This function computes Spherical Error Probable radius from inputs consisting of the square roots of the eigenvalues of a covariance matrix (equivalently, from sigma-x, sigma-y, and sigma-z, of a trivariate normal distribution in a coordinate system where there is no cross-correlation between variables.) This means that if you have a covariance matrix and wish to compute the S.E.P., simply obtain the square roots of the eigenvalues and use these as inputs. For example, list them via "sqrt(eig(C))" where C is your covariance matrix.
The S.E.P. is the radius of a sphere which contains a fraction of probability equal to the input "prob," which is asumed to be 0.5 if omitted.
Note: if one of the input sigmas is significantly smaller than both others, calculation time may rise.
By uncommenting a labeled line of code, the user can enter a diagnostic mode to verify the accuracy of this algorithm for whatever inputs are specified.
The mathematical formulas contained herein were created by the author and are copyrighted. Feel free to use them provided you credit the author: Kleder, Michael. "An Algorithm for Converting Covariance to Spherical Error Probable" Mathworks Central File Exchange, 2004.
Michael Kleder (2021). SEP - An Algorithm for Converting Covariance to Spherical Error Probable (https://www.mathworks.com/matlabcentral/fileexchange/5688-sep-an-algorithm-for-converting-covariance-to-spherical-error-probable), MATLAB Central File Exchange. Retrieved .
very useful. Thanks.
Does anyone know of a closed form equation for SEP 95%? or 99%
Very nice algorithm! Extremely useful for Monte Carlo simulation of missile systems where the engagement occurs in three dimensions instead of the two typically associated with CEP plots.
Inspired: Confidence Region Radius
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