Compressive Estimation of a Stochastic Process with Unknown Autocorrelation Function

In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in communication theory and signal processing. Due to stationarity, when the autocorrelation function or equivalently the power spectral density (PSD) of the process is available, the Minimum Mean Squared Error (MMSE) predictor is readily obtained. In particular, it is given by a linear operator that depends on autocorrelation of the process as well as the noise power in the observed samples. The prediction becomes, however, quite challenging when the PSD of the process is unknown. In this paper, we propose a blind predictor that does not require the a priori knowledge of the PSD of the process and compare its performance with that of an MMSE predictor that has a full knowledge of the PSD. To design such a blind predictor, we use the random spectral representation of a stationary Gaussian process. We apply the well-known atomic-norm minimization technique to the observed samples to obtain a discrete quantization of the underlying random spectrum, which we use to predict the process. Our simulation results show that this estimator has a good performance comparable with that of the MMSE estimator.


page 1

page 2

page 3

page 4


Mathematical Theory of Atomic Norm Denoising In Blind Two-Dimensional Super-Resolution (Extended Version)

This paper develops a new mathematical framework for denoising in blind ...

Asymptotic behavior of the prediction error for stationary sequences

One of the main problem in prediction theory of discrete-time second-ord...

On asymptotic behavior of the prediction error for a class of deterministic stationary sequences

One of the main problem in prediction theory of stationary processes X(t...

Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process

In this paper, we investigate Gaussian process regression with input loc...

On Spatial (Skew) t Processes and Applications

We propose a new model for regression and dependence analysis when addre...

Gaussian Function On Response Surface Estimation

We propose a new framework for 2-D interpreting (features and samples) b...

Predicting Flat-Fading Channels via Meta-Learned Closed-Form Linear Filters and Equilibrium Propagation

Predicting fading channels is a classical problem with a vast array of a...

Please sign up or login with your details

Forgot password? Click here to reset