Question

Global Navigation Satellite System can be used for positioning and timing. The average geometric dilution of precision (GDOP) at a location is 1.0 and positional dilution of precision (PDOP) is 0.8. With the precision of the measurements being 300 m, the achieved precision of timing is __________ ns (Answer in integer). Consider the speed of light is \( 3 \times 10^8 \, {m/s} \)

Hint:

To calculate timing precision using GNSS, use the relation: \[ {GDOP}^2 = {PDOP}^2 + {TDOP}^2 \] Then multiply TDOP with measurement precision and convert to time using the speed of light.

Answer 1

Given:
\[ \text{Measurement precision} = 300\, \text{m}, \quad \text{GDOP} = 1.0, \quad \text{PDOP} = 0.8 \] We know:
\[ \begin{aligned} \text{GDOP}^2 &= \text{PDOP}^2 + \text{TDOP}^2 \\ 1.0^2 &= 0.8^2 + \text{TDOP}^2 \\ 1 &= 0.64 + \text{TDOP}^2 \\ \text{TDOP}^2 &= 0.36 \\ \text{TDOP} &= 0.6 \end{aligned} \] Timing error in meters:
\[ \text{Timing precision (in m)} = 300 \times 0.6 = 180\, \text{m} \] Now convert distance into time using the speed of light:
\[ \text{Time (in seconds)} = \frac{180}{3 \times 10^8} = 6 \times 10^{-7} \, \text{s} = 600\, \text{ns} \] \[ \boxed{600 \, \text{ns}} \]