INVESTIGATIONS INTO PROPAGATION OF ERRORS IN ANALYTICAL AERIAL TRIANGULATION AND ADJUSTMENT

Abstract

Analytical aerial triangulation methods for the extension of controls are being practised more frequently than the analog methods because of the easy availability of fast digital computing facilities. The attempts in recent years have been to develop analytical aerial triangu lation methods which could give an accuracy of geodetic standard in the extension of controls. The necessary basic input in all the analytical aerotriangulation methods is the photo coordinates and ground controls of a few points* The major factor limiting the accuracy of controls generated by aerial triangulation is the residual errors from different sources that remain associated with the photo coordinates even after refinement. The behaviour of these errors in robbing the accuracy of controls generated by analytical aerial triangulation method is yet not fully known. Moreover} the role played by the errors in ground control data itself in vitiating the results of analytical aerial triangulation has not been quantitatively ascertained. The present investigations have been directed to study the propagation of errors in the generated control points due to the errors in photocoordinates from the following sources. i. Residual uniform film shrinkage ii. Residual differential film shrinkage 11 iii. Irregular film shrinkage iv• Residual systematic radial lens distortion v« Irregular radial and tangential lens distortion vi. Imperfect flatness of emulsion surface The effect of focal length error has also been investi gated. In addition to the above study, an attempt has also been made to ascertain quantitatively the contribution of the errors, present in the ground control points used towards the control points generated by analytical aerial triangulation. Out of various methods of analytical aerial triangu lation reported in the literature, two methods, one each from two broad categories namely, sequential approach and simulta neous approach have been selected for the present investigation* Very few organisations have developed triangula tion methods on both the approaches of computational techniques* Amongst these the notable organisations are National Research Council (NRC) of Canada and National Oceanic Survey (NOS) of USA etc. Both the methods of NOS, Strip and Block triangulation, are based on the same collinearity condition equation. Strip triangula tion me±hod of NRC is based on coplanarity condition whereas the Bundle adjustment method is based on collinea- rity condition* Though the methods of NRC are almost in a state of routine use yet no detailed investigation Ill about the error propagation is available* No study has so far been made to find the vitiating capacity of the particular error from a specific source* Under the above consideration the following two methods of National Research Council of Canada have been selected for investigation* i. Strip triangulation and adjustment method, developed by Schut [63,67], uses coplanarity condition for orientation and 3rd degree conformal polynomial for adjustment* ii. Bundle adjustment method, also developed by Schut [68], uses collinearity condition equa tion for simultaneous adjustment. One of the most important requirements of error propagation studies is the error free data* The synthetic data has been generated and successfully used by ITC [38,74], ISP [8,51] and many other investigators for error propagation studies in the past. Therefore, in the present investigation the synthetic data available in the form of mathematical blocks of photograra at the Roorkee University, generated by Oswal [52,53], has been employed. The investigation programme consisted of perfor ming the analytical aerial triangulation on the available computer, DEC system 2050, by both methods using synthetic data. The computer run has been made first with the error free input data, the results of which have been termed as IV system calibration. Subsequently the computer runs have been made a number of times. Each time the input data has been impregnated with the characteristic error from a specific source, as identified above. The results contain the standard errors derived from the residuals at the available check points in the model/photo, strips and block. The standard error of models/photos, strips and block are reduced to photo scale and are exi pressed in micrometers. The analysis of these results have been made separately for each method and the following conclusions have been drawn. i. The residual uniform film shrinkage error of .02/ which is 10/i of expected maximum film shrinkage error is completely taken care of by both the methods, namely, NRC Strip triangulation with polynomial adjustment and NRC Bundle adjustment. The re fore >the residual uniform film shrinkage error is not a vitiating element against the achievement of desired accuracy in any method of triangulation. Hence no great care is necessary for their complete removal from the photo coordinates. ii. The residual errors due to differntial film shrinkage of 0*02/ in x and 0.03/ in y are not properly taken care of in Strip triangulation with 3rd degree conformal polynomial adjustment. These errors damage the accuracy of the generated control points, parti cularly for Y-coordinates* The Bundle adjustment method with four added para meters is perfectly capable of taking care of the residual errors from differential film shrinkage. Therefore,the residual differential film shrinkage errors of 0.02/ in x and 0.03/ in y may be tolerated in Bundle adjustment. iii» The errors due to irregular film shrinkage play important role in vitiating the accuracy of the generated control points by both the method of triangulation. Therefore,a suitable adjustment technique is needed in either method to take care of these errors. iv. The residual systematic radial lens distortion error of lo/. of expected maximum systematic radial lens distortion will not cause any harmful effect on the accuracy of generated control points by both methods of triangulation. Therefore.no great importance for the complete elimination of this error need be given* So the omission of very high power terms in the correction equation for systematic radial lens distortion error may be justified. v. The errors due to irregular radial and tangential lens distortion can deteriorate the accuracy of the generated control points by both methods of triangulation. The Bundle adjustment fails to take necessary care of these errors. In strip triangulation method, the adjustment