Additional Random Error Research Articles

Parameter estimation methods for correlated observation mixed additive and multiplicative random error model

In the domain of geodetic adjustment, current methodologies addressing additive and multiplicative error models operate under the assumption of independence between additive and multiplicative random errors. However, limited research has been conducted on elucidating the correlation between the components of additive and multiplicative random errors. To extend a methodology of mixed error models with additive and multiplicative correlation observations, this paper derives three parameter adjustment methods: correlation observation least squares, correlation observation weighted least squares, and correlation observation bias-corrected weighted least squares, all based on the principles of least squares. Additionally, corresponding unit weight variance estimations are constructed. Finally, it is verified by two numerical simulation experiments and a real-world application example of a geodetic network that the correlated observation bcWLS studied in this paper proves to be the most efficient among the six methods for solving the correlated observation multiplication mixture error model.

Helmert variance component estimation for mixed additive and multiplicative random error model

With the development of surveying and mapping science, the object of measurement adjustment has been extended from a single observation of the same kind in the past to different precisions of the same kind, or different kinds of observations. There are additive and multiplicative errors related to electronic instrument measurements, which affect the quality of the adjustment results. A single additive error model is difficult to meet the accuracy requirements, so a mixed additive and multiplicative random error model (MAMREM) is needed. Aiming at the problem of inaccurate MAMREM stochastic model, this paper proposes Helmert Variance Component Estimation (VCE) to determine the weight matrix in different types of observations under MAMREM. In this paper, the formula and iterative algorithm of Helmert variance component estimation applied to MAMREM are derived, and the weights of different kinds of observations in the adjustment process are estimated. In order to verify the effectiveness of the method, the digital elevation model experiment and the side network experiment are used to verify the method. The results prove the effectiveness of the method.

M robust bias-corrected weighted least squares iteration solution of mixed additive and multiplicative random error model

There are many methods for outlier detection and robust estimation in the field of geodesy, but most of them are based on the additive random error model (AREM). In the multiplicative random error model (MREM) or mixed additive and multiplicative random error model (MAMREM), outlier detection or robust estimation is less studied. Based on the bias-corrected weighted least squares (bcWLS) iteration solution of the MAMREM, combined with the conventional M robust estimation in the AREM, this paper proposes an M robust bcWLS iteration solution suitable for the MAMREM. The analysis of the examples shows that the proposed method can obtain better parameter estimation and more reasonable mean square error of unit weight when the observations contain outliers, which verifies the feasibility and preponderance of the proposed method.

Improved artificial gorilla troops optimizer with chaotic adaptive parameters - application to the parameter estimation problem of mixed additive and multiplicative random error models

For mixed additive and multiplicative random error models (MAM models), due to the complex correlation between the parameters and the model power array, derivative operations will be inevitable in the actual calculation. When the observation equation is in nonlinear form, the operations will be more complicated. The swarm intelligence optimization algorithm (SIO) can effectively solve the derivative problem when estimating the nonlinear model parameters using conventional iterative algorithms. However, for different problems, the conventional SIO cannot effectively balance the ability of global and local behavior, resulting in the algorithm falling into prematureness and failing to output effective parameter information. To address the above problems, the improved artificial gorilla troops optimizer (CAGTO) algorithm with chaotic adaptive behavior is proposed. To address the problem that the population generated by the algorithm using pseudo-random numbers in the initialization population phase has poor traversability in the feasible domain, the chaotic sequence is applied to initialize the population instead of pseudo-random number generation to ensure that the population can traverse the feasible domain as much as possible and improve the global search capability of the algorithm. Adaptive parameters that vary linearly and nonlinearly with the algorithm process are constructed to balance the global search and local search ability, while accelerating the convergence speed. Two CAGTO algorithms with different parameter settings are constructed for different problems, and the experimental results show that both CAGTO algorithms can effectively solve the parameter estimation problem of MAM models with different nonlinear forms of observation equations compared with several other comparative algorithms.

MINQUE Method Variance Component Estimation for the Mixed Additive and Multiplicative Random Error Model

MINQUE Method Variance Component Estimation for the Mixed Additive and Multiplicative Random Error Model

The TSCR method for precision estimation of ill-posed mixed additive and multiplicative random error model

Estimating the precision information of parameter estimation can fully reflect the quality of parameter estimation. In this paper, we first derive the weighted least-square regularization iterative (WLSRI) solution and mean square error (MSE) matrix of the ill-posed mixed additive and multiplicative random error (MAMRE) model. Then, considering that the gradual iterative process of the WLSRI solution will affect the final parameter estimation and precision information and further lead to a complex nonlinear function relationship, the traditional Taylor expansion approximate function method cannot be used to solve. Therefore, this paper introduces the derivative-free third-degree spherical-radial cubature rule (TSCR) method for precision estimation of the ill-posed MAMRE model, which generates a series of samples with the same weight by the fixed sampling strategy and further uses the WLSRI method to calculate. Finally, the experiment research and analysis results illustrate that compared with the existing solutions without considering the ill-posed problem, the WLSRI method is applicable and can obtain reasonable parameter estimation and precision information in solving the ill-posed MAMRE model; while the TSCR method can obtain more accurate parameter estimation and precision information than the WLSRI method, which enriches the theoretical research on the precision estimation problem of ill-posed MAMRE model.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative (MAM) random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array, we introduce a derivative-free cat swarm optimization for parameter estimation. We embed the Powell method, which uses conjugate direction acceleration and does not need to derive the objective function, into the original cat swarm optimization to accelerate its convergence speed and search accuracy. We use the ordinary least squares, weighted least squares, original cat swarm optimization, particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity, respectively. The experimental results show that the improved cat swarm optimization has faster convergence speed, higher search accuracy, and better stability than the original cat swarm optimization and the particle swarm algorithm. At the same time, the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations. The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

A method for mixed additive and multiplicative random error models with inequality constraints in geodesy

In the geodetic data processing field, most methods for dealing with inequality constraints model are based on additive random error (ARE) models, and there have been few studies on mixed additive and multiplicative random error (MAAMRE) models with inequality constraints. To address this problem, a MAAMRE model with inequality constraints is first established based on the definition of inequality constraint equations, and then, a corresponding parameter estimation algorithm is proposed based on the idea of an exhaustive search method. In addition, considering a MAAMRE model for an ill-posed problem, an iterative regularization solution for an ill-posed MAAMRE model is first derived, and then, a specific parameter estimation algorithm for an ill-posed MAAMRE model with inequality constraints is further proposed by applying the exhaustive search approach. Finally, the feasibility and advantages of the proposed algorithms are verified by global positioning system (GPS) elevation fitting model and digital terrain model (DTM) examples.Graphical

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model (MAM error model), we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model. The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation. The experimental results show that based on the weighted least squares criterion, the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation. The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods, which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Impact of Meteorological Uncertainties in the Methane Retrieval Ground Segment of the MERLIN Lidar Mission

MERLIN (MEthane Remote sensing LIdar missioN) is a Franco-German space mission designed to provide weighted columns of atmospheric methane through an inversion of the lidar signal using a priori information on the atmospheric state. Uncertainties about the meteorological parameters of the observed scene used in the ground segment contribute to the error budget on the retrieved methane column. With the LIDSIM (LIDar SIMulator) data simulator and the PROLID (PROcessor LIDar) inversion processor developed for MERLIN, we perform an impact experiment using ECMWF (European Centre for Medium Weather Range Forecast) ensemble forecast data. In addition, we estimate the standard deviation of the error in the methane column due to the meteorological uncertainties to be about 0.6 ppb. In addition, we innovate by discussing the impact of interpolations both in time and space, focusing on vertical extrapolations under the topography by using state-of-the-art methods to determine from the scatter between these methods the range in which the actual profile should be. We conclude that, in areas where the topography variations exceed 10 m over 10 km, an additional random error of 0.1 ppb is due to our lack of knowledge of the adjustment of atmospheric profiles to terrain. Finally, we point out that further work needs to be performed on temporal interpolation. Indeed, the 3 h time interpolation of atmospheric tides can create regional biases of up to 2 ppm (which is a major problem for models trying to identify methane sinks and sources).

Virtual Observation Iteration Solution and A-Optimal Design Method for Ill-Posed Mixed Additive and Multiplicative Random Error Model in Geodetic Measurement

AbstractThe mixed additive and multiplicative random error model is a combination of the additive error random model and multiplicative random error model. Weakness is an attribute of the mixed add...

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

Reinforcement Learning for Robust Trajectory Design of Interplanetary Missions

This paper investigates the use of reinforcement learning for the robust design of low-thrust interplanetary trajectories in presence of severe uncertainties and disturbances, alternately modeled as Gaussian additive process noise, observation noise, and random errors in the actuation of the thrust control, including the occurrence of a missed thrust event. The stochastic optimal control problem is recast as a time-discrete Markov decision process to comply with the standard formulation of reinforcement learning. An open-source implementation of the state-of-the-art algorithm Proximal Policy Optimization is adopted to carry out the training process of a deep neural network, used to map the spacecraft (observed) states to the optimal control policy. The resulting guidance and control network provides both a robust nominal trajectory and the associated closed-loop guidance law. Numerical results are presented for a typical Earth–Mars mission. To validate the proposed approach, the solution found in a (deterministic) unperturbed scenario is first compared with the optimal one provided by an indirect technique. The robustness and optimality of the obtained closed-loop guidance laws is then assessed by means of Monte Carlo campaigns performed in the considered uncertain scenarios.

Deconvolution of with unknown error distributions

This paper is devoted to a nonparametric estimation of the probability where X, Y are continuous univariate random variables of interest and observed with additional random errors. We focus on the case where the distributions of the random errors are unknown but symmetric around zero and can be estimated from some additional samples. Using deconvolution techniques, we propose an estimator of θ which depends on a regularization parameter. We then establish upper and lower bounds on convergence rate of the estimator under mean squared error when error densities are assumed to be supersmooth.

Distributed Optimization Under Unbalanced Digraphs With Node Errors: Robustness of Surplus-Based Dual Averaging Algorithm

In this article, the robustness of distributed constrained optimization algorithms for weight-unbalanced directed multiagent networks is studied. Specifically, it is assumed that each agent is subject to additive random node errors , which are caused by the imperfect communication in networks. Under this framework, it is shown that a typical algorithm, called surplus-based dual averaging (SDA), can successfully achieve the convergence to the optimal value of the considered optimization problem, which exhibits the robustness to the node errors. Technically, in the proof of this result, an important augmentation of the node errors in the fusion and surplus variables is first introduced, and then by means of the random process theory and the attenuation effect of diminishing step size on node errors, the robustness of SDA is proved. In addition, inspired by the SDA, a robust algorithm is developed to solve the distributed online optimization problem with node errors. Finally, simulations are given to verify the theoretical results.

A network-based toolkit for evaluation and intercomparison of weather prediction and climate modeling

Model evaluation is a critical component in the development and applications of environmental modeling systems. Conventional metrics such as Pearson product-moment correlation coefficient (r), root-mean-square error (RMSE), and mean absolute error (MAE), albeit process-based and limited to point-to-point statistical comparison, have been widely used in model evaluations. In this study, we propose a network-based toolkit for evaluation of model performance and multi-model comparisons with applications to weather prediction and climate modeling. The model outputs are topologically quantified through a range of network metrics to provide a holistic measure of system dynamics. We first use this toolkit to evaluate the performance of air temperature simulated by the Weather Research and Forecasting model with station measurements over the contiguous United States (CONUS). Results of network analysis suggest a good match between simulation and measurement, as indicated by conventional metrics (r, RMSE, and MAE) as well. The sensitivity of these network metrics is then analyzed based on CONUS station measurements with additive random errors using Monte Carlo simulations. Network metrics show more sensitive and highly nonlinear responses to increasing random errors as compared to conventional ones. Moreover, we use the new toolkit for intercomparison of the downscaled historical air temperature outputs from four global climate models. The similarity in both metrics and spatial structure highlights the capability of network analysis for capturing system dynamics in models alike. The network theory is therefore promising for evaluation and intercomparison of various environmental modeling systems with complex dynamics.

Mitigating impact of spatial variance of turbulence in wind energy applications

Abstract. For the first time an analytical solution for the quantification of the spatial variance of the second-order moment of correlated wind speeds was developed in this work. The spatial variance is defined as random differences in the sample variance of wind speed between different points in space. The approach is successfully verified using simulation and field data. The impact of the spatial variance on three selected applications relevant to the wind energy sector is then investigated including mitigation measures. First, the difference of the second-order moment between front-row wind turbines of Lillgrund wind farm is investigated. The variance of the difference ranges between 25 % and 48 % for turbulence intensities ranging from 7 % to 10 % and a sampling period of 10 min. It is thus suggested to use the second-order moment measured at each individual turbine as input to flow models of wind farm controllers in order to mitigate random error. Second, the impact of the spatial variance of the measured second-order moment on the verification of wind turbine performance is investigated. Misalignment between the mean wind direction and the line connecting the meteorological mast and wind turbine is observed to result in an additional random error in the observed second-order moment of wind speed. In the investigated conditions the random error was up to 34 %. Such a random error adds uncertainty to the turbulence intensity-based classification of the fatigue loads and power output of a wind turbine. To mitigate the random error, it is suggested to either filter the measured data for low angles of misalignment or quantify wind turbine performance using the ensemble-averaged measurements of the same wind conditions. Third, the verification of sensors in wind farms was investigated with respect to the impact of distant reference measurements. In the case of a misalignment between the wind direction and the line connecting sensor and reference, an increased random error will hamper the comparison of the measured second-order moments. The suggested mitigation measures are equivalent to those for the verification of turbine performance.

The sensitivity of satellite-based PM2.5 estimates to its inputs: Implications to model development in data-poor regions

Exposure to fine particulate matter (PM2.5) has been associated with a wide range of negative health outcomes. The overwhelming majority of the epidemiological studies that helped establish such associations was conducted in regions with sufficient ground observations and other supporting data, i.e., the data-rich regions. However, air pollution health effects research in the data-poor regions, where pollution levels are often the highest, is still very limited due to the lack of high-quality exposure estimates. To improve our understanding of the desired input datasets for the application of satellite-based PM2.5 exposure models in data-poor areas, we applied a Bayesian ensemble model in the southeast U.S. that was selected as a representative data-rich region. We designed four groups of sensitivity tests to simulate various data-poor scenarios. The factors considered that would influence the model performance included the temporal sampling frequency of the monitors, the number of ground monitors, the accuracy of the chemical transport model simulation of PM2.5 concentrations, and different combinations of the additional predictors. While our full model achieved a 10-fold cross-validated (CV) R2 of 0.82, we found that when reducing the sampling frequency from the current 1-in-3 day to 1-in-9 day, the CV R2 decreased to 0.58, and the predictions could not capture the daily variations of PM2.5. Half of the current stations (i.e., 30 monitors) could still support a robust model with a CV R2 of 0.79. With 20 monitors, the CV R2 decreased from 0.71 to 0.55 when 100% additional random errors were added to the original CMAQ simulations. However, with a sufficient number of ground monitors (e.g., 30 monitors), our Bayesian ensemble model had the ability to tolerate CMAQ errors with only a slight decrease in CV R2 (from 0.79 to 0.75). With fewer than 15 monitors, our full model collapsed and failed to fit any covariates, while the models with only time-varying variables could still converge even with only five monitors left. A model without the land use parameters lacked fine spatial details in the prediction maps, but could still capture the daily variability of PM2.5 (CV R2 ≥ 0.67) and might support a study of the acute health effects of PM2.5 exposure.

Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error

Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an optimization problem and exchange messages with their neighbors over a connected network. The distributed algorithms are typically exposed to different types of errors in practice, e.g., due to quantization or communication noise or loss. We here focus on analyzing the convergence of distributed ADMM for consensus optimization in presence of additive random node error, in which case, the nodes communicate a noisy version of their latest estimate of the solution to their neighbors in each iteration. We present analytical upper and lower bounds on the mean squared steady state error of the algorithm in case that the local objective functions are strongly convex and have Lipschitz continuous gradients. In addition we show that, when the local objective functions are convex and the additive node error is bounded, the estimation error of the noisy ADMM for consensus optimization is also bounded. Numerical results are provided which demonstrate the effectiveness of the presented analyses and shed light on the role of the system and network parameters on performance.

Using Low Cost Erasure and Error Correction Schemes to Improve Reliability of Commodity DRAM Systems

Most server-grade systems provide Chipkill-Correct error protection at the expense of power and performance. In this paper we present a low overhead solution to improving the reliability of commodity DRAM systems with no change in the existing memory architecture. Specifically, we propose five erasure and error correction (E-ECC) schemes that provide at least Chipkill-Correct protection for x4 (Schemes 1, 2 and 3), x8 (Scheme 4) and x16 (Scheme 5) DRAM systems. All schemes have superior error correction performance due to the use of strong symbol-based codes. Synthesis results in 28 nm node show that the decoding latency of these codes is negligible compared to the DRAM access latency. In addition, we make use of erasure codes to extend the lifetime of the DRAM systems. Specifically, once a chip is marked faulty due to persistent errors, all E-ECC schemes correct erasures due to that faulty chip and also correct an additional random error in a second chip. Evaluation with SPEC2006 workloads show that compared to x4 Chipkill-Correct schemes, Scheme 5 has the highest IPC improvement (mean of 7 percent) and Scheme 4 has the largest power reduction (mean of 18 percent) and the largest increase in energy efficiency (mean of 25 percent).