Estimation of Ambiguity Functions With Limited Spread

Hindberg, Heidi; Olhede, Sofia C.

doi:10.1109/tsp.2009.2037663

Cited by 9 publications

(3 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, if the increments are correlated, then the process is not second‐order stationary (see, e.g. Gladyshev, ; Goodman, ; Yaglom, ; Lii and Rosenblatt, ; Hindberg and Olhede, ; Gorrostieta et al, ). Furthermore, the increment process yields information about the stationarity of the process in particular domains.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Domain Test for Stationarity of Spatio‐Temporal Data

Bandyopadhyay

Jentsch

Rao

2016

Journal Time Series Analysis

View full text Add to dashboard Cite

Many random phenomena in the environmental and geophysical sciences are functions of both space and time; these are usually called spatio‐temporal processes. Typically, the spatio‐temporal process is observed over discrete equidistant time and at irregularly spaced locations in space. One important aim is to develop statistical models based on what is observed. While doing so a commonly used assumption is that the underlying spatio‐temporal process is stationary. If this assumption does not hold, then either the mean or the covariance function is misspecified. This can, for example, lead to inaccurate predictions. In this article we propose a test for spatio‐temporal stationarity. The test is based on the dichotomy that Fourier transforms of stochastic processes are near uncorrelated if the process is second‐order stationary but correlated if the process is second‐order nonstationary. Using this as motivation, a discrete Fourier transform for spatio‐temporal data over discrete equidistant times but on irregularly spaced spatial locations is defined. Two statistics which measure the degree of correlation in the discrete Fourier transforms are proposed. These statistics are used to test for spatio‐temporal stationarity. It is shown that the same statistics can also be adapted to test for the one‐way stationarity (either spatial or temporal stationarity). The proposed methodology is illustrated with a small simulation study.

show abstract

Section: Introductionmentioning

confidence: 99%

A Spectral Domain Test for Stationarity of Spatio‐Temporal Data

Bandyopadhyay

Jentsch

Rao

2016

Journal Time Series Analysis

View full text Add to dashboard Cite

show abstract

“…where G(ω, λ) is the Loéve dual frequency spectrum. The Loéve dual frequency spectrum is used to describe nonstationary features in a time series and has been extensively studied in Gladyšev (1963), Lund et al (1995), Lii and Rosenblatt (2002), Jensen and Colgin (2007), Hindberg and Olhede (2010), Olhede (2011), Olhede and Ombao (2013), Gorrostieta et al (2019), Aston et al (2019).…”

Section: Transformation To the Fourier Domainmentioning

confidence: 99%

Graphical models for nonstationary time series

Basu¹,

Rao²

2021

Preprint

View full text Add to dashboard Cite

We propose NonStGGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and stationary time series Gaussian Graphical model (StGGM), and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGGM, the proposed framework captures conditional noncorrelations (both intertemporal and contemporaneous) in the form of an undirected graph. In addition, to describe the more nuanced nonstationary relationships among the components of the time series, we introduce the new notion of conditional nonstationarity/stationarity and incorporate it within the graph architecture. This allows one to distinguish between direct and indirect nonstationary relationships among system components, and can be used to search for small subnetworks that serve as the "source" of nonstationarity in a large system. Together, the two concepts of conditional noncorrelation and nonstationarity/stationarity provide a parsimonious description of the dependence structure of the time series.In GGM, the graphical model structure is encoded in the sparsity pattern of the inverse covariance matrix. Analogously, we explicitly connect conditional noncorrelation and stationarity between and within components of the multivariate time series to zero and Toeplitz embeddings of an infinite-dimensional inverse covariance operator. In order to learn the graph, we move to the Fourier domain. We show that in the Fourier domain, conditional stationarity and noncorrelation relationships in the inverse covariance operator are encoded with a specific sparsity structure of its integral kernel operator. Within the local stationary framework we show that these sparsity patterns can be recovered from finite-length time series by node-wise regression of discrete Fourier Transforms (DFT) across different Fourier frequencies. We illustrate the features of our general framework under the special case of timevarying Vector Autoregressive models. We demonstrate the feasibility of learning NonStGGM structure from data using simulation studies.

show abstract

“…The ambiguity function [11][12][13][14] as a tool of time-frequency analysis indicates the correlation of the signals and the time lag or the frequency lag. It was first applied in the analysis of radar signals, mainly for analyzing the resolution of the signals which have matched and filtered with the transmitted signals.…”

Section: Introductionmentioning

confidence: 99%

Bearing and Range Estimation for Multiple Near-Field Sources based on Ambiguity Function

Sun¹,

Jiang

Wang

2012

AISS

View full text Add to dashboard Cite

AD-MUSIC is introduced to near-field to investigate the bearing and range estimation for the mixed source localization of sinusoidal signal and LFM signal. Firstly, a near-field two-dimensional MUSIC method based on ambiguity function distribution is put forward. Further, a novel Root-MUSIC method which constructs two ambiguity function distribution matrices is proposed for near-field source localization. The simulation results show that the two ambiguity function based methods have higher accuracy and resolution for the position estimation of the mixed-source signals compared with WVD based methods and conventional algorithms, even when the signal-to-noise ratio is low.

show abstract

Estimation of Ambiguity Functions With Limited Spread

Cited by 9 publications

References 35 publications

A Spectral Domain Test for Stationarity of Spatio‐Temporal Data

A Spectral Domain Test for Stationarity of Spatio‐Temporal Data

Graphical models for nonstationary time series

Bearing and Range Estimation for Multiple Near-Field Sources based on Ambiguity Function

Contact Info

Product

Resources

About