Application of GPS to a railroad navigation system using two satellites and a stored database

DETAILED DESCRIPTION What is claimed is: 1.
A method of determining the location of a vehicle whose movement is constrained to a route whose location is fixed and known, comprising the steps of: (a) estimating the vehicle's location along the route; (b) receiving signals from two global position satellites; (c) determining an angle from a vector tangent to the route at the estimated location to each of the two satellites; (d) for each of the two satellites, determining a range error between an estimated range from the estimated location of the vehicle to the satellite and a measured range from the vehicle to the satellite; (e) using the determined angles and determined range errors for only the two satellites, determining a distance error in the estimated location of the vehicle along the route; and (f) combining the distance error with the estimated location to provide a determined location of the vehicle along the route.
2.
The method of claim 1 wherein the method further comprises the step of selecting one of the satellites forward of the vehicle's direction of movement and the other of the satellites rearward thereof.
3.
The method of claim 1 wherein the step of estimating the vehicle's location along the route comprises the step of using a dead reckoning system to estimate a location along the route.
4.
The method of claim 1 wherein the step of determining a distance error in the estimated location of the vehicle along the route comprises the step of solving the following, where the distance error is .
DELTA.
s, the determined angles are .
theta.
.
sub.
i, the determined range errors are .
delta.
P.
sub.
i, c is a constant and .
DELTA.
B is an unknown: ##EQU11## 5.
The method of claim 4 further comprising the steps of determining the norm of ?.
DELTA.
s .
DELTA.
B!.
sup.
T, and accepting the determined distance error if the determined norm is less than a threshold amount.
6.
The method of claim 1 further comprising the steps of computing a route unit vector that is tangent to the route at the estimated location, and computing satellite unit vectors from the estimated location to each of the two satellites, wherein the determined angles are between the route unit vector and the satellite unit vectors