Passive bearing estimation of a broad-band source

The variance on the bearing estimates of a wide-band source is relaxed, and the resulting statistical measures are derived. Those lower bound measures depend on the tangent of the true bearing to the source, and the bearing variance as derived with an unbiased condition. In the far field, the resulting bias is given simply by A (tan true bearing) bearing variance where A is a constant. The bias size can be in the order of the unbiased bearing variance. The variance is the sum of the unbiased variance and a combination of the bias and the bearing variance. The variance is contrasted against the Cramer-Rao bound developed for the biased estimate. Such statistical results enable the sizing of the bias and its deteriorating effect on the estimation process for the specific case of interest. When the bias is unacceptable, averaging should be applied to the time delays rather than the bearings. The bias impact is also of interest when noisy bearings are applied to estimate other functions such as passive source motion at long ranges.