The quality of models for ARMA processes

In the next example, the signal vector randomization method (SVR1) as given in (9), the deterministic SVR method (SVR2) as given in (11), the frequency estimation method (TK) outlined in Section III, and the spatial smoothing methods are compared. All three sources are perfectly correlated, i.e., they have a zero relative phase angle at each iteration, e.g., multipath propagation where the path delays are the same. The analyses using SVR1, SVR2, and TK start by estimating the bearings with the frequency estimation method using one snapshot. The analysis using spatial smothing uses the first ten snapshots to estimate the spatial smoothing (SS) matrix. The results in Fig. 2 indicate the following. • The frequency method is less accurate than the SVR and SS methods at an SNR of 10 dB. This is because the TK method uses a single snapshot, whereas SVR uses a weighted sum of, effectively, [1=(1 0)] snapshots ([] is the smallest integer larger than), which is the equivalent window width for exponential averaging. • The performance of the SVR1, SVR2, and SS methods is about the same. In the final example, bearings are tracked for 500 snapshots. The SNR is 10 dB, and the sources are stationary at 60 , 80 , and 100. In Table I, standard deviations for each of the three source bearings are listed for the SVR1, SVR2, frequency estimation, and spatial smoothing methods. V. CONCLUSION Two algorithms for the tracking of correlated signals have been presented. A frequency estimator is used to obtain the initial estimate of the DOA's in the presence of signal correlation. Signal vector randomization (SVR) can be employed to eliminate any correlation during the subspace tracking process, and this can be done automatically without any knowledge of the presence or absence of correlation. The SVR method does not reduce the effective array aperture as the spatial smoothing method does, and this becomes important in situations where the number of sensors in the array is small. REFERENCES [1] J. Cadzow, " Multiple source location—The signal subspace approach, " IEEE Trans. Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes, " IEEE Trans. Adaptive beamforming using split-polarity transformation for correlated signal and interference, " IEEE Trans. Abstract—The model error (ME) is an objective measure for assessing the quality of different models of a given ARMA process. The expression for ME can be evaluated …