Pseudoranging

Pseudoranging is a method of satellites - locating , in the so-called " pseudoranges be used" for determining the location. They deviate from the true distances by a constant, but initially unknown amount.

First, the transit time of the radio signals from the satellites used to the observer's receiver is measured. This results in the current distances to the satellites, which, however, are still subject to clock errors (satellite, receiver) and other small influences.

However, if the satellite clocks are precisely synchronized with each other, all measured transit times are practically only affected by the synchronization error of the receiver clock - i.e. H. all falsified by almost the same amount. This is a constant for long or short distances pseudoranges (pseudoranges) mentioned.

Curved cut with true and pseudo stretch

The position of a point in the plane ( 2D space) can be determined from two lines with the arc cut: the intersection of two circles around the appropriate points. While there are two intersections , this ambiguity of the point of view can always be clarified.

Point determination (2-dimensional) with 3 pseudo-sections: the distances r1, r2 from the fixed points P1, P2 are falsified by a small amount. The intersection of the associated (black) circles K1, K2 must therefore be corrected (red circles), which is possible with a third measurement (circle K3).

If the 2 lines are falsified by a constant, i.e. if they are pseudo lines, the point of intersection will also be faulty (especially with grinding cuts). However, if you have measured a third (just as much falsified) segment, the constant can easily be determined: the 3 circles do not intersect at one point , but rather form a small, curvilinear error triangle . Its center of the circle is the point you are looking for.

In the figure, the constant corresponds to the correction from the black circles K1, K2, K3 to the red circles.

Spatial arc cut

The situation is analogous in three-dimensional space, only three routes (or 4 pseudo-routes) are required to determine the location . You hit a ball around the appropriate points with the distance as radius, whereby two balls always intersect along a circle , which in turn intersects the third ball at the point you are looking for (and a second one).

If pseudo-stretches are present, all 3 spherical radii are falsified by the same amount that can be determined using a fourth sphere (distance to a fourth point or satellite).

Use with GPS

This measuring principle is used in the satellite navigation of the Global Positioning System . The atomic clocks of all GPS satellites (or in the case of GLONASS ) run synchronously to a high degree (accuracy 10 ⁻¹⁴ ), which means errors far below the millimeter even at the speed of light. The route correction (constant in all pseudo-routes) therefore only depends on the clock correction of the receiving quartz clock and can be considered constant for the short time of the measurements. This allows the clock error to be determined in the same way as above and represents the 4th unknown - in addition to the 3 coordinates of your own position to be determined.

The method of route corrections (pseudorange correction) can be applied in a similar way if the position of a reference station is already known exactly. Various navigation services transmit these corrections by radio , which means that the positioning errors are reduced from a few tens of meters to a tenth or a hundredth ( DGPS ).