Phase estimation in a navigation receiver

This thesis proposes a new method for estimating the unknown phase of a sampled sinusoid of known frequency. The method is called phase corrected correlation (PCC) and it is targeted specifically for the case, when there is a non-integer number of cycles in the measurement interval. Performance of the PCC phase estimate is studied by comparing its mean squared error (MSE) with the Cramér-Rao lower bound (CRLB). In order to simplify analysis and comparison with related methods, the selected signal model is a single sinusoid in additive white Gaussian noise. Two additional algorithms, burst noise removal and partition outlier removal, are proposed for decreasing the MSE of phase estimates in the presence of disturbances such as lightnings and interfering transmitters. PCC frequency estimate is obtained by observing signal phase change in consecutive measurement intervals. Frequency estimation performance and computational burden of the PCC is compared with Interpolated DFT (IDFT). The application domain is a meteorological sounding system for upper-air wind finding using Very Low Frequency (VLF) navigation systems. The problem is to estimate a minute frequency offset caused by the Doppler effect. Frequencies transmitted especially by the Russian Alpha radionavigation system are challenging: the estimation algorithm must be able handle a non-integer number of signal cycles in the 400 ms measurement interval. Most of the related frequency and phase estimation methods are not applicable to this estimation problem. Interpolated DFT (IDFT) may be feasible and therefore it is used as a benchmark. It is shown with computer simulations, that MSE of the phase estimate is close to the CRLB. The same applies to frequency estimates obtained by observing signal phase change in consecutive measurement intervals. Comparison with IDFT shows, that MSE of the PCC frequency estimate is closer to the CRLB as MSE of the IDFT frequency estimate. Moreover, PCC achieves this performance with lower computational burden, making it the preferred choice in this application. It is also shown that MSE of the phase estimate decreases as sampling rate or measurement interval is increased, and that MSE of the phase estimate decreases when interference is removed using burst noise removal and partition outlier removal algorithms. Finally, to achieve a computationally efficient digital signal processor (DSP) implementation, a number of implementation issues are covered.