The Helmert–Wolf blocking (HWB) is a
least squares solution method for the solution of a
sparse block
Block or blocked may refer to:
Arts, entertainment and media Broadcasting
* Block programming, the result of a programming strategy in broadcasting
* W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 ...
system of linear equations. It was first reported by
F. R. Helmert for use in
geodesy problems in 1880;
(1910–1994) published his direct semianalytic solution in 1978.
It is based on ordinary
Gaussian elimination in
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
form
or partial
minimization form.
Description
Limitations
The HWB solution is very fast to compute but it is optimal only if observational errors do not correlate between the data blocks. The
generalized canonical correlation
In statistics, the generalized canonical correlation
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X''&n ...
analysis (gCCA) is the statistical method of choice for making those harmful cross-covariances vanish. This may, however, become quite tedious depending on the nature of the problem.
Applications
The HWB method is critical to satellite geodesy and similar large problems. The HWB method can be extended to
fast Kalman filter The fast Kalman filter (FKF), devised by Antti Lange (born 1941), is an extension of the Helmert–Wolf blocking (HWB) method from geodesy to safety-critical real-time applications of Kalman filtering (KF) such as GNSS navigation up to the centim ...
ing (FKF) by augmenting its
linear regression equation system to take into account information from numerical forecasts, physical constraints and other ancillary data sources that are available in realtime. Operational accuracies can then be computed reliably from the theory of minimum-norm quadratic unbiased estimation (
Minque
In statistics, the theory of minimum norm quadratic unbiased estimation (MINQUE) was developed by C. R. Rao. Its application was originally to the problem of heteroscedasticity and the estimation of variance components in random effects model
I ...
) of
C. R. Rao
Calyampudi Radhakrishna Rao FRS (born 10 September 1920), commonly known as C. R. Rao, is an Indian-American mathematician and statistician. He is currently professor emeritus at Pennsylvania State University and Research Professor at the Un ...
.
See also
*
Block matrix
Notes
Statistical algorithms
Least squares
Geodesy
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