Carbon dioxide retrieval from OCO-2 satellite observations using the nonlinear least squares four-dimensional variational method: observing system simulation experiments

2020 ◽  
Author(s):  
Zhe Jin ◽  
Xiangjun Tian
Keyword(s):  
Carbon Dioxide ◽  
Cost Function ◽  
Least Squares ◽  
System Simulation ◽  
Nonlinear Least Squares ◽  
Satellite Observations ◽  
Forward Model ◽  
Simulation Experiments ◽  
Normal Distributions ◽  
The Cost

<p>In this study, we apply the nonlinear least squares four-dimensional variational (NLS-4DVar) method to the retrieval of the column-averaged dry air mole fraction of carbon dioxide (X<sub>CO2</sub> ) from the Orbiting Carbon Observatory-2 (OCO-2) satellite observations. The NLS-4DVar method avoids the computation of the tangent linear and adjoint models of the forward model, which reduces the computational and implementation complexity greatly. We use the forward model from the Atmospheric CO<sub>2</sub> Observations from Space (ACOS) X<sub>CO2</sub> retrieval algorithm. The inverse model is constructed of two parts, generating samples and minimizing the cost function. For the CO<sub>2</sub> profile, we apply an improved sampling algorithm based on ensemble singular value decomposition (SVD). For the other elements in the state vector, we apply a sampling algorithm based on normal distributions, and values of standard deviations of normal distributions are vital to the accuracy of retrieval. To minimize the cost function, the NLS-4Dvar method rewrite it into a nonlinear least squares problem, and solve it by a Gauss-Newton iterative method. We have tested our method in summer and winter at four sites through observing system simulation experiments, which are Lamont, Bremen, Wollongong and an ocean site in the North Pacific respectively. All the four sites show an improved X<sub>CO2</sub> and CO<sub>2</sub> profile after the retrieval.</p>

scholarly journals Robust Homography Estimation Based on Nonlinear Least Squares Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Wei Mou ◽  
Han Wang ◽  
Gerald Seet
Keyword(s):  
Cost Function ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Optimization Approach ◽  
Homography Estimation ◽  
Least Squares Optimization ◽  
Image Pairs ◽  
Computation Algorithms ◽  
The Cost ◽  
Geometric Relationship

The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.

Applications of an Interactive Balancing Procedure for Gas Turbines and Other Turbomachinery

2009 ◽  
Author(s):  
Timothy C. Allison ◽  
Harold R. Simmons
Keyword(s):  
Cost Function ◽  
Least Squares ◽  
Gas Turbine ◽  
Case Studies ◽  
Gas Turbines ◽  
Interactive Approach ◽  
Interactive Method ◽  
Balance Weight ◽  
The Cost

Least squares balancing methods have been applied for many years to reduce vibration levels of turbomachinery. This approach yields an optimal configuration of balancing weights to reduce a given cost function. However, in many situations, the cost function is not well-defined by the problem, and a more interactive method of determining the effects of balance weight placement is desirable. An interactive balancing procedure is outlined and implemented in an Excel spreadsheet. The usefulness of this interactive approach is highlighted in balancing case studies of a GE LM5000 gas turbine and an industrial fan. In each case study, attention is given to practical aspects of balancing such as sensor placement and balancing limitations.

scholarly journals A Counterexample to Temporal Differences Learning

1995 ◽  
Vol 7 (2) ◽  
pp. 270-279 ◽  
Author(s):  
Dimitri P. Bertsekas
Keyword(s):  
Neural Network ◽  
Markov Chain ◽  
Cost Function ◽  
Least Squares ◽  
Temporal Differences ◽  
Q Learning ◽  
Absorbing Markov Chain ◽  
Transition Costs ◽  
Compact Representations ◽  
The Cost

Sutton's TD(λ) method aims to provide a representation of the cost function in an absorbing Markov chain with transition costs. A simple example is given where the representation obtained depends on λ. For λ = 1 the representation is optimal with respect to a least-squares error criterion, but as λ decreases toward 0 the representation becomes progressively worse and, in some cases, very poor. The example suggests a need to understand better the circumstances under which TD(0) and Q-learning obtain satisfactory neural network-based compact representations of the cost function. A variation of TD(0) is also given, which performs better on the example.

A NLS-4Dvar Assimilation System of Surface PM2.5 with WRF-CMAQ Model : Observing System Simulation Experiments

2020 ◽  
Author(s):  
Shan Zhang ◽  
Xiangjun Tian ◽  
Hongqin Zhang ◽  
Xiao Han ◽  
Meigen Zhang
Keyword(s):  
Data Assimilation ◽  
Atmospheric Chemistry ◽  
Initial Conditions ◽  
System Simulation ◽  
Fine Particulate Matter ◽  
Wrf Model ◽  
Nonlinear Least Squares ◽  
Simulation Experiments ◽  
Improve Model ◽  
Assimilation System

<p>        While complete atmospheric chemical transport models have been developed to understanding the complex interactions of atmospheric chemistry and physics, there are large uncertainties in numerical approaches. Data assimilation is an efficient method to improve model forecast of aerosols with optimized initial conditions. We have developed a new framework for assimilating surface fine particulate matter (PM<sub>2.5</sub>) observations in coupled Weather Research and Forecasting (WRF) model and Community Multiscale Air Quality (CMAQ) model, based on nonlinear least squares four-dimensional variational (NLS-4DVar) data assimilation method. The NLS-4DVar approach, which does not require the tangent and adjoint models, has been extensive used in meteorological and environmental areas due to the low computational complexity. Two parallel experiments were designed in the observing system simulation experiments (OSSEs) to evaluate the effectiveness of this system. Hourly PM2.5 observations over China be assimilated in WRF-CMAQ model with 6-h assimilation window, while the background state without data assimilation is conducted as control experiment. The results show that the assimilation significantly reduced the uncertainties of initial conditions (ICs) for WRF-CMAQ model and leads to better forecast. The newly developed PM<sub>2.5</sub> data assimilation system can improve PM<sub>2.5</sub> prediction effectively and easily. In the future, we expect emission to be optimized together with concentrations, and integrate meteorological assimilation into aerosol assimilation system.</p>

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

2009 ◽  
Vol 06 (03) ◽  
pp. 459-479
Author(s):  
SUMITRA GANESH ◽  
RUZENA BAJCSY
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Estimation Method ◽  
Nonlinear Least Squares ◽  
Performance Criterion ◽  
Human Motion ◽  
Human Actions ◽  
Mode Estimation ◽  
Nonlinear Least Squares Problem ◽  
The Cost

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

An optimal true‐amplitude least‐squares prestack depth‐migration operator

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 508-515 ◽  
Author(s):  
Guy Chavent ◽  
René‐Edouard Plessix
Keyword(s):  
Least Squares ◽  
Ray Tracing ◽  
Forward Model ◽  
Weight Matrix ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Operator ◽  
Amplitude Correction ◽  
Points Approximation ◽  
The Cost

In order to define an optimal true‐amplitude prestack depth migration for multishot and multitrace data, we develop a general methodology based on the least‐squares data misfit function associated with a forward model. The amplitude of the migrated events are restored at best for any given geometry and any given preliminary filtering and amplitude correction of the data. The migrated section is then the gradient of the cost function multiplied by a weight matrix. A study of the Hessian associated with this data misfit shows how efficiently to find a good weight matrix via the computation of only few elements of this Hessian. Thanks to this matrix, the resulting migration operator is optimal in the sense that it ensures the best possible restoration of the amplitudes among the large class of least‐squares migrations. Applied to a forward model based on Born, ray tracing, and diffracting points approximation, this optimal migration outperforms or at least equals the classic Kirchhoff formula, since the latter belongs to the class of least‐squares migrations and is only optimal for one shot and an infinite aperture. Numerical results illustrate this construction and confirm the above expectations.

scholarly journals DOA-Based Localization Method with Multiple Screening K-Means Clustering for Multiple Sources

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Yankui Zhang ◽  
Daming Wang ◽  
Weijia Cui ◽  
Jiangdong You ◽  
Hao Li ◽  
...  
Keyword(s):  
Cost Function ◽  
Complexity Analysis ◽  
Multiple Target ◽  
Clustering Method ◽  
Multiple Sources ◽  
Simulation Experiments ◽  
Complete Set ◽  
And Performance ◽  
The Cost ◽  
Fuzzy Target

The existing angle-based localization methods are mainly suitable for the single source. Actually, there often exists situation which contains multiple target sources. To solve the problem of localization of multitarget sources, this paper presents a K-means clustering method based on multiple screening, which can effectively realize the localization of multiple sources based on DOA (direction of arrival) parameters. The method firstly establishes a cost function of position coordinates by using DOA parameters from the measuring position coordinates and then solves the cost function to obtain a complete set of real position coordinates and fuzzy position coordinates. As the distribution of real target coordinates is concentrated and the fuzzy target positions are scattered, the K-means clustering method is adopted to classify the coordinate set. In order to improve the positioning accuracy, a multiscreening process is introduced to screen the input samples before each clustering, and it can be finally concluded that clustering centers are the position coordinates of the target sources. Meanwhile, the complexity analysis and performance verification of this method are proposed. Simulation experiments show that this method can efficiently realize ambiguity-free, highly precise localization of multitarget sources.

Assimilation of Nonlinear Observations with the Maximum Likelihood Ensemble Filter

2021 ◽  
Author(s):  
Saori Nakashita ◽  
Takeshi Enomoto
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Satellite Observations ◽  
Observation Error ◽  
Nonlinear Operators ◽  
Linear And Nonlinear ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

<p>Satellite observations have been a growing source for data assimilation in the operational numerical weather prediction. Remotely sensed observations require a nonlinear observation operator.  Most ensemble-based data assimilation methods are formulated for tangent linear observation operators, which are often substituted by nonlinear observation operators. By contrast, the Maximum Likelihood Ensemble Filter (MLEF), which has features of both variational and ensemble approaches, is formulated for linear and nonlinear operators in an identical form and can use non-differentiable observation operators.<span> </span></p><p>In this study, we investigate the performance of MLEF and Ensemble Transform Kalman Filter (ETKF) with the tangent linear and nonlinear observation operators in assimilation experiments of nonlinear observations with a one-dimensional Burgers model.</p><p>The ETKF analysis with the nonlinear operator diverges when the observation error is small due to unrealistically large increments associated with the high order observation terms. The filter divergence can be avoided by localization of the extent of observation influence, but the analysis error is still larger than that of MLEF. In contrast, MLEF is found to be more stable and accurate without localization owing to the minimization of the cost function. Notably, MLEF can make an accurate analysis solution even without covariance inflation, eliminating the labor of parameter adjustment. In addition, the smaller observation error is, or the stronger observation nonlinearity is, MLEF with the nonlinear operators can assimilate observations more effectively than MLEF with the tangent linear operators. This result indicates that MLEF can incorporate nonlinear effects and evaluate the observation term in the cost function appropriately. These encouraging results imply that MLEF is suitable for assimilation of satellite observations with high nonlinearity.</p>

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