Statistics::GaussHelmert 0.05

Statistics::GaussHelmert is a general weighted least squares estimation module.

SYNOPSIS

use Statistics::GaussHelmert;

# create an empty model
my $estimation = new Statistics::GaussHelmert;

# setup the model given observations $y, covariance matrices
# $Sigma_yy, an initial guess $b0 for the unknown parameters.
$estimation->observations($y);
$estimation->covariance_observations($Sigma_yy);
$estimation->initial_guess($b0);

# specify the implicit model function and its Jacobians by using
# closures.
$estimation->observation_equations(sub { ... });
$estimation->Jacobian_unknowns(sub { ... });
$estimation->Jacobian_observations(sub { ... });

# Maybe we want to impose some constraints on the unknown
# parameters, this is not mandatory
$estimation->constraints(sub { ... });
$estimation->Jacobian_constraints(sub { ... });

# start estimation
$estimation->start(verbose => 1);

# print result
print $estimation->estimated_unknown(),
$estimation->covariance_unknown();

This module is a flexible tool for estimating model parameters given a set of observations. The module provides function for a linear estimation model, the underlying model is called Gauss-Helmert model.

Statistics::GaussHelmert is different to modules such as Statistics::OLS in the sense that it may fit arbitrary functions to data of any dimensions. You have to specify an implicit minimization function (in contrast to explicit functions as in traditional regression methods) and its derivatives with respects to the unknown and the observations. You may also specify constraint function on the unknowns (with its derivative). Furthermore you already need an approximate solution. For some problems it is easy finding approximate solutions by directly solving for the unknown parameters with some well chosen observations.