A statistical filter for geodetic observations

A method for filtering of geodetic observationwhich leaves the final result normally distributed, is presented. Furthermore, it is shown that if you sacrifice100.a% of all the observations you may be (1−β).100% sure that a gross error of the size Δ is rejected. Another and, may be intuitively, more appealing method is presented; the two methods are compared and it is shown why Method 1 should be preferred to Method 2 for geodetic purposes. Finally the two methods are demonstrated in some numerical examples.     

THE CONFORMAL TRANSFORMATION OF A NETWORK OF TRIANGULATION

Abstract

In a recent issue of this Review, an example is given of the conformal transformation of a network of triangulation using Newton's interpolation formula with divided differences. While the application of the method appears to be new, attention should be drawn to the fact that Kruger employed Lagrange's interpolation formula in a discussion and extension of the Schols method in a paper which was published in the Zeitschrift für Vermessungswesen in 1896. A reference to this paper was given at the end of the paper, “Adjustment of the Secondary Triangulation of South Africa”, published in a previous issue of the E.S.R. (iv, 30, 480).     

INTERPOLATING FROM TRAVERSE TABLES TO SECONDS

Abstract

In the Empire Survey Review, no. 4, 1932, Mr. Clendinning has described a method of interpolating from traverse tables to seconds. Below is another method, due to Prof. Nekrassov, for use with traverse tables published by him. The method is described in The Geodezist, Moscow, 1936, no. I, pp. 47–52.     

TRIANGULATION: BEARINGS VERSUS ANGLES

Abstract

There has always been a marked difference of opinion on the relative merits of the methods of bearings and of angles as applied to triangulation, though it is probable that the majority of writers prefer the method of bearings for first-order work. The subject was mentioned in a recent issue of this Review (vii, 47, 19).     

ADJUSTMENT OF SIMPLE FIGURES—II

Abstract

3. Adjustment of a Polygon.—The adjustment of a polygon by the method of the preceding paragraph leads to results similar to that for a quadrilateral, although not quite so simple, since there are two correlatives, k₁ k₂ , for deducing the corrections.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

Terrain radiometric calibration of airborne UAVSAR for forested area

In the field of biomass estimation, terrain radiometric calibration of airborne polarimetric SAR data for forested areas is an urgent problem. Illuminated area correction of σ -naught could not completely remove terrain features. Inspired by Small and Shimada, this paper tested gamma-naught on one mountainous forested area using airborne Uninhabited Aerial Vehicle Synthetic Aperture Radar data and found it could remove most terrain features. However, a systematic increasing trend from far range to near range is found in airborne SAR cases. This paper made an attempt to use the relationship between distance to SAR sensor and γ-naught to calibrate γ -naught. Two quantitative evaluation methods are proposed. Experimental results demonstrate that variation of γ -naught can be constrained to a limited extent from near range to far range. Since this method is based on ground range images, it avoids complicated orthorectification.     

ON THE ORTHOMORPHIC PROPERTY OF SCHOLS ADJUSTMENT

Abstract

In vol. iv, nos. 29 and 30, of the E.S.R., there appeared an article by Mr. D. R. Hendrikz on the “Adjustment of the Secondary Triangulation of South Africa”. He shows that, in applying the Schols method of orthomorphic transmission to the adjustment of a secondary net to a primary triangle, the secondary sides suffer small displacements.     

LONG LINES ON THE EARTH

Abstract

The Arc of the Geodesic.—In the first part of this paper a method was given for computing the azimuth of a geodesic. The method gives the convergence of the geodesic correctly up to the second power of e the eccentricity. The formula (9), however, also depends on the assumption that σ, the arc-length of the geodesic, can be obtained with sufficient accuracy from the Supplemental Dalby Theorem, that is to say, by a purely spherical computation. It is, therefore, needful to show that this supposition is justifiable; a means must in fact be indicated for verifying the assumption.     

A NOTE ON AZIMUTH DETERMINATION

Abstract

The purpose of this note is twofold; first, to criticize the “azimuth” section of the paper “Some Notes on Astronomy as Applied to Surveying”, by R. W. Pring (E.S.R., July 1952, xi, 85, 309–318),and secondly, out of these criticisms to develop an alternative method of making observations for azimuth. It will be apparent that this method owes much to the ideas put forward by Mr. Pring.     

ELIMINATION OF ERRORS OF LATITUDE AND REFRACTION IN THE PAIRING OF AZIMUTH OBSERVATIONS

Abstract

In a previous Article (Empire Survey Review, ii, II) I described a simple graphical method for the elimination of latitude error in observations for azimuth. It was pointed out that the ideal method of adjustment of azimuths would be a simultaneous elimination of both latitude and refraction errors and, with that in view, a purely theoretical method of such an adjustment was demonstrated in the last paragraph of the article. It has now occurred to me that a fairly simple mathematical solution is possible.     

Fractional vegetation cover estimation in heterogeneous areas by combining a radiative transfer model and a dynamic vegetation model

ABSTRACT

A fractional vegetation cover (FVC) estimation method incorporating a vegetation growth model and a radiative transfer model was previously developed, which was suitable for FVC estimation in homogeneous areas because the finer-resolution pixels corresponding to one coarse-resolution FVC pixel were all assumed to have the same vegetation growth model. However, this assumption does not hold over heterogeneous areas, meaning that the method cannot be applied to large regions. Therefore, this study proposes a finer spatial resolution FVC estimation method applicable to heterogeneous areas using Landsat 8 Operational Land Imager reflectance data and Global LAnd Surface Satellite (GLASS) FVC product. The FVC product was first decomposed according to the normalized difference vegetation index from the Landsat 8 OLI data. Then, independent dynamic vegetation models were built for each finer-resolution pixel. Finally, the dynamic vegetation model and a radiative transfer model were combined to estimate FVC at the Landsat 8 scale. Validation results indicated that the proposed method (R²?=?0.7757, RMSE?=?0.0881) performed better than either the previous method (R²?=?0.7038, RMSE?=?0.1125) or a commonly used method involving look-up table inversions of the PROSAIL model (R²?=?0.7457, RMSE?=?0.1249).     

THE DERIVATION OF CERTAIN PROJECTION FORMULAE FOR THE SPHERE

Abstract

The purpose of this article is to make available to readers of the Review a simple method of derivation from first principles of the projection farmulae for same of the more impartant normal conical projections.     

NOTE ON THE REDUCTION OF CIRCUMMERIDIAN ALTITUDES TO THE MERIDIAN

Abstract

The method of reducing circummeridian altitudes or zenith distances to the meridian, using the factors m and n as tabulated by Chauvenet, is well known. The following method, which does not use these factars, has been faund both more convenient and more accurate in practice. The formula can be easily obtained by expanding m and n in powers of t, but far the sake af campleteness the derivatian is here given from the beginning.     

A NOVEL METHOD OF MEASURING THE COEFFICIENT OF THERMAL EXPANSION OF INVAR

Abstract

In a letter published in a recent issue of Nature, Prof. L. F. Bates and Mr J. C. Wilson, of University College, Nottingham, have described a new and novel method of determining the coefficient of thermal expansion of invar. Although this method is hardly likely to be applied to the measurement of the coefficient of expansion of long invar tapes, such as are used by surveyors, yet it is so novel and ingenious in itself that a short reference to it may not be out of place in this Review. One extremely interesting thing about it is that no measurements of a length, or of changes of length, are involved.     

LONG LINES ON THE EARTH: VARIOUS FORMULAE

Abstract

Extensions were given for all these formulae, so that precise results may now be obtained even for lines of 500 miles in latitudes above 45°. The present instalment gives the extension of the Clarke approximate (sic) formulae to lines of 500miles, with a practical example and general conclusions: the great advantage of the method is that 8-figuretables sufficeto give rigorous results.     

FURTHER NOTES ON RANGE-FINDING WITH A THEODOLITE

Abstract

Since writing the article which appeared in E.S.R., no. 36, p. 364, the writer has used this method to obtain thousands of spot heights with differences of elevation varying up to 7,500 feet in a single shot. The results of this experience and the modifications introduced in the method may be of some iilterest.     

THE TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID

Abstract

In January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method.     

Determination of complexity factor and its relationship with accuracy of representation for DEM terrain

Based on the estimating rule of the normal vector angles between two adjacent terrain units, we use the concept of terrain complexity factor to quantify the terrain complexity of DEM, and then the formula of terrain complexity factor in Raster DEM and TIN DEM is deduced theoretically. In order to make clear how the terrain complexity factor E _CF and the average elevation h affect the accuracy of DEM terrain representation RMSE _Et , the formula of Gauss synthetical surface is applied to simulate several real terrain surfaces, each of which has different terrain complexity. Through the statistical analysis of linear regression in simulation data, the linear equation between accuracy of DEM terrain representation RMSE _Et , terrain complexity factor E _CF and the average elevation h is achieved. A new method is provided to estimate the accuracy of DEM terrain representation RMSE _Et with a certain terrain complexity and it gives convincing theoretical evidence for DEM production and the corresponding error research in the future.