ASSORTED MATHEMATICS

The following are an assortment of equations and derivation for the more mathematically advanced and interested reader:

Mean or expectation:

RMS (Root Mean Squared):

Standard deviation:

Variance:

Covariance:

Correlation:

Bivariate normal distribution density function:

Density function for bivariate normal distribution with zero correlation and equal variances:

Probability that the error is less than D using the above (the result is Weibull with shape parameter b=2 or Rayleigh distribution):

Inverse formula:

RMS Error (RMS_R):

Median (50% error or CEP):

95% Error:

Mean (average) Error:

Mean absolute error using normal distribution (altitude):

Sketch of weighting by HDOP analysis:

Setting:

and solving for m gives the following weighted estimator for m:

( Return to http://www.erols.com/dlwilson/gps.htm )