Browse Prior Art Database

APPROACHES TO RAPID DISTANCE CALCULATION

IP.com Disclosure Number: IPCOM000009268D
Original Publication Date: 1999-Jun-01
Included in the Prior Art Database: 2002-Aug-14
Document File: 5 page(s) / 271K

Publishing Venue

Motorola

Related People

Susan Chen: AUTHOR [+2]

Abstract

In Satellite Communication Systems, dynamic resource management requires the calculation of beam to beam distances or interference/isolation cost. Such resource management schemes are exem- plified by the IRIDIUM Space Vehicle Real-Time (SVRT) and Dynamic Channel Management System (DCMS). On-line calculation of the distances is expensive, whether using Euclidean distance or great circle distance, since it involves earth geome- try and coordinate transforms.

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Page 1 of 5

MOTOROLA Technical Developments

APPROACHES TO RAPID DISTANCE CALCULATION

by Susan Chen and Shawn Hogberg

INTRODUCTION

  In Satellite Communication Systems, dynamic resource management requires the calculation of beam to beam distances or interference/isolation cost. Such resource management schemes are exem- plified by the IRIDIUM Space Vehicle Real-Time (SVRT) and Dynamic Channel Management System (DCMS). On-line calculation of the distances is expensive, whether using Euclidean distance or great circle distance, since it involves earth geome- try and coordinate transforms.

  One approach of prior art (SVRT and DCMS) uses a look up table that stores pre-computed beam to beam distance for every beam on every satellite The shortcoming of this approach is that the memo- ry space required to store the table and the complex- ity in managing the table goes up exponentially with the increase of number of beams and number of satellites. For the next generation IRIDIUM sys- tems such as Macrocell that uses hundreds of spot beams, the table size is prohibitive (over 1 Gigabyte).

  This publication describes a scheme that is com- putationally inexpensive and requires only reason- able storage, which includes the following approach:

1. a rapid calculation of the beam to beam distance by approximation;

2. a simplified distance lookup table in which the required memory space does not increase exponen- tially with the number of beams and satellites;

3. a combination of approach 1 and 2 to achieve the optimum usage of computation power and storage.

ON-LINE CALCULATlOk USING APPROXlMATldN

  Let J. be the latitude ;and 0 be the longitude, a point on the earth (assume a spherical earth) can be expressed in the ECEF coordinate as:

COS(a)?cos(e)

X = cos(L)?sin(@) (1) sin(A)

  The Euclidean distance of two points on the earth is calculated as:

d, =1x, -X,I?R

(2)

where R is the radius of the spherical earth.

  The great circle distance of the two points is cal- culated by:

d, =cos-'(X, ( X,)?R (3)

  The computational complexity involved in these distance calculation is due to the fact that latitude, longitude coordinates have to be converted to ECEF coordinate and vector operations applied.

  An approach to a rapid calculation of the dis- tance is an approximation using a direct calculation from latitude and longitude:

              1, +A, d= (A, -4)' + cos(~)?(EI, -6',) ?R

(4)

0 MOlomla.hC. 1993 152 June 1999

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Developments Technical 0 M MOTOROLA

  Note that there is no need to actually compute the square root and the multiplication by the earth radius R, since only the relative scale of the distance is of concern in resource management. The cosine function can be stored as a look up table. This leaves the computation with only a few simple arith- metic operations.

  The approximation produces zero error for points along the equator when compared to the great circle distance, but degrades for points at higher lati- t...