A real-world signal is always corrupted with noise. The separation between a signal and noise is an indispensable step in a variety of signal-analysis applications across different scientific domains. In this paper, we propose a double least-squares projections (DLSPs) method to estimate a signal from the noisy data. The first least-squares projection is to find a signal-dimensional optimal approximation of the noisy data in the least-squares sense. In this step, a rough estimation of the signal is obtained. The second least-squares projection is to find an approximation of a signal in another crossed signal-dimensional space in the least-squares sense. In this step, a much improved signal estimation that is close to orthogonal to the separated noise subspace can be obtained. The DLSP implements projection operation twice to obtain an almost perfect estimation of a signal. The application of the DLSP method in seismic random noise attenuation and signal reconstruction demonstrates the successful performance in seismic data processing.

Double Least-Squares Projections Method for Signal Estimation

Observational data sets in space physics often contain instrumental and sampling errors, as well as large gaps This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time-continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994 Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth "signal" that captures coherent modes, while "noise" is discarded In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time-continuous, and generalizing it to multivariate geophysical data consisting of gappy "driver" and continuous "response" records The reconstruction error estimates provide information on the physics of co-variability between particular solar-wind parameters and geomagnetic indices Copyright 2010 by the American Geophysical Union

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Gap filling of solar wind data by singular spectrum analysis

Aquaculture is an important part of agricultural economy. In the past, major farming accidents often occurred due to subjective experience. There are many factors affecting the water quality of aquaculture. Maintaining an ecological environment with good water quality is the most critical link to ensure the production efficiency and quality of aquaculture. With the continuous development of science and technology, intelligence and informatization in aquaculture has become a new trend. Smart aquaculture cannot only realize real-time monitoring, prediction, warning, and risk control of the physical and chemical factors of the aquaculture environment but can also conduct real-time monitoring of the characteristics and behaviors of the fish, which infers the changes of the aquaculture ecological environment. In this paper, the research achievements over past two decades both are summarized from four aspects: water quality factor acquisition and pre-processing, water quality factor prediction, morphological characteristics, and behavioral characteristic recognition of fish and the mechanism between fish behavior and water quality factors. The advantages and disadvantages of existing research routes, algorithm models, and research methods in smart aquaculture are summarized. The work in this paper can provide a well-organized and summative knowledge reference for further study on the dynamic mechanism between the changes of water quality factors and the fish body characteristics and behavior. Meanwhile, the work can also provide valuable reference for promoting the smart, ecological, and efficient development of aquaculture.

A method overview in smart aquaculture.

Singular spectrum analysis (SSA) is a well-studied approach in signal processing. SSA has originally been designed to extract information from short noisy chaotic time series and to enhance the signal-to-noise ratio. SSA is good for offline applications; however, many applications, such as modelling, analysis, and prediction of time-varying and non-stationary time series, demand for online analysis. This study introduces a recursive algorithm called recursive SSA as a modification to regular SSA for dynamic and online applications. The proposed method is based on eigenvector matrix perturbation approach. After recursively calculating the covariance matrix of the trajectory matrix, R-SSA updates the eigenvalues and eigenvectors for new samples by considering the effect of the new sample as perturbation in the covariance matrix and its singular value decomposition. The eigenvalues and eigenvectors adapt simultaneously to track their true values as would be calculated from the current covariance matrix. Analysis of two well-known chaotic time series: Mackey-Glass and Lorenz chaotic time series and two natural time series: Darwin sea-level pressure and Sunspot number as non-stationary processes are considered in this study to examine the performance of the proposed recursive method. The obtained results depict the power of the proposed method in online spectral analysis of non-linear time-varying systems.

Recursive spectral analysis of natural time series based on eigenvector matrix perturbation for online applications

A novel PEM fuel cell remaining useful life prediction method based on singular spectrum analysis and deep Gaussian processes

A novel interval quartering algorithm (IQA) is proposed to overcome insufficiency of the conventional singular spectrum analysis (SSA) iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.

Wei Liu

Papers

Improved interpolation method based on singular spectrum analysis iteration and its application to missing data recovery