Equivalent Bandwidth of a General Class of Polynomial Smoothers: With Application to Bearing Tracker Random Error Evaluation

摘要

Random bearing error is a major performance measure of a sonar bearing tracker. Programs currently employed in calculating random bearing error from measured tracker bearing error data use a standard polynomial Least Mean Square Fit (LMSF) algorithm to remove an unknown time varying mean. Previously, the effect of the LMSF algorithm on the residuals of the measured tracker bearing error data was not fully accounted for. In addition, when processing correlated bearing error residuals, the optimum choice of the order of the LMSF and appropriate bias correction factor as a function of signal-to-noise ratio (SNR) were not known. This study investigates the properties of the LMSF in detail and shows that the LMSF behaves as a low-pass filter, the frequency response characteristics of which can be calculated exactly. The equivalent noise bandwidth of the LMSF is shown to be a function of the sample size, the sampling time and the order of the fit. The appropriate bias correction factor, when processing correlated data, is shown to be determined by the ratio of the LMSF bandwidth to the equivalent tracker bandwidth. Results of the analysis are verified by extensive simulation. Finally, an operational procedure is given to obtain an unbiased estimate of the variance for at-sea measured tracker data. (Author)