Helmert-Wolf blocking

Helmert-Wolf blocking

The Helmert-Wolf blockingfn|1 (HWB) is a least squares solution [http://fkf.net/Wolf.gifmethod] for a sparse [http://fkf.net/equations.gifcanonical block-angular] (CBA) system of linear equations. Friedrich Robert Helmert (1843-1917) reported on the use of such systems for geodesy in his book "Die mathematischen und physikalischen Theorieen der höheren Geodäsie, 1. Teil" published in Leipzig, 1880. [http://www.fkf.net/Wolf.html Helmut Wolf] (1910-1994) published his direct [http://www.fkf.net/Wolf.jpgsemianalytic solution] fn|2 based on ordinary Gaussian elimination in matrix formfn|3 in his paper "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. The HWB solution is really fast to compute but it is optimal only if observational errors do not correlate between the data blocks. Fortunately, the generalized canonical correlation 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.

Notes

*fnb|1 see [http://www.ngs.noaa.gov/GRD/GPS/DOC/gpscom/mca.html GPScom Software Documentation] from Geoscience Research Division of NOAA.

*fnb|2 see formulas (15.56-58) on pages 507-508 of Strang, G. and Borre, K. (1997): "Linear Algebra, Geodesy, and GPS", Wellesley-Cambridge Press.

*fnb|3 see the HWB formula (unnumbered) at the end of page 508 of Strang, G. and Borre, K. (1997): "Linear Algebra, Geodesy, and GPS", Wellesley-Cambridge Press.

Applications

The HWB method is a "must" in Satellite Geodesy and similar large problems. 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 minimum-norm quadratic unbiased estimation (Minque) of C. R. Rao (1920- ).

References and external links

*http://www.ngs.noaa.gov/GRD/GPS/DOC/gpscom/mca.html


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Friedrich Robert Helmert — (July 31 1843 ndash; June 15 1917) was a German geodesist and an important writer on the theory of errors.Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg and Dresden, he entered the Polytechnische Schule, now… …   Wikipedia

  • Helmut Wolf (Geodät) — Helmut Wolf (* 2. Mai 1910 in Werdau; † 6. Juni 1994) war ein deutscher Geodät und Professor an der Universität Bonn. Ihm sind wesentliche Schritte zum Aufbau eines Europanetzes zu verdanken, sowie die erste länderübergreifende Geoidbestimmung in …   Deutsch Wikipedia

  • Fast Kalman filter — The fast Kalman filter (FKF), devised by Antti Lange (1941 ), is an extension of the Helmert Wolf blockingfn|1 (HWB) method from geodesy to real time applications of Kalman filtering (KF) such as satellite imaging of the Earth. Kalman filters are …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Generalized canonical correlation — In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross correlation matrices between the sets of random variables when there are more than two sets. It is a generalization of the Principal component …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”