Fusing adjacent-track InSAR datasets to densify the temporal resolution of time-series 3-D displacement estimation over mining areas with a prior deformation model and a generalized weighting least-squares method

2020 ◽  
Vol 94 (5) ◽  
Author(s):  
Yuedong Wang ◽  
Zefa Yang ◽  
Zhiwei Li ◽  
Jianjun Zhu ◽  
Lixin Wu
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Temporal Resolution ◽  
Least Squares Method ◽  
Deformation Model ◽  
Displacement Estimation ◽  
Prior Deformation ◽  
Mining Areas

On the estimation of a harmonic component in a time series with stationary dependent residuals

1973 ◽  
Vol 5 (02) ◽  
pp. 217-241 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Harmonic Component ◽  
Asymptotic Distributions ◽  
Finite Variance ◽  
Rigorous Derivation ◽  
Image Position ◽  
Vector Valued ◽  
Special Case

Let observations (X 1, X 2, …, Xn ) be obtained from a time series {Xt } such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu (θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu (θ) = 0 for u > 0, the parameter θ thus being absent.

Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake

1992 ◽  
Vol 82 (4) ◽  
pp. 1840-1866
Author(s):  
Yijun Du ◽  
Atilla Aydin ◽  
Paul Segall
Keyword(s):  
Least Squares ◽  
Penalty Function ◽  
Least Squares Method ◽  
Slip Distribution ◽  
Deformation Model ◽  
Long Wavelength ◽  
Inversion Technique ◽  
Elevation Changes ◽  
Damped Least Squares ◽  
Selection Of

Abstract A number of techniques are employed to overcome nonuniqueness and instability inherent in linear inverse problems. To test the factors that enter into the selection of an inversion technique for fault slip distribution, we used a penalty function with smoothness (PF + S), a damped least-squares method (DLS), damped least-squares method with a positivity constraint (DLS + P), and a penalty function with smoothness and a positivity constraint (PF + S + P) for inverting the elevation changes for slip associated with the 1983 Borah Peak earthquake. Unlike solving an ill-posed inverse problem using a gradient technique (Ward and Barrientos, 1986), we have restored the well-posed character between the elevation changes and normal slip distribution. Studies showed that the constraints based on sound understanding of the physical nature of the problem are crucial in the derivation of a meaningful solution and dictates primarily the selection of a particular inversion technique. All available geological and geophysical information were used to determine a geophysical deformation model for the earthquake. It is suggested that the PF + S + P solution for a fault length of 75 km is the preferred model. The long wavelength features in the estimated slip distribution are similar to those obtained by Ward and Barrientos (1986), whereas the shorter wavelength features differ between two solutions. The fault dips 49° to the southwest. The slipped zones deepen from the surface at the northwest to about 20-km downdip depth at the southeast. The fault extends to the southeast beyond the epicenter of the mainshock. It is also shown that only the long wavelength features of the slip distribution are well resolved. The resolution is better at shallower levels than at deeper levels. The resolution deteriorates when the deformation sources are away from the leveling lines. Smoothness constraints provide better resolution than damping does at depth. The addition of a positivity constraint significantly improves the model resolution.

scholarly journals Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method

2014 ◽  
Vol 490 ◽  
pp. 012040
Author(s):  
Cyril Voyant ◽  
Wani Tamas ◽  
Christophe Paoli ◽  
Aurélia Balu ◽  
Marc Muselli ◽  
...  
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Modeling ◽  
Multi Layer Perceptron ◽  
Damped Least Squares

RECONSTRUCTING DIFFERENTIAL EQUATION FROM A TIME SERIES

2003 ◽  
Vol 13 (11) ◽  
pp. 3307-3323 ◽  
Author(s):  
VALKO PETROV ◽  
JUERGEN KURTHS ◽  
NIKOLA GEORGIEV
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Small Error ◽  
Mathematical Algorithm ◽  
Right Hand ◽  
Polynomial Differential Equation ◽  
Observational Noise

This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient.

On the first-order bilinear time series model

1981 ◽  
Vol 18 (03) ◽  
pp. 617-627 ◽  
Author(s):  
Tuan Dinh Pham ◽  
Lanh Tat Tran
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Time Series Model ◽  
First Order ◽  
Strongly Consistent

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

MEASURING THE PREDICTABILITY OF NOISY RECURRENT TIME SERIES

1993 ◽  
Vol 03 (03) ◽  
pp. 797-802
Author(s):  
R. WAYLAND ◽  
D. PICKETT ◽  
D. BROMLEY ◽  
A. PASSAMANTE
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Additive Noise ◽  
Nearest Neighbor ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Short Time Series ◽  
Forecasting Method ◽  
Noisy Time Series ◽  
Short Time

The effect of the chosen forecasting method on the measured predictability of a noisy recurrent time series is investigated. Situations where the length of the time series is limited, and where the level of corrupting noise is significant are emphasized. Two simple prediction methods based on explicit nearest-neighbor averages are compared to a more complicated, and computationally expensive, local linearization technique based on the method of total least squares. The comparison is made first for noise-free, and then for noisy time series. It is shown that when working with short time series in high levels of additive noise, the simple prediction schemes perform just as well as the more sophisticated total least squares method.

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