ubx-cfg

Static ESP Testing - Sampling Rates

Theory

See what Google says if you enter the following search term:

• “gaussian error propagation reduction in error with twice as many measurements”

You will probably be given results that touch on the following points:

• Doubling the number of measurements (N) reduces the error of the mean by a factor of sqrt(2).
• Error scales inversely with sqrt(N), taking twice as many measurements decreases your uncertainty to about 70.7%.

That is the theory, but does it really apply to GNSS measurements?

• Gaussian error propagation relies upon two assumptions
  • The errors are random and normally distributed
  • The measurements are independent of one another
• It is somewhat questionable whether these are sound assumptions u-blox output
  • u-blox receivers make use of a Kalman filter to minimise noise in the NAV solution
  • The Kalman filter directly impacts future positions and speeds… that is how they work

Anyway, putting the theory aside, Gaussian error propagation is still useful when debating the benefits of 5 Hz and 10 Hz.

Practice

The static testing of the SYNAC GPS concluded with Phase 7 which clearly demonstrated that 5 Hz performs better than 10 Hz.

The mean values for Speed Over Ground (SOG) were as follows:

• 10 Hz = 0.042 kt
• 5 Hz = 0.024 kt

Since 10 Hz has twice as many samples as 5 Hz, 70% of 0.042 kt can be directly compared to 0.024 kt.

i.e. +/- 0.030 kt vs +/- 0.024 kt

Thus, if these magnitudes of error were to be applied to kinematic data, 5 Hz would still be better than 10 Hz.

The differences are small, but there is no reason to double file sizes (and increase processing) for zero benefit.

Links

Some relevant statistical concepts:

• Law of large numbers
• Central limit theorem
• Propagation of uncertainty

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