Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra

Lau, Soon-Sen; Sherman, Peter; White, L.B.

doi:10.1109/18.992779

Cited by 7 publications

References 22 publications

(33 reference statements)

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Autoregressive frequency detection using Regularized Least Squares

Chen

Gel²

2010

Journal of Multivariate Analysis

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a b s t r a c tTracking of an unknown frequency embedded in noise is widely applied in a variety of applications. Unknown frequencies can be obtained by approximating generalized spectral density of a periodic process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure and its parameters can be easily estimated iteratively, which is crucial for online (real-time) applications. Typically, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size, model order may change, which leads to re-estimation of all model parameters. We propose a new iterative procedure for frequency detection based on a regularization of an empirical information matrix. The suggested method enables to avoid the repeated model selection as well as parameter estimation steps and therefore optimize computational costs. The asymptotic properties of the proposed regularized AR (RAR) frequency estimates are derived and performance of RAR is evaluated by numerical examples.

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Autoregressive frequency detection using Regularized Least Squares

Chen

Gel²

2010

Journal of Multivariate Analysis

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Detection of sinusoids in unknown coloured noise using ratios of AR spectrum estimates

White¹,

Sherman²

1999

1999 Information, Decision and Control. Data and Information Fusion Symposium, Signal Processing and Communications Symposium A

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This paper is an introductory exposition of the application of the ratio of the 2pth order autoregressive (AR) power spectrum estimate to the p t h order AR power spectrum estimate to the problem of detecting sinusoids of unknown frequency in additive coloured noise with unknown power spectral density. The resulting threshold test is independent of a priori knowledge of both the sinusoid's parameters and the PSD of the additive noise. Simulations are presented for the Gaussian case, focussing primarily on the SNR thresholding behaviour of the scheme. These simulations illustrate the power of the technique when highly resonant background noise is present, such as is often the case in rotating machinery, for example.Significant threshold extension, and slightly superior subthreshold performance compared to the energy detector is observed in these cases. The paper also examines the application of the technique to the problem of identifying tones in diesel engine vibration data.

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MCMC-based iterative method for mixed spectrum estimation

Liu

et al. 2009

2009 IEEE Radar Conference

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From the Bayesian statistical inference theory, a new mixed spectrum estimation method, which is based on Markov chain Monte Carlo (MCMC) approach, is proposed in this paper. The proposed method iteratively extracts the estimates of sinusoid parameters via the traditional methods, and estimates the ones of AR clutter parameters via the MCMC approach. Because the MCMC approach can fully dig the inherent information among the samples, it is more suitable for estimating the AR parameters from the less samples. Consequently, the proposed method is an efficient method for extracting the parameters of mixed spectrum for the applications with a small number of samples. Simulation results show that, comparing with the similar structure method, the method presented in this paper behaves superior estimation performance for the less samples case, and the estimation performance is less influenced by the signal-toclutter ratio.

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Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra

Cited by 7 publications

References 22 publications

Autoregressive frequency detection using Regularized Least Squares

Autoregressive frequency detection using Regularized Least Squares

Detection of sinusoids in unknown coloured noise using ratios of AR spectrum estimates

MCMC-based iterative method for mixed spectrum estimation

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