Understanding Automotive Electronics 8th - Appendix F

APPENDIX

GPS THEORY

F

In this appendix, the determination of the vehicle position from satellite pseudorange measurements is

explained first by trilateration then by the far superior method of a Kalman filter. Trilateration as a

method of calculating the position of a point in a three-dimensional Cartesian coordinate system

has existed long before GPS and is not practical for the precision required for GPS navigational ap-

plications. Nevertheless, it is presented here in a highly simplified illustration of position determination

from distance measurements to three or more points of known location.

is taken as the point of tangency of the lateral coordinate to the earth. The notation for the coordinates

of any point in an ECEF coordinate system is x

E

,y

E

,z

E

tem is denoted (x

nates x

y

E,

z

E

is explained in Appendix E and in general involves a rotation matrix R and a translation

One of the simplest solutions to the trilateration calculation of vehicle position involves another

coordinate system that is denoted x

s

,y

s

1 and 2 with the origin at satellite 1 position. For computational simplicity, the ECEF coordinate system

x is taken as parallel to x

axis. Conversion of vehicle position to any other coordinate system involves a

simple transformation using matrices for rotation and transl ation as explained in Appendix E.

The position of satellite n in the EF coordinate system is denoted x

k

are denoted:

Satellite n position: