RU1784976C - Co-ordinate converter - Google Patents

Abstract

The invention relates to the field of automation and computer engineering and can be used in geodetic systems to transform spatial coordinates. The aim of the invention is to expand the class of tasks at the expense of the possibility of determining the intersection point of three rotation ellipsoids. The device comprises a matrix inversion block, a constant memory block, three groups of multipliers, four adder groups, two matrix multiplication blocks, a group of division blocks, a subtractor for the fractional rational function 2 il.

Description

The invention relates to the field of processing measurement information and can be used in geodetic systems to transform spatial coordinates.

Coordinate transforming devices are known, comprising registers, counters, logic circuits, and arithmetic devices.

The disadvantage of these devices is that they perform simple linear coordinate transformations and cannot perform transformations with non-linear coupling of parameters, in particular, they cannot be used to determine the spatial location of the intersection point of three spherical position surfaces.

The closest in technical essence is a coordinate transformer comprising a control unit, a read-only memory unit, coordinate adders, a master oscillator, an arithmetic unit,

comparison circuit, key, three coordinate registers and multiplexer. This device can be used to determine the spatial location of the intersection point of three spherical surfaces.

However, this device has a low speed (due to the use of an iterative (multi-step) procedure for generating estimates), as well as limited functional capabilities - it does not allow to determine the intersection point of three rotation ellipsoids (but only the intersection point of three spheres) and therefore cannot be used Used in elliptical measuring systems.

The purpose of the invention is to expand the class of tasks to be solved by the possibility of determining the intersection point of three rotation ellipsoids,

The goal is achieved in that in a known device containing a unit

cl

WITH

,

N

Xi

™

matrix rotations, constant memory block, ri group of multipliers, four groups of ummators, according to the invention, two matrix multiplication blocks, a group of division blocks, a block for calculating a fractional-national function are introduced, the inputs of the first, second and third operands of the converter connected to the inputs of the divider of the corresponding blocks the division of the group, and the inputs of the respective factors of the corresponding multipliers of the first group, the inputs of the divisible blocks of the division of the group are connected to the corresponding outputs of the constant memory block, the outputs of the block the divisions of the group are connected to the inputs of the corresponding terms of the corresponding adders of the first group, the outputs of the adders of the first group are connected to the corresponding information inputs of the matrix reversal unit, the outputs of which are connected to the corresponding inputs of the first factors of the first block and matrix multiplication, the inputs of the second co-residents of which are connected to the outputs the corresponding adders of the first group, the outputs of the first block of matrix multiplication are connected to the corresponding inputs of the first factors of the second Olock multiplier no matrices whose inputs of the second factors are connected to the corresponding outputs of the constant memory block, the outputs of the second matrix multiplication block are connected to the inputs of the first terms of the corresponding adders of the second group, the inputs of the second terms of which are connected to the corresponding outputs of the constant memory block, the outputs of the multipliers of the first group, the second block multiplication of matrices and adders of the second group Connected to the inputs of the respective factors of the corresponding multipliers of the second group, the outputs of which are connected to the input the corresponding terms of the corresponding adders of the third group, the outputs of which are connected to the inputs of the operands of the fractional rational function calculator, the output of which is connected to the inputs of the first factors of the multipliers of the third group, the outputs of which are connected to the inputs of the first terms of the adders of the fourth group, the outputs of the first matrix multiplier connected to the inputs of the second factors of the corresponding multipliers of the third group and the inputs of the second terms of the corresponding adders of the fourth group, outputs b eye calculating fractional rational function, and the outputs of the adders of the fourth group are connected to the outputs of the converter result.

The following procedure is used to transform coordinates. The initial data are the sums of the distances (Fig. 2). Roi Ri + Ro, Ro2 R2 + Ro, Ro3 Ra + Ro.

We write the following relations for the parameters Ri:

Ri R0i-Ro, Ri2 Roi2-; 2R0iRo + Ro2 at the same time by the cosine theorem

Ri2 Ro2 + R201 - 2R0Bo cos - R02 + B201 - - X0pl - X0 +

 - Yo Yi - Y0J + tZ - ZoJZi - ZoB,

where X, Y, Z are the coordinates of the desired point, Xi, YI, Zi are the coordinates of the corresponding reference point.

Equating the right parts of these equations and the corresponding transformations, it is easy to obtain the equation

m ..-%,, UGUR | y 1,. h ROI n and, TGio - - -p - "o

noi%

"To

"To

Wire similar calculations for the parameters Ra and RS, we obtain the equations

) .- h

.

35 Subtracting the equation of the parameter RI from these equations, we obtain a system of two equations of the form

40

sous + oЈu + oga {zh + 83y f u3e dj

Where

Bj-bo

at -

. e 2 s

“I-Sfe-Sfe-5 -).

50 Solving this system of equations with respect to the unknown coordinate Y, we obtain

55

I .HSHttg c, v l g fx 1 tr vg g l, oa 1

Kg4 W Kg

It should be noted that the above equation set determines the direct

which lies the desired point. The direct is described by equations of the form

fxfz

those. the straight line is defined by the point (dx, 0, gz) and the direction vector (fx, I. fz).

Consider a rotation ellipsoid formed by the sum of the distances R01 Ri + 10 + Ro (points O and 1 are the foci of the ellipsoid). In a coordinate system whose center coincides with the center of the base B0i, and the X axis is parallel to this base, the ellipsoid is described by equations of the form15

: +

a2

., Y2 + Z2

i

Rol, b2 (R2o1-B2ol)

The target point is the intersection point of the ellipsoid and the straight line described above. To search for this point, we write the Equation of the straight line in the coordinate system associated with the center of the Boi base. having the form

XR

 At

Where

+ Vzi

cos / J sin / О -sln / 3

ABOUT

cosa

Oh - sin a

in arcsln

Uo U1 B01

those. corresponding transfer and rotation of said straight line are carried out. Expressing the parameters X, Y, Z through the parameter Y and substituting them in the equations of the ellipsoid, we obtain quadratic equations for Y whose solutions are of the form

yyw

sЈ + s

D- i ..

 g r

55

iS + pS

 -a -1

well

Of the two roots of the quadratic equation, one (corresponding to the sign

5

U 15

twenty

25

thirty

35

40

45

fifty

55

plus in front of the square root), which has physical meaning, namely, satisfying the condition Y 0 (the point lies in the upper hemisphere), which is typical for coordinate transformation in geodetic systems. After calculating the Y value, X and Z are calculated according to the above formulas. It should be noted that these calculations are somewhat simplified when moving to the coordinate system associated with point O, i.e. at X0 Y0 - Z0 0. Therefore, the proposed coordinate transformer generates estimates of the parameters X, Y, Z in the coordinate system with a beginning at the point

Ho, YO, ZQ.

The coordinate converter (Fig. 1) comprises a group of division blocks 1 consisting of 15 division blocks 1.1-1.15; the first group of adders 2.1, consisting of 8 adders 2 1 1-2.1.8; matrix inversion unit 3; the first and second blocks of matrix multiplication 4.1, 4.2; block 5 memory constants 5; the second, third and fourth groups of adders 2 2, 2.3, 2.4; a first group of multipliers 6.1 consisting of four multipliers 6.1.1-1.6.4; as well as the second and third groups of multipliers 2.2, 2.3. The input of the first operand of the coordinate converter with the inputs of the divisors of the divisions 1.1-1.4 and the input of the divisible divisions 1.5; the input of the second operand is connected to the inputs of the dividers of blocks 1.6-1.9 and the input of the dividend block 1 10 of the division; the input of the third operand of the converter is connected to the inputs of the dividers of the division blocks 1.11-1T14 and the input of the dividend division block 1.15; the output of the first division block 1.1 is connected to the inputs of the first terms of the adders 2.1.1-2.1,2 of the first group; the output of the second division block 1.2 is connected to the inputs of the first terms of the adders 2.1.3-2.1.4 of the first group; the output of the third division block 1.3 is connected to the inputs of the first terms of the fifth, sixth, seventh and eighth adders 2.1.5-2.1.8 of the first group; the outputs of the seventh, eighth, twelfth and thirteenth division blocks 1.7, 1.8, 1.12, 1.13 are connected to the inputs of the second terms of the third, fourth, fifth, sixth, seventh and eighth adders 2.1.3-2.1.8 of the first group; the output of the fifth division block 1.5 is connected to the inputs of the second terms of the first and second adders 2.1.1, 2.1.2 of the first group; the outputs of the fifth and tenth division blocks 1.5, 1.10 are connected to the inputs of the third terms of the first and second adders 2.1.1, 2.1 2 of the first group, respectively; the outputs of the eleventh and fifteenth division blocks 1.11, 1.15 are connected to the inputs of the fourth terms of the first and second adders 2.1.1, 2.1.2 of the first group, respectively. The outputs of the adders 2.1.1-2.1.8 of the first group are connected to the corresponding information inputs of the matrix inversion block 3, the outputs of which are connected to the inputs of the first factors of the first matrix multiplication block 4.1, the inputs of the second factors of which are connected to the outputs of the first, second, fifth and sixth adders 2.1.1,2.1.2, 2.1.5, 2.1.6 of the first group. The outputs of the first matrix multiplying unit 4.1 are connected to the corresponding inputs of the first factors of the second matrix multiplying unit 4.2, the inputs of the second factors of which are connected to the corresponding outputs of the constant memory unit 5. The first group of outputs of the second matrix multiplying unit 4.2 is connected to the inputs of the first terms of the adders of the second group of adders 2.2, the inputs of the second terms of which are connected to the corresponding outputs of the constant memory unit 5.

The input of the first operand of the coordinate converter is also connected to the inputs of the first and second factors of the first and second multipliers 6.1.1, 6.1.2 of the first group, and the input of the first factor of the third multiplier 6.1.3 of the first group, the input of the second factor of which is connected to the corresponding output of the memory unit 5 ty constants; outputs of the first and second multipliers 6.1.1. 6.1.2 of the first group are connected respectively to the inputs of the first and second factors of the fourth multiplier 6.1.4 of the first group; the outputs of the first multiplier 6.1.1 of the first group are connected to the inputs of the inter multipliers of the multipliers of the second group of 6.2 multipliers, the inputs of the second multipliers of which are connected to the outputs of the second block 4.2, multiplying the matrices and adders of the second group of adders 2.2. The outputs of the multipliers of the second group of multipliers 6.2 are connected to the corresponding inputs of the adders of the third group of adders 2.3, the outputs of which are connected to the inputs of the block 7 for calculating the rational function, the output of which is connected to the inputs of the first factors of the multipliers of the third group 6.3 of multipliers, the outputs of which are connected to the inputs of the first terms of the adders the fourth group of adders 2.4. The outputs of the first block 4.1 of matrix multiplication are connected to the inputs of the second factors of the multipliers of the third group of multipliers 6.3 and the inputs of the second terms of the adders of the fourth group of adders 2.4. The outputs of the fractional rational function calculator 7 and the adders of the fourth group of adders 2.4 are connected to the outputs of the converter result. The clock inputs of the converter are connected to the clock inputs of the matrix multiplier blocks, division blocks, multiplier blocks.

The coordinate converter works as follows.

The values of the parameters R01, Ro2, Ro3, received at the input of the coordinate converter, go to the corresponding inputs of the “division blocks 1.1-1.15 of the group of division blocks 1. The corresponding inputs of the division blocks 1.1-1.15 come from the block

5 value constant memory

0

5

5

jB2oi, xi, yi.zi, 1 1-3,

as a result, values are formed at the outputs of the division blocks

Be. P

-G 2P

I02J 02

R03B03

,

h

Ј

of

Ј

{blocks 1.1 - 1.6), (blocks 1.6 - 1.10),

(blocks 1.11 .16).

These values are input and the inputs are sum | Mathors 2.1.1-2.1.8 of the first group of adders 2.1, at the outputs of which the values

s, -tg- 1 oG

With s- -.ft

 oi

2 (

5G.

U (U

But OG

e-3fe-36r-V. . arriving at the corresponding inputs of the matrix inversion block 3 and the first matrix multiplication block 4.1, as a result of which the values of 0 parameters are formed at the outputs of the latter

The parameters gx, gz, fx, fz are supplied to the corresponding inputs of the second matrix multiplying block 4.2, the inputs of which also receive the values of the elements of the constant matrix H from the inputs of the constant memory block 5. The result of the multiplication comes from the outputs of the second block 4.2 of matrix multiplication by the corresponding adders of the second group of adders 4.2, as a result of which values are generated at the outputs of these adders

1

sx

s.-ni

Jx I 1 (Xr

where -TJ H yi I is the vector of constants, l l. I Z1 l

3Z

At the same time, the value of the input parameter of the coordinate transformer R01 is supplied to the corresponding inputs of the multipliers 6.1.1-6.1.4 of the first group of multipliers 6.1, and the value of B201 from the corresponding output of the constant memory unit 5 is also input to the multiplier 6.1.3. As a result of multiplication, the values of R012, Roi4, B0i2Roi are formed at the outputs of the respective multipliers. These values, as well as the above values of Px, Py, PZ. Sx, Sy. Sz from the outputs of the adders of the second group 4.2, go to the corresponding inputs of the multipliers of the second group 6.2, at the inputs of which the values Roi2Sx2 are formed accordingly. B0i2Sx2, Roi2Sy, Roi2S72. RoiW, Boi2Px2, RoiW. RoCSxPx,

x - Ro12B012

Bo12PxSx, Ro12PxSy,

Ro12Pz2, Po / PzSz.

These values are fed to the corresponding inputs of the adders of the third group 2.3, as a result of which the values are formed

Wo Roi2Sx2 - B0i2Sx2 + Roi2Sy2 + + Roi2Sz2.

V0 RolSxPx - B01 PxSx + Ro12PxSy +

+ Roi2PzSz.

Oh Ro12Px2 - B012Px2 + Ro12Pz2 - - Rol + Boi2Roi.

These values - the normalized coefficients of the above quadratic equation - are input to the block 7 for calculating the fractional rational function, the output of which is formed by the value of the coordinate e according to the formula

V0

+ 4

at a)

This value goes to the output of the coordinate converter, as well as to the corresponding inputs of the multipliers of the third group 6.3. The corresponding inputs of the same multipliers also receive the values of fx, fz from the output of the first block 4.1 of matrix multiplication, as a result of which the values fxy, fzy calculated at the inputs of the adders of the fourth group 2.4 are calculated. The inputs of the same adders receive the values of Qx, Qz from the outputs first matrix multiplication block 4.1. Coordinate values are calculated.

X gx +, 2 dg + tgu,

arriving at the outputs of the coordinate transformer.

Technical appraisal and economic advantages of the claimed technical solution for

5 in relation to the prototype is that as a result of the introduction of distinctive features significantly improved performance through the use of a direct (non-iterative) calculation method

10 (estimates are formed in one pass). In addition, the proposed device has wider functionality - allows you to find the intersection point of three ellipsoids, and can be

15 is used not only in trilateration (as a prototype), but also in elliptical systems, i.e. for a wider class of measuring systems.

Claims (1)

0 Claims A coordinate converter comprising a matrix inversion unit, a constant memory unit, three groups of multipliers, four groups of adders, 5 in that, in order to expand the class of problems to be solved by providing the possibility of determining the intersection point of three rotation ellipsoids, two matrix multiplication units are additionally introduced into it, 0 is a group of division blocks, a block for calculating a fractional rational function, and the inputs of the first, second, and third operands of the converter are connected to the inputs of the dividers of the corresponding division blocks 5 groups and the inputs of the respective factors of the respective multipliers of the first group, the inputs of the divisible blocks of the division of the group are connected to the corresponding outputs of the constant memory block, the outputs 0 division blocks of group 1 are connected to the inputs of the corresponding terms of the corresponding adders of the first group, the outputs of the adders of the first group are connected to the corresponding information inputs of the matrix reversal unit, the outputs of which are connected to the corresponding inputs of the first factors of the first matrix multiplication unit, the inputs of the second factors of which are connected 0 with the outputs of the corresponding adders of the first group, the outputs of the first block of matrix multiplication are connected to the corresponding inputs of the first factors of the second block of matrix multiplication, inputs 5 second factors of which are connected to the corresponding outputs of the instruction memory block, the outputs of the second matrix multiplication block are connected to the inputs of the first terms of the corresponding adder sums of the second group, the inputs of the second terms of which connected to the corresponding outputs of the constant memory block, the outputs of the first group multipliers, the second matrix multiplier and second group adders are connected to the inputs of the corresponding factors of the second group multipliers, the outputs of which are connected to the inputs of the corresponding terms of the corresponding adders of the third group, the outputs of which are connected to the inputs of the operands unit for calculating a fractional rational function, the output of which is connected with the inputs of the first multipliers of the third group, the outputs of which are connected to the inputs of the first terms of the adders of the fourth group / outputs of the first block matrix multiplications are connected to the inputs of the second factors of the corresponding factors of the third group and the inputs of the second terms of the respective adders of the fourth group, the outputs of the fractional rational function calculator and the outputs of the adders of the fourth group are connected to the outputs of the converter result. Shchig2