1981 Vol. 6, No. 1
On the basis of deducting the best linear unbiased estimation of stochastic parameters by applying the generalized matrix inverses,the generalized estimate formulas of filtering prediction and collocation etc.are obtained,the advantage being that the covariance matrix of the observations need not necessarily be full rank.Finally,a new method concerning the adjustment of free networks with stochastic parameters is given.
Based upon the point of view of classical adjustment of observations,this paper deals with the analyses and discussions of the characteristics of the solution of the adjustment with rank-defects of a free network.Conclusions are made concerning the following points:1,The result obtained from the adjustment with rank-defects of a free net-work by"the method of auxiliary condition",is the same as that by"the method of pseudo-observation",but the former is more appropriate than the latter.2,The solution of the adjustment with rank-defects has the characteristics of least variance as well as unbiasedness.3,The relationship between the solution of the adjustment with rank-defects and its system of reference.besides,the relationship between the solutions of the adjustment with rank-defecst and the classical adjustment of a free network;the relationship between the adjustment with rank-defects and the generalized inverses;the condition of invariant as well as some methods of calculation are also dealt with.
This paper deals with the intersection principle of a D.S.type analytical plotter by using three planes to determine the model point.Of all these planes,one passes through the model point while the other two planes are the so called "x-plane" and the "y-plane",passing through one or two corresponding image points.After that,the unknown image coordinates to be controlled by a servo-system are calculated by a collinear epuation the same as that on an AP type analytical plotter.Based upon this principle,the author has derived several formulae for the different types of operation(point determination,contouring and profiling) on a D.S.type analytical plotter.
Besides the normal distribution errors,there are other varieties of measuring errors,such as,the uniform distribution errors or the errors subjected to the distribution of the sum of a uniform distribution and a normal distribution.This paper is intended mainly to discuss the distribution of the sum of a uniform distribution and a normal distribution.The formulas of the distribution density and the probability of this distribution are derived and a comparison between this distribution and the normal distribution is made.Then the author analyses the sighting error of a precision theodolite or level influenced by the run error of the micrometer and points out that this error subordinates to the distribution discussed above.The limit of the run error is suggested as 2β=3σ,where σ is the standard deviation of the sighting error Finally opinions are expressed for the revision of the current official specification for the run error limit of the then dolits J07,J1 and the level S05.
Die Hauptinhalte des vorliegenden Artikels sind folgende:Basierend auf einen Datenbankinterface wird eine Methode der gruppenweise automatischen Generalisierung von Höhenlinien(d.h.unier Berüclcsichtigung der Nachbarhöhenlinien) vorgestellt,wobei die Strukturlinien(hauptsachlich Tallinien) als natürliches Verbindungsband der Höhenlinien angesehen werden.Der Kern des problems ist es,in der Menge der digitalisierten Daten der Höhenlinien die Sirukturpunkte(Tallinienpunkte ttnd Kammlinienpunkte) zu finden and die Sirukturlinien automatisch zu verfolgen,Danach kann man die Strukturlinienlängen als zahlenmäβige Grundlage für die Generalisierung berechnen.Vor der automatischen Generalisierung muβ man die Ursprungsdaten Komprimieren und dabei alle punkte entfernen,die nicht Strukturpunkte sind.Dabei werden die meisten kurzen Tälchen durch kurze konkave Trichterkurven mit drei Stützpunkien dargestellt.Die automatische Generalisierung besteht nun darin,alle Tallinien,deren Langen kleiner als ein vorgegebenes Grenzmaβ sind,zu finden und die in ihnen enthaltenen Hohenlinienpunkte zu entfernen.So werden alle kurzen trichierförmigen Kurven im Bereich der weggefallenen Tälchen geglättet,weil ihre auf den Tallinien liegenden Scheitelpunkie entfernt worden sind.
This paper deals with the application of a posteriors variance estimation in space resection of a single photograph.In this case the weights to be estimated are those of the ground coordinates and of the image coordinates.If the ground coordinates have equal variances such as the signalized points,we may consider them as fixed points rather than weighted observations and needn't perform a posteriors variances estimation.But if their variances are not equal,such as in the case of using natural objects(the images of which have to be identified and transferred),they should be regarded as weighted observations and their variances should be estimated point by point.In this way the accuracy of adjusted results can be improved.
In this paper the authors have derived the formulas used for setting the elements of rectification on rectifiers based upon the elements of exterior orientation:φ,ω,κ,XS,YS,ZS(H) of the photograph obtained from the output of an analytical aerial triangulation.Through the comparative tests between rectifications with control points and that with predetermined settings,the derived formulas have been proved to be correct while the latter method of rectification shows a higher efficiency.
In order to solve the problem of dynamic adjustment of repeating levelling networks covering a vast area,the author starts out from a classical dynamic linear mathematical model,and then derives a basic equation for the dynamic adjustment of repeating levelling networks.On account of the adjustment of free levelling networks without datum,this paper deals with the pseudoobservation adjustment method,and gives a concrete form of the supplementary matrix GT in performing the overall free-net-adjustment in two periods and has derived different kinds of formulas for accuracy estimating in this case.Finally,two methods for dynamic adjustment are given,when the levelling networks of two periods do not coincide completely.
This paper is a study report after having attended the lectures by Prof.W.Welsch of West Germany,given at Wuhan in May 1980.The theory of the adjustment with rank-defects by using the generalized inverse is discribed.while the coefficient matrix of the pseudo-observations equation must satisfy ABT=0 and BBT=I as is required in the above mentioned lectures,it is shown here in this article that only ABT=0 and rank =d is necessary.That is to say that,in order to realize the minimum biased adjustment in the case of rank defects,we need not use the pseudo-inverse(AT A)+ but may use the generalized inverse(AT A)-,which meets the Penrose conditions(1) and(4) only.Thus the conditions needed for the pseudo-observations can be reduced.
The zoom system is applied widely in the orthoprojector,working on the principle of the functional or the photographic projection.In this paper the characteristics of the vari-focal kernel with two elements is analysed and the design idea of the zoom system applied to orthoprojectors is described.Futhermore,an example of design with two zooms is given.
The pseudo-azimuthal projection has a closed isoline of deformation.It is suitable for regional maps usually put forward certain requirements in both areal and angular deformations.In this paper,through analyzing the forms of ρ and δ,and the functions of different parameters,following points have been discussed:1,The influence of the forms of ρ and δ and the value of parameters upon the size and distribution of deformations,and the interrelations between them.2,The principles of defining the forms of ρ and δ and of selecting parameters when designing a pseudo-azimuthal projection.3,The approach to design a good pseudo-azimuthal projection in accordance with the predetermined values.Lastly,based on different viewpoints,four pseudo-azimuthal projection schemes for the whole Chinese territory have been suggested.