Helmert–Wolf blocking
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The Helmert–Wolf blocking^{[1]} (HWB) is a least squares solution method^{[2]} for a sparse canonical blockangular^{[3]} (CBA) system of linear equations. Helmert (1843–1917) reported on the use of such systems for geodesy in 1880.^{[4]} Wolf (1910–1994)^{[5]} published his direct semianalytic solution^{[6]}^{[7]} based on ordinary Gaussian elimination in matrix form ^{[8]} in 1978.^{[9]}
Contents
Description
This section requires expansion. (May 2015)

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 analysis (gCCA) is the statistical method of choice for making those harmful crosscovariances vanish. This may, however, become quite tedious depending on the nature of the problem.
Applications
The HWB method is a "must" in Satellite Geodesy and similar large problems.^{[citation needed]} The HWB method can be extended to fast Kalman filtering (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 minimumnorm quadratic unbiased estimation (Minque) of C. R. Rao (1920– ).
See also
Notes
 ↑ see GPScom Software Documentation from Geoscience Research Division of NOAA.
 ↑ http://fkf.net/Wolf.gif
 ↑ http://fkf.net/equations.gif
 ↑ Friedrich Robert Helmert, "Die mathematischen und physikalischen Theorien der höheren Geodäsie, 1. Teil" published in Leipzig, 1880
 ↑ http://www.fkf.net/Wolf.html
 ↑ http://www.fkf.net/Wolf.jpg
 ↑ see formulas (15.56–58) on pages 507–508 of Strang & Borre (1997)
 ↑ see the HWB formula (unnumbered) at the end of page 508 of Strang & Borre (1997)
 ↑ Helmut Wolf, "The Helmert block method, its origin and development", Proceedings of the Second International Symposium on Problems Related to the Redefinition of North American Geodetic Networks, Arlington, Va. April 24–April 28, 1978, pages 319–326.
References
 Strang, G.; Borre, K. (1997). Linear Algebra, Geodesy, and GPS. WellesleyCambridge Press. ISBN 0961408863.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
External links
 http://www.ngs.noaa.gov/GRD/GPS/DOC/gpscom/mca.html GPScom Software Documentation
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