Parameters Of Autoregressive Processes Research Articles

GLR, Rao, and Wald Tests for Distributed Parametric Detection in Subspace Interference

This paper considers the detection of a target in a distributed radar system, wherein the received reflections from the said target are contaminated with heterogeneous clutter returns. We model this clutter, and possibly additional interference, as a superposition of an auto-regressive process and deterministic interference coming from a known subspace. Parametric adaptive detectors for this scenario are derived based on the Generalized Likelihood Ratio (GLR), Rao, and Wald tests, and are analyzed and compared with their non-adaptive, clairvoyant counterparts, which assume a priori knowledge of the auto-regressive process parameters. Using numerical simulations, the proposed detectors are shown to have detection performances that are robust to strong subspace interference.

Wavelet Covariance Matrix Structure and Bayesian-Wavelet Estimation of Autoregressive Process Parameters with Long-Term Memory

Wavelet Covariance Matrix Structure and Bayesian-Wavelet Estimation of Autoregressive Process Parameters with Long-Term Memory

Overlay Cognitive Radio Based on OFDM with Channel Estimation Issues

Cognitive radio (CR) has been proposed as a technology to improve the spectrum efficiency by giving an opportunistic access of the licensed-user spectra to unlicensed users. We consider an overlay CR consisting of a primary macro-cell and cognitive small cells of cooperative secondary base stations (SBS). We suggest studying a CR where an orthogonal frequency division multiplexing is used for both the primary users (PU) and the secondary users (SU). In order to cancel the interferences, a precoding is required at the SBS. Therefore, we first derive the interferences expression due to SU at the PU receiver. Then, zero forcing beamforming (ZFBF) is considered to cancel the interferences. However, applying ZFBF depends on the channels between the SBS and the PU. A channel estimation is hence necessary. For this purpose, we propose to approximate the channel by an autoregressive process (AR) and to consider the channel estimation issue by using a training sequence. The received signals, also called the observations, are considered to be disturbed by an additive white measurement noise. In that case, the AR parameters and the channel can be jointly estimated from the received noisy signal by using a recursive approach. Nevertheless, the corresponding state space representation of the system is non-linear. Then, we propose to carry out a complementary study by compare non-linear Kalman filter based approaches.

Parameters Estimations for Autoregressive Process

Autoregressive process is better than other stochastic processes, which models flexibility, and simulates some other stochastic processes by setting the parameters of model. This paper firstly describes in detail the basic definition of autoregressive process and its stationary conditions, and then studies estimation autoregressive process parameters with residuals briefly in order to research Hubors М-estimation for autoregressive process with symmetric stable residuals. Secondly, prove autoregressive processes with residuals, which are-stable random variables, are also stationary processes, and use Markov's inequality and related theories to discuss Hubors М-estimation for autoregressive process with symmetric stable residuals. Finally, prove the consistency and asymptotic normality of this estimate further.

Corrected prediction intervals for change detection in paired watershed studies

Hydrological data may be temporally autocorrelated requiring autoregressive process parameters to be estimated. Current statistical methods for hydrological change detection in paired watershed studies rely on prediction intervals, but the current form of prediction intervals does not include all appropriate sources of variation. Corrected prediction intervals for the analysis of paired watershed study data that include variation associated with covariance and linear model parameter estimation are presented. We provide an example of their application to data from the Hinkle Creek Paired Watershed Study located in the western Cascade foothills of Southern Oregon, USA. Research implications of using the correct prediction limits and incorporating the estimation uncertainty of autoregressive process parameters are discussed. Editor D. Koutsoyiannis Citation Som, N.A., Zégre, N.P., Ganio, L.M. and Skaugset, A.E., 2012. Corrected prediction intervals for change detection in paired watershed studies. Hydrological Sciences Journal, 57 (1), 134–143.

High-Accuracy Instrumental Variable Identification of Continuous-Time Autoregressive Processes From Irregularly Sampled Noisy Data

A computationally efficient estimator of continuous-time autoregressive (AR) process parameters from irregularly sampled data affected by discrete-time white measurement noise is presented. It is described how an instrumental variable approach can be used for estimating the AR process parameters with high accuracy. Possible estimators of the incremental variance of the driving continuous-time white noise source and of the variance of the discrete-time white measurement noise are also discussed.

Consistent estimation of autoregressive parameters from noisy observations based on two interacting Kalman filters

The estimation of the parameters of an autoregressive process (AR) from noisy observations is still a challenging problem. In this paper, we propose to sequentially estimate both the signal and the parameters, avoiding a non-linear approach such as the extended Kalman filter. The method is based on two conditionally linked Kalman filters running in parallel. Once a new observation is available, the first filter uses the latest estimated AR parameters to estimate the signal, while the second filter uses the estimated signal to update the AR parameters. This approach can be viewed as a recursive instrumental variable-based method and hence has the advantage of providing consistent estimates of the parameters from noisy observations. A comparative study with existing algorithms illustrates the performances of the proposed method when the additive noise is either white or coloured.

Estimation of continuous-time AR process parameters from discrete-time data

The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression, and using the least squares method. Such a procedure is simple to apply, computationally flexible and efficient, and may have good numerical properties. It is known, however, that all standard approximations of the highest order derivative, such as repeated use of the delta operator, gives a biased least squares estimate, even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then. two new methods, which avoid the shift in our previous results, are presented. One of them, which is termed bias compensation, is computationally very efficient. Finally, the relationship of the above least squares approaches with an instrumental variable method is investigated. Comparative simulation results are also presented.

Multichannel signal detection involving temporal and cross-channel correlation

This paper considers the Gaussian multichannel binary detection problem. A multichannel generalized likelihood ratio is derived using a model-based approach where the signal and nonwhite additive noise are characterized by autoregressive (AR) vector processes. Detection performance is obtained via the Monte Carlo procedure for the special case where the AR process parameters of the observation processes are assumed to be known. Specifically, detection performance is obtained for two-channel observation vectors containing various temporal and cross-channel correlation on both the signal and nonwhite additive noise. The computed results are compared with known optimal detection curves using coherent (both in time and across channels) as well as noncoherent integration. In addition, the degradation in performance due to a low signal-to-noise ratio on a specific channel is also considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Autoregressive spectral estimation in noise with reference to speech analysis

An improved “frequency-weighted” method of spectral estimation is described. Discussion of the method is directed toward the problem of estimating autoregressive process parameters from discrete-time observations corrupted by additive independent noise with known power spectral density. This problem often occurs in speech analysis and other applications. The estimation procedure is cast as the problem of minimizing a frequency-weighted information measure and has theoretical foundations relating it to asymptotic maximum likelihood and minimum information divergence procedures as well as the linear predictive procedures popular for speech analysis. Topological properties of the frequency-weighted measure are developed and used to prove that the solution to the minimization problem is global and unique. Computational procedures are developed for both the estimation problem and the related problem of testing multiple simple hypotheses. Simulation results are used to support the theoretical development and demonstrate the advantages of the method as compared to “noise filtering” methods that have been popular for speech analysis.

Maximum Likelihood Estimation of Parameters of Autoregressive Processes with Moving Average Residuals and Other Covariance Matrices with Linear Structure

The autoregressive process with moving average residuals is a stationary process $\{y_t\}$ satisfying $\sum^p_{s = 0} \beta_sy_{t - s} = \sum^q_{j = 0} \alpha_j\nu_{t - j}$, where the sequence $\{\nu_t\}$ consists of independently identically distributed (unobservable) random variables. The distribution of $y_1,\cdots, y_T$ can be approximated by the distribution of the $T$-component vector $\mathbf{y}$ satisfying $\sum^p_{s = 0} \beta_s\mathbf{K}_s\mathbf{y} = \sum^q_{j = 0} \alpha_j\mathbf{J}_j\mathbf{v}$, where $\mathbf{v}$ has covariance matrix $\sigma^2\mathbf{I}, \mathbf{K}_s = \mathbf{J}_s = \mathbf{L}^s$, and $\mathbf{L}$ is the $T \times T$ matrix with 1's immediately below the main diagonal and 0's elsewhere. Maximum likelihood estimates are obtained when $\mathbf{v}$ has a normal distribution. The method of scoring is used to find estimates defined by linear equations which are consistent, asymptotically normal, and asymptotically efficient (as $T\rightarrow \infty$). Several special cases are treated. It is shown how to calculate the estimates.