Inherent bias in wavefront curvature ranging

The presence of an inherent bias in conventional wavefront curvature ranging systems is demonstrated, and an approximate form is derived. This bias represents a fundamental limit on the ranging performance of such systems and results from the nonlinear character of the ranging equation, in concert with random measurement noise. The bias is shown to be positive (range is overestimated) and proportional to range cubed. The presence of this range-dependent bias also results in an rms estimation error which is larger than that predicted by an analysis which assumes an unbiased range estimator. The increase in actual rms error relative to predicted error is calculated.