Turn signal time into range

A satellite navigation receiver compares a signal’s transmission time with its reception time. In a simplified vacuum model, distance equals signal speed multiplied by travel time. The receiver also needs the satellite’s position when the signal was sent; knowing a distance to an unknown point would not locate the receiver.

The clock in an ordinary receiver is not perfectly synchronized with the satellite time reference. Its offset appears in the measured range, which is therefore called a pseudorange. Satellite-clock corrections and propagation effects also matter. The calculation is more than reading the number printed beside a satellite icon.

Use an original exercise with an approximate radio-signal speed of 300,000,000 metres per second. A timing offset of 100 nanoseconds is 0.0000001 second. Multiplying gives a 30-metre range-equivalent error. This is a one-way broadcast measurement, so no round-trip division by two belongs in this calculation.

Thirty metres of range-equivalent error is not automatically a thirty-metre error in the final position. The receiver solves from several measurements, their geometry and its clock offset; corrections and other errors also enter. The example shows why precise timing matters without claiming an exact NavIC user error or a guaranteed accuracy.

From timing offset to a range-equivalent error

An unaided three-dimensional position solution has three position coordinates plus one receiver-clock offset to determine. Four suitable independent satellite measurements provide the basic information for those four unknowns. Additional measurements can help, but merely counting four signals does not guarantee a good solution if their information is unusable or their geometry is poor.

Aided cases differ. For example, a known height or an accurately constrained clock supplies information that an ordinary unconstrained solution lacks. Do not generalize a classroom two-dimensional construction into a claim that every real receiver can solve full position and time from only two or three satellites.