Difference between revisions of "User:Herb"

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[[Sighting a Weapon]]
 
[[Sighting a Weapon]]
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[[Extreme Spread]]
  
 
[[Mean Radius]]
 
[[Mean Radius]]

Revision as of 18:58, 5 June 2015

Dispersion Assumptions

MediaWiki:Sidebar

Figure of Merit

Sighting a Weapon

Extreme Spread

Mean Radius

Derivation of the Rayleigh Distribution Equation

Measuring Precision

Fliers vs. Outliers

--- Carnac the Magnificent


sighting shot distribution

The Mean Radius is the average distance over all shots to the groups center.

Given
  • set of n shots {\( (h_1, v_1), (h_2, v_2), ..., (h_n, v_n) \)}
    for which all of the (h,v) positions are known
Assumptions
  • Origin at \((r,\theta) = (0,0)\)
  • Rayleigh Distribution for Shots
    • \(\sigma_h = \sigma_v\)
    • \(\rho = 0\)
    • \(PDF_{r_i}(r) = \frac{r}{\sigma^2}e^{-r^2/2\sigma^2}\)
  • With conversion from Cartesian coordinates to Polar coordinates, \(\theta\) will be entirely random and independent of radius
  • No Flyers
Data Pretreatment Shot impact positions converted from Cartesian Coordinates (h, v) to Polar Coordinates \((r,\theta)\)
  • Origin translated from Cartesian Coordinate (\(\bar{h}, \bar{v}\)) to Polar Coordinate \((r = 0, \theta = 0)\)
Experimental Measure \(\bar{r_n}\) - the average radius of n shots

\(\bar{r_n} = \sum_{i=1}^n r_i / n\)
    where \(r_i = \sqrt{(h_i - \bar{h})^2 + (v_i - \bar{v})^2}\)

\(PDF_{r_0}(r; n, \sigma)\) \(\frac{nr}{\sigma^2}e^{-nr^2/2\sigma^2}\)
\(CDF_{r_0}(r; n, \sigma)\) \(1 - e^{-nr^2/2\sigma^2}\)
Mode of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\)
Median of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\sqrt{ln{(4)}}\)
Mean of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\sqrt{\frac{\pi}{2}}\)
(h,v) for all points? Yes
Symmetric about Measure?
NSPG Invariant No
Robust No