Effect of Bias on Estimates of the Circular Probable Error

Abstract

Two estimates for the Circular Probable Error (CEP) are studied to determine their effectiveness when the aim point is shifted from the target center to another point. It is assumed that the distribution of points is bivariate circular normal, with mean value (or aim point) at ( m 1 , m 2 ) and variances σ x 2 = σ y 2 = σ 2 . Both estimates are unbiased and asymptotically efficient when the aim point is at (0, 0). When the aim point is shifted, only one of the estimates is unbiased, but it requires estimation of the coordinates of the shifted aim point. If the amount of shift is known to be small, or suspected of being so, this estimate may not be as good as the biased estimate, which is employed as though the mean were (0,0). In this study the precision of the estimates is determined as well as the transition bias which marks the point where one estimate becomes more effective than the other.