithm when the model
parameters are constant
smcovps determination of
smoothed covariance matrix and
state based on
Rautch-Tung- Striebel algorithm
when
the model parameters are
constant
xgobsd main program
generating the observed data
(measurements) for a
linear time-invariant model
xgobsdr main program
generating the observed data
(measurements) for a
simplified linear time-
invariant model
xkfcov main program
executing the covariance analysis by
using the conventional
or alternate conventional
Kalman filter formulation
xkfcovps main program executing the
discrete Kalman filter
(covariance and state
analysis) by using the
conventional Kalman
filter formulation
xmdric main program
computing the steady-state solution of
the discrete matrix
Riccati equation by using two
different iterative
methods
xmndec main program
executing the decorrelation of the
measurement noise
xsdkf main program
computing the suboptimal (constant
gain) discrete Kalman
filter by using conventional
formulation
xsmcov main program
executing the Rautch-Tung-Striebel
smoothing for covariance
matrix, when model
parameters are constant
xsmcovps main program executing the
Rautch-Tung-Striebel
smoothing for covariance
matrix and state, when
model parameters are
constant
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Specialized U-D Kalman Filter
Functions
mcud
covariance matrix determination from its U-D factors
mr1up updating the
U-D factors when a rank one matrix
modification is applied
mreast measurement
reasonableness test for a given scalar
measurement
mudd U-D
factorization of a real symmetric, positive
(semi)definite matrix by
using modified Cholesky
decomposition
mudm U-D
measurement updating by using Bierman algorithm
for one measurement,
when the measurement is the
input
mudm1 U-D
measurement updating by using Bierman algorithm
for one measurement,
when the measurement residual
is the input
mudst standard
deviations (sigmas) determination from the
U-D factors
mwgs1 U-D factors
determination from the un-normalized W-DW
factors (used in the
modified weighted Gram-Schmidt
algorithm)
tpudd time
propagation of U-D factors by using the direct
method
tpudgs time propagation
of U-D factors by using the
modified weighted
Gram-Schmidt method
tpuds time
propagation of U-D factors by using the rank
one matrix updating
method
xkfud main program
implementing the discrete U-D form
Kalman filter for a
specified application. Several
options related to the
input/output data and
selection of variant to
be used are available
xmuddu main program
executing the decomposition and
reconstruction of a real
symmetric positive (semi)
definite matrix into and
from its U-D factors
xmudm main program
executing the discrete Kalman filter
Biermna's U-D measurement
updating algorithm
xmudst main program
determining sigmas (standard
deviations) of a
covariance matrix from its U-D
factors
xtpud main program
executing time propagation of the U-D
factors by using three
different methods (direct
method, rank one matrix
updating method, and modified
weighted Gram-Schmidt
method)
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Application
Dependent Modules
hmat
measurement matrix computation
phimat transition matrix
computation
qmat process
noise matrix computation
rmat measurement
noise matrix computation
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GPS Application Modules
eleva
elevation angle and the ECEF unit line-of-sight
vector computation
svpalm ECEF satellite
position determination based on
almanac data
tgdecef geodetic to ECEF
coordinates transformation
uverv unit
vertical vector for a given ECEF position
vector
vecefenu ECEF (Earth Centered Earth
Fixed) to ENU (East,
North, Up) transformation
wgs84con setting of most used WGS-84
constants
xgpsr5s main program performs
covariance analysis for the
5-state GPS receiver
model (for near-stationary user)
xgpsr8s main program
performing covariance analysis for the
8-state GPS receivermodel(for
near-constant velocity
user)
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