Passive bearing estimation: The removal of bias and 2π ambiguities

Averaging across frequency presents one means of combating noise in split‐beam bearing estimation. Unfortunately, simple phase averaging is a biased estimator, and, in the case of split‐beam analysis, suffers as well from spatial aliasing. Both of these difficulties arise from the 2πn uncertainty inherent in any phase angle observation. This paper provides several algorithms utilizing an iterative averaging technique which circumvents these problems. Convergence theorems are provided for the algorithms and an evaluation on synthetic data shows them to be highly successful. The techniques developed are quite general and should find use in many situatios in which angle averaging or averaging of functions of angles is pertinent.