Quantitative assessment of the accuracy of the GPS-navigator by location.

Here is a simple test that allows you to visually see the errors of your GPS receiver, periodically recording the readings of a stationary receiver for a sufficiently large period of time. For example, once a minute during the day. This will be convenient to do with a chartplotter or computer connected to GPS, or use the built-in function to record the coordinates of points traveled. 

Quantitative assessment of the accuracy of the GPS-navigator by location.

By downloading these coordinates to a computer, we get a picture similar to the figures below. The present experiment was carried out using the same GPS receiver. 1024 points recorded at 30 second intervals.

Quantitative assessment of the accuracy of the GPS-navigator by location.

GPS Navigation Position Charts for Longitude and Latitude.

Quantitative assessment of the accuracy of the GPS-navigator by location.

It is believed that the distribution of the GPS position is in good agreement with the normal Gaussian law. That is, for a larger number of measurements, the bias or bias is zero. Civilian GPS navigation provides accuracy: without SA RMS = 15 meters, and in SA mode 2DRMS = 100 meters. What does this mean?

RMS (Root Mean Square) – the square root of the sum of the squared deviations, divided by the number of measurements, or standard deviation (standard deviation or a). 65% of the points fall into a circle of radius RMS. 2DRMS (Distance RMS) means twice the distance of the RMS (2a). For a spatial two-dimensional Gaussian distribution, 95% of the points fall into a circle with a radius of 2DRMS, if the distribution is elliptical, errors in latitude and longitude are different, up to 98% with a circular distribution.

The distribution of the GPS position becomes elliptical, for example, when the sky on one side is closed to signals. The radius of the circle with 95% coverage – this is the characteristic that is given in the instructions for the GPS receiver. Less commonly used is the CEP parameter – Circular Error Probable, approximately equal to CER = 2DRMS / 2.5. The probable circular error determines the error region with the radius of the circle into which 50% of the obtained points fall. To assess the accuracy of the three-dimensional position, there are spherical versions of all these parameters.

The error in determining the height, as a rule, is one and a half times higher than the horizontal error. The histograms of the distribution of deviations in our experience are shown in the figure below. You can see that after the cancellation of SA, the standard deviation of the position is only 3.2 meters, but short-term deviations of up to 100 meters or more are still quite real.

Quantitative assessment of the accuracy of the GPS-navigator by location.

In this case, the duration of such an “ejection” of more than 40 meters did not exceed 3 minutes. The likely cause is the poor location of the satellites. Conclusion: in most cases, the receiver of the GPS navigator provides accuracy even higher than the stated 15 meters, however, the probability of major errors, although small, exists.

Causes of GPS Navigation Errors with SA Mode On and Off.

Quantitative assessment of the accuracy of the GPS-navigator by location.

It is always advisable to use more than one navigation tool. In critical cases, when deciding whether to trust the readings of a GPS navigator, one should pay attention to the receiver’s information about the location of the satellites, their signal level, the presence of objects obscuring the antenna, the likelihood of heading and speed readings compared to other sources of this data, and sharp changes in the trajectory the distance traveled, which is displayed on the GPS receiver display. You also need to remember that the maximum errors of your GPS navigation are summed from the maximum errors of the entire chain: satellites receiver map user.

Based on materials from the book All About GPS Navigators.
Naiman V.S., Samoilov A.E., Ilyin N.R., Sheinis A.I..

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