Comparison of the vector-sum and angle-sum angle of arrival averaging methods – Mathematical derivations


  1. Wang, S.
  2. Inkol, R.
  3. Rajan, S.
  4. Patenaude, F.
Corporate Authors
Defence R&D Canada - Ottawa, Ottawa ONT (CAN)
The accuracy of direction finding (DF) systems can often be improved by the time averaging of multiple measurements, particularly when the signal-to-noise ratio is low. Many DF techniques involve the computation of the emitter angle of arrival (AOA) from the phase angle of a complex-valued signal. For this type of system, there are two closely related, but distinctly different approaches for averaging AOA information. The first approach uses the complex value formed by averaging or summing the individual complex signal values. The second approach reverses the previous order of operations by first computing the phase angle for each complex signal value and then forming the average of the resultant set of phase angle measurements. Experiments performed using off-the-air signal data have shown that the first approach is preferable. This report gives a theoretical proof for this result given the assumption that the complex data sequence processed by the AOA estimator is i.i.d. Gaussian distributed.

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Report Number
DRDC-OTTAWA-TM-2010-131 — Technical Memorandum
Date of publication
01 Jul 2010
Number of Pages
Electronic Document(PDF)

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