closed form equation for spherical error probable 9sep0

huangyhg

closed form equation for spherical error probable (sep)
hi.
does anyone know of a closed-form equation for the spherical error probable (sep) 95% or 99%?
thanks,
tina
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for ballistic projectiles, guided projectiles, missiles?  what kind of guidance?  what temperature, windspeed, altitude, humidity corrections allowed?  what training level of gunner/operator assumed?  what range vs. max. operating range of device?
even assuming a gaussian distribution, the "closed form equation" will require a numerical integration (or solution of a numerical series).
if you haven't guessed by now, your "closed form equation" seems nonsensical in real world conditions, with real world devices.  you will need to define an algorithm, and probably conduct a series of worst-case estimates, then an exhaustive monte carlo simulation, and finally a test series to verify the estimates from the monte carlo models.
well, this is not the reply i was looking for....
in any case, the application is not important here.
and yes, this is gaussian distributed.
there is a closed form equation for the sep 50% probable. i just need it for 95% and/or 99%.
thanks again.
tina
additionally, you seen to be mixing concepts.  sep, ostensibly is the spherical radius at which 50% of whatever occurs within that radius.  95% or 99% would therefore not fit within that definition.
or are you asking about conversion?:
well, what i am looking for is an approximation to closed form integral of the trivariate gaussian probability density function in spherical coordinates which can be solved for other probabilites other than 50%. i can certainly do a numerically integration of this gaussian and get a reasonable answer, but this takes up cpu time, something i rather not do. yes, sep is typically defined for 50% probable but it can be defined for 95% probable or 99% probable. many people when they say sep, assume you are taking about 50% probable, but this does not have to the case.
i am not sure if there is a reasonable (accurate enough) approximation, the ones i have seen have not been. i figured i'd try this forum and see.