نکته ای چند در بکارگیری صحیح روش کمترین مربعات

نوع مقاله: مقاله پژوهشی

نویسنده

چکیده

امروزه همه نقشه­ برداران می ­دانند که نمی­ توان یک طول یا زاویه را بدون خطا اندازه گرفت. برای برقراری روابط ریاضی حاکم بر مشاهدات، لازم است سرشکنی صورت گیرد. یکی از روش های موجود برای توزیع خطاها روش کمترین مربعات است. متأسفانه بسیاری از همکاران از نکته­ های ظریف نظریه کمترین مربعات بی­ اطلاع­اند. در این مقاله به صورت گام به گام به بررسی نظریه کمترین مربعات و روش بکارگیری آن خواهیم پرداخت.

عنوان مقاله [English]

A Few Points on Correct Utilization of the Least Squares Methods

نویسنده [English]

  • Alireza Azmudeh Ardalaan
چکیده [English]

Today, all surveyors know that it is not possible to measure a length or angle without error. To establish mathematical relations governing observations, it is necessary to perform adjustment. One of the available methods for distributing errors is the least squares method. Unfortunately, many colleagues are not aware of the finer points of the theory of least squares. In this paper, we will examine the least squares theory and its method of application step-by-step.

1) Amer, F. 1979. “Theoretical Reliability Studies for some Elementary Photographmmetries procedures.” Aerial Triangulation Symposium, Department of Surveying, Queensland , Australia.

2) Bearda, W. 1967, Statistical concepts in Geodesy, new series, vol. 2, no. 4. Delft: Netherlands Geodetic Committee.

3) Bearda, W. 1968. A Testing Procedure for use in Geodetic Networks, new series, vol. 2, no. 5. Delft: Netherlands Geodetic Committee.

4) Buckner, R.B., 1983. Surveying Measurements and their Analysis. Rancho cordova, California, Landmanrk Enterprises.

5) El-Hakim, S.F.1981. “A Practical Study of Gross Error Detection in Bundle Adjustment . “The Canadian Surveyor, vol. 35, no.4, PP. 373-386.

6) آزموده اردلان علیرضا، «تعیین ارتفاع ارتومتریک با استفاده از GPS » سپهر، نشریه علمی فنی سازمان جغرافیایی، دوره اول ، شماره اول، بهار 1369، ص 38 – 49.

7) Draper, N.R., and H. Smith 1981. Applied Regression Analysis, New York: John Wiley Sons.

8) Krohn, David K. 1988. “Weighting Angles.

9) Mikhail, Edward M. 1976. Observations and Least Suuares. Washington, D.C.: University Press of America Inc.

10) Mikhail, Edward M., and Gordon Gracie. 1981, Analysis and Adjustment of Survey Measurments. New York: Van Nostrand Reinhold Company

11) Shrestha, Ramesh L. 1989, “NAD 83 Geodetic and State Plane Coordinate Computation.” Surveying and Mapping, vol. 49, no. 2, PP. 87-93.

12)Sten, James E. 1989. State Plane Coordinate System of 1983, NOAA Manual NOS NGS 5. Rockville, Mary land: U.S. Department of Commerce.

13) Stroughton, Herbert W. 1977. Papers from the 1977 ACSM Fall Technical Meeting.

14) Vincenty, T. 1989, “The Flat Earth Concepts in Local Surveys.” Surveying and Mapping, vol. 49 no. 2,PP. 101-102.

15) White, L.A. 1987. Calculus of Observations, 380/580 Department of Surveying and Mapping, western Australia Institute of Technology.

16) Wolf, Paul R. 1989 Elementary Surveying, Eighth edition. New York, Harper & Row Publishers.

17) Wolf, paul R. 1987. Adjustment Computations: Practical Least Suares for Surveyors, Second edition. Rancho Cordova, California: Landmartk Enterprises.

18) Weber G. and Zomorrodian H. “Regional Geopotention.” Bull. Geod.62 (1988) PP.125-141.

19) Edward J. Krakwisky. “Conformal projections in Geodesy.” Department of Surveying Eng. UNB. LN37.

20) Edward J.Krakiwisky. “Papers for the CISM Adjustment and Analysis Seminars. The Canadian Institute of Surveying and Mapping.