Positioning Error Probabilities for Some Forms of Center-of-Gravity Algorithm Calculated with the Cumulative Distributions. Part II
Abstract
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial complications compared to the approaches used in a previous publication on similar problems. The combinations of random variables considered are: Xg3=θ(x2-x1) (x1-x3)/(x1+x2+x3) + θ(x1-x2)(x1+2x4)/(x1+x2+x4) and Xg4=(θ(x4-x5)(2x4+x1-x3)/(x1+x2+x3+x4)+ θ(x5-x4)(x1-x3-2x5)/(x1+x2+x3+x5) The complete and partial forms of the probability density functions of these expressions of the center-of-gravity algorithms are calculated for general probability density functions of the observation noise. The cumulative probability distributions are the essential steps in this study, never calculated elsewhere.