MSE will be the sum of the variance of the range error plus the variance of the azimuth error plus the covariance of the range error with the azimuth error plus the square of the bias. Thus the MSE results from pooling all these sources of error, geometrically corresponding to radius of a circle within which 50% of rounds will land. Several methods have been introduced to estimate CEP from shot data. Included in these methods are the plug-in approach of Blischke and Halpin (1966), the Bayesian approach of Spall and Maryak (1992), and the maximum likelihood approach of Winkler and Bickert (2012). The Spall and Maryak approach applies when the shot data represent a mixture of different projectile characteristics (e.g., shots from multiple munitions types or from multiple locations directed at one target). Conversion While 50% is a very common definition for CEP, the circle dimension can be defined for percentages. Percentiles can be determined by recognizing that the horizontal position error is defined by a 2D vector which components are two orthogonal Gaussian random variables (one for each axis), assumed uncorrelated, each having a standard deviation . The distance error is the magnitude of that vector; it is a property of 2D Gaussian vectors that the magnitude follows the Rayleigh distribution, with a standard deviation , called the distance root mean square (DRMS). In turn, the properties of the Rayleigh distribution are that its percentile at level is given by the following formula: or, expressed in terms of the DRMS: The relation between and are given by the following table, where the values for DRMS and 2DRMS (twice the distance root mean square) are specific to the Rayleigh distribution and are found numerically, while the CEP, R95 (95% radius) and R99.7 (99.7% radius) values are defined based on the 68–95–99.7 rule We can then derive a conversion table to convert values expressed for one percentile level, to another. Said conversion table, giving the coefficients to convert into , is given by: For example, a GPS receiver having a 1.25 m DRMS will have a 1.25 m1.73 = 2.16 m 95% radius. Warning: often, sensor datasheets or other publications state "RMS" values which in general, but not always, stand for "DRMS" values. Also, be wary of habits coming from properties of a 1D normal distribution, such as the 68-95-99.7 rule, in essence trying to say that "R95 = 2DRMS".