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Kalman Filtering Toolbox List of Modules and Programs

To go to one of the below section click the desired link

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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