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Journal articles on the topic 'Stochastic errors'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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1

Lv, Pin, Jizhou Lai, Jianye Liu, and Mengxin Nie. "The Compensation Effects of Gyros' Stochastic Errors in a Rotational Inertial Navigation System." Journal of Navigation 67, no. 6 (2014): 1069–88. http://dx.doi.org/10.1017/s0373463314000319.

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The errors of an inertial navigation system (INS) in response to gyros' errors can be effectively reduced by the rotation technique, which is a commonly used method to improve an INS's accuracy. A gyro's error consists of a deterministic contribution and a stochastic contribution. The compensation effects of gyros' deterministic errors are clear now, but the compensation effects of gyros' stochastic errors are as yet unknown. However, the compensation effects are always needed in a rotational inertial navigation system's (RINS) error analysis and optimization study. In this paper, the compensation effects of gyros' stochastic errors, which are modelled as a Gaussian white (GW) noise plus a first-order Markov process, are analysed and the specific formulae are derived. During the research, the responses of an INS's and a RINS's position error equations to gyros' stochastic errors are first analysed. Then the compensation effects of gyros' stochastic errors brought by the rotation technique are discussed by comparing the error propagation characteristics in an INS and a RINS. In order to verify the theory, a large number of simulations are carried out. The simulation results show a good consistency with the derived formulae, which can indicate the correctness of the theory.
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Zheng, Zhichao, Songlai Han, Jin Yue, and Linglong Yuan. "Compensation for Stochastic Error of Gyros in a Dual-axis Rotational Inertial Navigation System." Journal of Navigation 69, no. 1 (2015): 169–82. http://dx.doi.org/10.1017/s037346331500051x.

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A dual-axis rotational Inertial Navigation System (INS) has received wide attention in recent years because of high performance and low cost. However, some errors of inertial sensors such as stochastic errors are not averaged out automatically during navigation. Therefore a Twice Position-fix Reset (TPR) method is provided to enhance accuracy of a dual-axis rotational INS by compensating stochastic errors. According to characteristics of an azimuth error introduced by stochastic errors of an inertial sensor in the dual-axis rotational INS, both an azimuth error and a radial-position error are much better corrected by the TPR method based on an optimised error propagation equation. As a result, accuracy of the dual-axis rotational INS is prominently enhanced by the TPR method, as is verified by simulations and field tests.
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3

Ozendi, M., D. Akca, and H. Topan. "STOCHASTIC SURFACE MESH RECONSTRUCTION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2 (May 30, 2018): 805–12. http://dx.doi.org/10.5194/isprs-archives-xlii-2-805-2018.

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A generic and practical methodology is presented for 3D surface mesh reconstruction from the terrestrial laser scanner (TLS) derived point clouds. It has two main steps. The first step deals with developing an anisotropic point error model, which is capable of computing the theoretical precisions of 3D coordinates of each individual point in the point cloud. The magnitude and direction of the errors are represented in the form of error ellipsoids. The following second step is focused on the stochastic surface mesh reconstruction. It exploits the previously determined error ellipsoids by computing a point-wise quality measure, which takes into account the semi-diagonal axis length of the error ellipsoid. The points only with the least errors are used in the surface triangulation. The remaining ones are automatically discarded.
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Grooms, I., Y. Lee, and A. J. Majda. "Ensemble Filtering and Low-Resolution Model Error: Covariance Inflation, Stochastic Parameterization, and Model Numerics." Monthly Weather Review 143, no. 10 (2015): 3912–24. http://dx.doi.org/10.1175/mwr-d-15-0032.1.

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Abstract The use of under-resolved models in ensemble data assimilation schemes leads to two kinds of model errors: truncation errors associated with discretization of the large-scale dynamics and errors associated with interactions with subgrid scales. Multiplicative and additive covariance inflation can be used to account for model errors in ensemble Kalman filters, but they do not reduce the model error. Truncation errors can be reduced by increasing the accuracy of the numerical discretization of the large-scale dynamics, and subgrid-scale parameterizations can reduce errors associated with subgrid-scale interactions. Stochastic subgrid-scale parameterizations both reduce the model error and inflate the ensemble spread, so their effectiveness in ensemble assimilation schemes can be gauged by comparing with covariance inflation techniques. The effects of covariance inflation, stochastic parameterizations, and model numerics in two-layer periodic quasigeostrophic turbulence are compared on an f plane and on a β plane. The stochastic backscatter schemes used here model backscatter in the inverse cascade regime of quasigeostrophic turbulence, as appropriate to eddy-permitting ocean models. Covariance inflation improves the performance of a benchmark model with no parameterizations and second-order numerics. Fourth-order spatial discretization and the stochastic parameterizations, alone and in combination, are superior to covariance inflation. In these experiments fourth-order numerics and stochastic parameterizations lead to similar levels of improvement in filter performance even though the climatology of models without stochastic parameterizations is poor.
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Ijaz, Muhammad, Syed Azhar Ali Zaidi, and Aamir Rashid. "Uniform patterns based area-efficient and accurate stochastic computing finite impulse response filter." PLOS ONE 16, no. 1 (2021): e0245943. http://dx.doi.org/10.1371/journal.pone.0245943.

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Stochastic computing has recently gained attention due to its low hardware complexity and better fault tolerance against soft errors. However, stochastic computing based circuits suffer from different errors which affect the output accuracy of these circuits. In this paper, an accurate and area-efficient stochastic computing based digital finite impulse response filter is designed. In the proposed work, constant uniform patterns are used as stochastic numbers for the select lines of different MUXes in the filter and the error performance of filter is analysed. Based on the error performance, the combinations of these patterns are proposed for reducing the output error of stochastic computing based filters. The architectures for generating these uniform patterns are also proposed. Results show that the proposed design methodology has better error performance and comparable hardware complexity as compared to the state-of-the-art implementations.
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6

Cheng, Qiang, Can Wu, Peihua Gu, Wenfen Chang, and Dongsheng Xuan. "An Analysis Methodology for Stochastic Characteristic of Volumetric Error in Multiaxis CNC Machine Tool." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/863283.

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Traditional approaches about error modeling and analysis of machine tool few consider the probability characteristics of the geometric error and volumetric error systematically. However, the individual geometric error measured at different points is variational and stochastic, and therefore the resultant volumetric error is aslo stochastic and uncertain. In order to address the stochastic characteristic of the volumetric error for multiaxis machine tool, a new probability analysis mathematical model of volumetric error is proposed in this paper. According to multibody system theory, a mean value analysis model for volumetric error is established with consideration of geometric errors. The probability characteristics of geometric errors are obtained by statistical analysis to the measured sample data. Based on probability statistics and stochastic process theory, the variance analysis model of volumetric error is established in matrix, which can avoid the complex mathematics operations during the direct differential. A four-axis horizontal machining center is selected as an illustration example. The analysis results can reveal the stochastic characteristic of volumetric error and are also helpful to make full use of the best workspace to reduce the random uncertainty of the volumetric error and improve the machining accuracy.
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Zhu, Luhua, and Erlei Yao. "An Improved Hilbert Spectral Representation Method for Synthesizing Spatially Correlated Earthquake Ground Motions and Its Error Assessment." Mathematical Problems in Engineering 2020 (May 16, 2020): 1–21. http://dx.doi.org/10.1155/2020/2127374.

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This paper is an extension of the random amplitude-based improved Hilbert spectral representation method (IHSRM) that the authors developed previously for the simulation of spatially correlated earthquake ground motions (SCEGMs) possessing the nonstationary characteristics of the natural earthquake record. In fact, depending on the fundamental types (random phase method and random amplitude method) and matrix decomposition methods (Cholesky decomposition, root decomposition, and eigendecomposition), the IHSRM possesses various types. To evaluate the influence of different types of this method on the statistic errors, i.e., bias errors and stochastic errors, an error assessment for this method was conducted. First, the random phase-based IHSRM was derived, and its reliability was proven by theoretical deduction. Unified formulas were given for random phase- and random amplitude-based IHSRMs, respectively. Then, the closed-form solutions of statistic errors of simulated seismic motions were derived. The validness of the proposed closed-form solutions was proven by comparing the closed-form solutions with estimated values. At last, the stochastic errors of covariance (i.e., variance and cross-covariance) for different types of IHSRMs were compared, and the results showed that (1) the proposed IHSRM is not ergodic; (2) the random amplitude-based IHSRMs possessed higher stochastic errors of covariance than the random phase-based IHSRMs; and (3) the value of the stochastic error of covariance for the random phase-based IHSRM is dependent on the matrix decomposition method, while that for the random amplitude-based one is not.
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8

Anant, Venkat, and Roland Priemer. "Adjacent errors of stochastic gradient algorithms under general error criteria." Computer Standards & Interfaces 20, no. 6-7 (1999): 475. http://dx.doi.org/10.1016/s0920-5489(99)91053-x.

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Doerr, Daniel, Ilan Gronau, Shlomo Moran, and Irad Yavneh. "Stochastic errors vs. modeling errors in distance based phylogenetic reconstructions." Algorithms for Molecular Biology 7, no. 1 (2012): 22. http://dx.doi.org/10.1186/1748-7188-7-22.

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10

Alderov, Zaur A., Evgeny V. Rozengauz, and Denis Nesterov. "How CT reconstruction parameters effect measurement error of pulmonary nodules volume." HERALD of North-Western State Medical University named after I.I. Mechnikov 12, no. 3 (2020): 73–77. http://dx.doi.org/10.17816/mechnikov44920.

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One of the the widely used way to follow up oncological disease is estimation of lesion size differences. Volumetry is one of the most accurate approaches of lesion size estimation. However, being highly sensitive, volumetric errors can reach 60%, which significantly limits the applicability of the method.
 Purpose was to estimate the effect of reconstruction parameters on volumetry error.
 Materials and methods. 32 patients with pulmonary metastases underwent a CT scanning with 326 foci detected. 326 pulmonary were segmented. Volumetry error was estimated for every lesion with each combination of slice thickness and reconstruction kernel. The effect was measured with linear regression analysis
 Results. Systematic and stochastic errors are impacted by slice thickness, reconstruction kernel, lesion position and its diameter. FC07 kernel and larger slice thickness is associated with high systematic error. Both systematic and stochastic errors decrease with lesion enlargment. intrapulmonary lesions have the lowest error regardless the reconstruction parameters.
 Lineal regression model was created to prognose error rate. Model standart error was 6.7%. There was corelation between model remnants deviation and slice thickness, reconstruction kernel, lesion position and its diameter.
 Conclusion. The systematic error depends on the focal diameter, slice thickness and reconstruction kernel. It can be estimated using the proposed model with a 6% error. Stochastic error mainly depends on lesion size.
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11

Valdés, Rosenda A., Denise P. V. Sato, and Roxana M. Martinez Orrego. "A stochastic model for volumetric errors." Journal of the Brazilian Society of Mechanical Sciences and Engineering 28, no. 2 (2006): 161–68. http://dx.doi.org/10.1590/s1678-58782006000200005.

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Shykula, Mykola, and Oleg Seleznjev. "Stochastic structure of asymptotic quantization errors." Statistics & Probability Letters 76, no. 5 (2006): 453–64. http://dx.doi.org/10.1016/j.spl.2005.08.022.

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13

Wu, Yueqiu, Liping Wang, Yi Wang, et al. "Risk Analysis for Short-Term Operation of the Power Generation in Cascade Reservoirs Considering Multivariate Reservoir Inflow Forecast Errors." Sustainability 13, no. 7 (2021): 3689. http://dx.doi.org/10.3390/su13073689.

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In the short-term operation of the power generation of cascade reservoirs, uncertainty factors such as inflow forecast errors could cause various types of risks. The inflow to a downstream reservoir is not only affected by inflow forecast errors from upstream reservoirs but also the forecast errors associated with inflow to the stream segment between the reservoirs, such as from a tributary. The inflow forecast errors of different forecast periods may also be correlated. To address this multivariate problem, the inflow forecast error variables were jointly fitted in this study using the Gaussian mixture model (GMM) and a t-Copula function based on the analysis of the error distribution characteristics in different forecast periods. Therefore, a stochastic model that coupled with the GMM and t-Copula to calculate inflow forecast errors in multiple forecast periods was established. Furthermore, according to the simulation results of the stochastic model and the predicted runoff series, a set of simulated runoff processes were obtained. Then they were combined with the existing power generation plan to carry out the risk analysis for short-term operation of the power generation in a cascade reservoir. The approach was evaluated using the Jinguan cascade hydropower system within the Yalong River basin as a case study. For this case study, the risk analysis for short-term operation of the power generation was analyzed based on stochastic simulation of the inflow forecast errors; the results show the feasibility and effectiveness of the proposed methods.
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Liu, Feng, and Xin Li. "Formulation of scale transformation in a stochastic data assimilation framework." Nonlinear Processes in Geophysics 24, no. 2 (2017): 279–91. http://dx.doi.org/10.5194/npg-24-279-2017.

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Abstract. Understanding the errors caused by spatial-scale transformation in Earth observations and simulations requires a rigorous definition of scale. These errors are also an important component of representativeness errors in data assimilation. Several relevant studies have been conducted, but the theory of the scale associated with representativeness errors is still not well developed. We addressed these problems by reformulating the data assimilation framework using measure theory and stochastic calculus. First, measure theory is used to propose that the spatial scale is a Lebesgue measure with respect to the observation footprint or model unit, and the Lebesgue integration by substitution is used to describe the scale transformation. Second, a scale-dependent geophysical variable is defined to consider the heterogeneities and dynamic processes. Finally, the structures of the scale-dependent errors are studied in the Bayesian framework of data assimilation based on stochastic calculus. All the results were presented on the condition that the scale is one-dimensional, and the variations in these errors depend on the differences between scales. This new formulation provides a more general framework to understand the representativeness error in a non-linear and stochastic sense and is a promising way to address the spatial-scale issue.
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Meyer, Fabian, Christian Rohde, and Jan Giesselmann. "A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method." IMA Journal of Numerical Analysis 40, no. 2 (2019): 1094–121. http://dx.doi.org/10.1093/imanum/drz004.

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Abstract In this article we present an a posteriori error estimator for the spatial–stochastic error of a Galerkin-type discretization of an initial value problem for a random hyperbolic conservation law. For the stochastic discretization we use the stochastic Galerkin method and for the spatial–temporal discretization of the stochastic Galerkin system a Runge–Kutta discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos (2016, Hyperbolic Conservation Laws in Continuum Physics, 4th edn., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 325, Berlin, Springer, pp. xxxviii+826), this leads to computable error bounds for the space–stochastic discretization error. Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretization. We conclude with some numerical examples confirming the theoretical findings.
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Short, Michael. "Bounds on Worst-Case Deadline Failure Probabilities in Controller Area Networks." Journal of Computer Networks and Communications 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/5196092.

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Industrial communication networks like the Controller Area Network (CAN) are often required to operate reliably in harsh environments which expose the communication network to random errors. Probabilistic schedulability analysis can employ rich stochastic error models to capture random error behaviors, but this is most often at the expense of increased analysis complexity. In this paper, an efficient method (of time complexityO(n log n)) to bound the message deadline failure probabilities for an industrial CAN network consisting ofnperiodic/sporadic message transmissions is proposed. The paper develops bounds for Deadline Minus Jitter Monotonic (DMJM) and Earliest Deadline First (EDF) message scheduling techniques. Both random errors and random bursts of errors can be included in the model. Stochastic simulations and a case study considering DMJM and EDF scheduling of an automotive benchmark message set provide validation of the technique and highlight its application.
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Hornberger, Zachary, Bruce Cox, and Raymond R. Hill. "Analysis of the effects of spatiotemporal demand data aggregation methods on distance and volume errors." Journal of Defense Analytics and Logistics 5, no. 1 (2021): 29–45. http://dx.doi.org/10.1108/jdal-03-2020-0003.

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Purpose Large/stochastic spatiotemporal demand data sets can prove intractable for location optimization problems, motivating the need for aggregation. However, demand aggregation induces errors. Significant theoretical research has been performed related to the modifiable areal unit problem and the zone definition problem. Minimal research has been accomplished related to the specific issues inherent to spatiotemporal demand data, such as search and rescue (SAR) data. This study provides a quantitative comparison of various aggregation methodologies and their relation to distance and volume based aggregation errors. Design/methodology/approach This paper introduces and applies a framework for comparing both deterministic and stochastic aggregation methods using distance- and volume-based aggregation error metrics. This paper additionally applies weighted versions of these metrics to account for the reality that demand events are nonhomogeneous. These metrics are applied to a large, highly variable, spatiotemporal demand data set of SAR events in the Pacific Ocean. Comparisons using these metrics are conducted between six quadrat aggregations of varying scales and two zonal distribution models using hierarchical clustering. Findings As quadrat fidelity increases the distance-based aggregation error decreases, while the two deliberate zonal approaches further reduce this error while using fewer zones. However, the higher fidelity aggregations detrimentally affect volume error. Additionally, by splitting the SAR data set into training and test sets this paper shows the stochastic zonal distribution aggregation method is effective at simulating actual future demands. Originality/value This study indicates no singular best aggregation method exists, by quantifying trade-offs in aggregation-induced errors practitioners can utilize the method that minimizes errors most relevant to their study. Study also quantifies the ability of a stochastic zonal distribution method to effectively simulate future demand data.
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Ashraf, Zeeshan, and Wajeeha Nafees. "Error Modeling and Analysis of Inertial Measurement Unit Using Stochastic and Deterministic Techniques." Advanced Materials Research 403-408 (November 2011): 4447–55. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4447.

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The measurements provided by inertial measurement unit (IMU) are erroneous due to certain noise parameters which are needed to be taken into account because the corrupted data is of little practical value in inertial navigation systems (INS). By integrating the IMU data in navigation algorithm, these errors are accumulated, leading to significant drift in the attitude, position and velocity outputs. Several techniques have been devised for the error modeling of this error by way of Neural Networks (NNs), PSD, ARMA, etc. In this paper, the deterministic and stochastic approach is followed to model the noise parameters of a low cost IMU. The error parameters thus determined by using the both techniques help in the development of an effective navigation algorithm. Deterministic errors are calculated by the help of Up-Down Test and the Rate Table test. While the stochastic errors, which are more random in nature, are recognized using Power Spectral Density (PSD) Analysis and Allan Variance techniques.
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Eshagh, Mehdi. "Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation." Contributions to Geophysics and Geodesy 40, no. 1 (2010): 1–30. http://dx.doi.org/10.2478/v10126-010-0001-9.

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Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation Errors of estimated parameters in an adjustment process should be scaled according to the size of the estimated residuals or misclosures. After computing a quasi-geoid (geoid), its biases and tilts, due to existence of systematic errors in the terrestrial data, are removed by fitting a corrective surface to the misclosures of the differences between the GNSS/levelling data and the quasi-geoid (geoid). Variance component estimation can be used to re-scale or calibrate the error of the GNSS/levelling data and the quasi-geoid (geoid) model. This paper uses this method to calibrate the errors of the recent quasi-geoid model, the GNSS and the normal heights of Sweden. Different stochastic models are investigated in this study and based on a 7-parameter corrective surface model and a three-variance component stochastic model, the calibrated error of the quasi-geoid and the normal heights are 6 mm and 5 mm, respectively and the re-scaled error of the GNSS heights is 18 mm.
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Zhao, Luodi, and Long Zhao. "An Algorithm for Online Stochastic Error Modeling of Inertial Sensors in Urban Cities." Sensors 23, no. 3 (2023): 1257. http://dx.doi.org/10.3390/s23031257.

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Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models.
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Gillijns, S., and B. De Moor. "Model error estimation in ensemble data assimilation." Nonlinear Processes in Geophysics 14, no. 1 (2007): 59–71. http://dx.doi.org/10.5194/npg-14-59-2007.

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Abstract. A new methodology is proposed to estimate and account for systematic model error in linear filtering as well as in nonlinear ensemble based filtering. Our results extend the work of Dee and Todling (2000) on constant bias errors to time-varying model errors. In contrast to existing methodologies, the new filter can also deal with the case where no dynamical model for the systematic error is available. In the latter case, the applicability is limited by a matrix rank condition which has to be satisfied in order for the filter to exist. The performance of the filter developed in this paper is limited by the availability and the accuracy of observations and by the variance of the stochastic model error component. The effect of these aspects on the estimation accuracy is investigated in several numerical experiments using the Lorenz (1996) model. Experimental results indicate that the availability of a dynamical model for the systematic error significantly reduces the variance of the model error estimates, but has only minor effect on the estimates of the system state. The filter is able to estimate additive model error of any type, provided that the rank condition is satisfied and that the stochastic errors and measurement errors are significantly smaller than the systematic errors. The results of this study are encouraging. However, it remains to be seen how the filter performs in more realistic applications.
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Varotsos, George K., Hector E. Nistazakis, Konstantinos Aidinis, Fadi Jaber, Mohd Nasor, and Kanhira Kadavath Mujeeb Rahman. "Error Performance Estimation of Modulated Retroreflective Transdermal Optical Wireless Links with Diversity under Generalized Pointing Errors." Telecom 2, no. 2 (2021): 167–80. http://dx.doi.org/10.3390/telecom2020011.

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Recent developments in both optical wireless communication (OWC) systems and implanted medical devices (IMDs) have introduced transdermal optical wireless (TOW) technology as a viable candidate for extremely high-speed in-body to out-of-body wireless data transmissions, which are growing in demand for many vital biomedical applications, including telemetry with medical implants, health monitoring, neural recording and prostheses. Nevertheless, this emerging communication modality is primarily hindered by skin-induced attenuation of the propagating signal bit carrier along with its stochastic misalignment-induced fading. Thus, by considering a typical modulated retroreflective (MRR) TOW system with spatial diversity and optimal combining (OC) for signal reception in this work, we focus, for the first time in the MRR TOW literature, on the stochastic nature of generalized pointing errors with non-zero boresight (NZB). Specifically, under these circumstances, novel analytical mathematical expressions were derived for the total average bit error rate (BER) of various system configurations. Their results revealed significant outage performance enhancements when spatial diversity was utilized. Moreover, taking into consideration the total transdermal pathloss along with the effects of stochastic NZB pointing errors, the critical average signal-to-noise ratio (SNR) metric was evaluated for typical power spectral-density values.
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Lim, Chot Hun, Tien Sze Lim, and Voon Chet Koo. "Stochastic Error Modeling of MEMS Inertial Sensor with Implementation to GPS-Aided INU System for UAV Motion Sensing." Applied Mechanics and Materials 464 (November 2013): 240–46. http://dx.doi.org/10.4028/www.scientific.net/amm.464.240.

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The resided stochastic error in Micro-Electro-Mechanical-System (MEMS) Strapdown Inertial Navigation Unit (INU) had caused the instrument not being able to operate as a standalone device for navigation applications. The conventional Global Positioning System (GPS)-aided strapdown INU system is commonly adopted to tackle such issue. Note that the estimation accuracy of such system depends on how precise the modeling of the stochastic error. In this paper, a comprehensive stochastic error modeling through three distinct approaches, namely the Gauss-Markov (GM) modeling, the Allan Variance (AV) analysis, and the Autoregressive (AR) modeling, are presented. The analysis shows that AR model achieved better modeling accuracy than the other two approaches. Next, the modeled stochastic errors were implemented on a GPS-aided strapdown INU system for UAV airplane's motion sensing, and the results shown that AR model achieved lower RMSE than the GM model, indicating that AR model is more suitable than GM model in representing the stochastic error model of MEMS strapdown INU.
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Xia, Yu, Jing Chen, Jun Du, Xiefei Zhi, Jingzhuo Wang, and Xiaoli Li. "A Unified Scheme of Stochastic Physics and Bias Correction in an Ensemble Model to Reduce Both Random and Systematic Errors." Weather and Forecasting 34, no. 6 (2019): 1675–91. http://dx.doi.org/10.1175/waf-d-19-0032.1.

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Abstract This study experimented with a unified scheme of stochastic physics and bias correction within a regional ensemble model [Global and Regional Assimilation and Prediction System–Regional Ensemble Prediction System (GRAPES-REPS)]. It is intended to improve ensemble prediction skill by reducing both random and systematic errors at the same time. Three experiments were performed on top of GRAPES-REPS. The first experiment adds only the stochastic physics. The second experiment adds only the bias correction scheme. The third experiment adds both the stochastic physics and bias correction. The experimental period is one month from 1 to 31 July 2015 over the China domain. Using 850-hPa temperature as an example, the study reveals the following: 1) the stochastic physics can effectively increase the ensemble spread, while the bias correction cannot. Therefore, ensemble averaging of the stochastic physics runs can reduce more random error than the bias correction runs. 2) Bias correction can significantly reduce systematic error, while the stochastic physics cannot. As a result, the bias correction greatly improved the quality of ensemble mean forecasts but the stochastic physics did not. 3) The unified scheme can greatly reduce both random and systematic errors at the same time and performed the best of the three experiments. These results were further confirmed by verification of the ensemble mean, spread, and probabilistic forecasts of many other atmospheric fields for both upper air and the surface, including precipitation. Based on this study, we recommend that operational numerical weather prediction centers adopt this unified scheme approach in ensemble models to achieve the best forecasts.
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Wong, Raymond K. W., and Norman Chidambaram. "Gamma Size Distribution and Stochastic Sampling Errors." Journal of Climate and Applied Meteorology 24, no. 6 (1985): 568–79. http://dx.doi.org/10.1175/1520-0450(1985)024<0568:gsdass>2.0.co;2.

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Chan, David, Robert Kohn, and Chris Kirby. "Multivariate Stochastic Volatility Models with Correlated Errors." Econometric Reviews 25, no. 2-3 (2006): 245–74. http://dx.doi.org/10.1080/07474930600713309.

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Reilman, Miriam A., Richard F. Gunst, and Mani Y. Lakshminarayanan. "Stochastic Regression with Errors in Both Variables." Journal of Quality Technology 18, no. 3 (1986): 162–69. http://dx.doi.org/10.1080/00224065.1986.11979004.

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Ting, Paishun, and John P. Hayes. "Removing constant‐induced errors in stochastic circuits." IET Computers & Digital Techniques 13, no. 3 (2019): 187–97. http://dx.doi.org/10.1049/iet-cdt.2018.5017.

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RAPP, P. E., T. A. A. WATANABE, P. FAURE, and C. J. CELLUCCI. "NONLINEAR SIGNAL CLASSIFICATION." International Journal of Bifurcation and Chaos 12, no. 06 (2002): 1273–93. http://dx.doi.org/10.1142/s021812740200508x.

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In this contribution, we show that the incorporation of nonlinear dynamical measures into a multivariate discrimination provides a signal classification system that is robust to additive noise. The signal library was composed of nine groups of signals. Four groups were generated computationally from deterministic systems (van der Pol, Lorenz, Rössler and Hénon). Four groups were generated computationally from different stochastic systems. The ninth group contained inter-decay interval sequences from radioactive cobalt. Two classification criteria (minimum Mahalanobis distance and maximum Bayesian likelihood) were tested. In the absence of additive noise, no errors occurred in a within-library classification. Normally distributed random numbers were added to produce signal to noise ratios of 10, 5 and 0 dB. When the minimum Mahalanobis distance was used as the classification criterion, the corresponding error rates were 2.2%, 4.4% and 20% (Expected Error Rate = 89%). When Bayesian maximum likelihood was the criterion, the error rates were 1.1%, 4.4% and 21% respectively. Using nonlinear measures an effective discrimination can be achieved in cases where spectral measures are known to fail. Most classification errors occurred at low signal to noise ratios when a stochastic signal was misclassified into a different group of stochastic signals. When the within-library classification exercise is limited to the four groups of deterministic signals, no classification errors occurred with clean data, at SNR = 10 dB, or at SNR = 5 dB. A single classification error (Observed Error Rate = 2.5%, Expected Error Rate = 75%) occurred with both classification criteria at SNR = 0 dB.
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30

Guan, Hua, and De Wei Chen. "Stochastic Analysis of Prestressed Concrete Cable-Stayed Bridges Considering Construction Errors." Advanced Materials Research 255-260 (May 2011): 1023–28. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.1023.

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There is a deviation between finished bridge and design requirement of prestressed concrete (PC) cable-stayed bridge due to the construction errors in construction process. Besides, the randomness of construction errors will cause the variability of structure system in construction state. However, the most common analyses considering construction errors are based on deterministic analysis method, which concern the mean errors effect merely. These are inadequate obviously. In this paper the main construction errors of PC cable-stayed bridge and corresponding distributions are outlined firstly. Also several common stochastic analysis methods are introduced. Using Monte-Carlo method with ANSYS finite element analysis (FEA) software, then, a stochastic analysis of a single tower PC cable-stayed bridge considering construction errors is completed, and the probability characteristics of structural response under dead load are obtained. Finally, from the reliability point of view, the influence of randomness of construction errors on structural safety and the necessity of stochastic analysis for PC cable-stayed bridges are discussed.
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31

Afifah, Salma Inayatul, and Suwanda. "Analisis Pengukuran Tingkat Efisiensi Perusahaan Menggunakan Metode Stochastic Frontier Analysis (SFA)." Bandung Conference Series: Statistics 3, no. 2 (2023): 459–65. http://dx.doi.org/10.29313/bcss.v3i2.8369.

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Abstract. The stochastic frontier has two error components, namely errors originating from random errors and errors originating from other factors than can be controlled, namely inefficiency errors. The Stochastic Frontier Analysis model is an extension of the deterministic frontier model developed by Aigner and Chu (1968) in Coelli et al (1998). Stochastic Frontier Analysis (SFA) is one of the best known techniques for determining efficiency. So to overcome the level of efficiency of a company researchers will use the stochastic frontier with the Cobb-Douglas production function model. The profit function (profit) is a two-way approach, and is often used to measure the level of production efficiency. Measuring the level of production efficiency, both technical and allocative efficiency, using the commonly used profit function is only relative. This study aims to rank the level of efficiency of companies in Indonesia. The results of the research based on 10 life insurance companies in Indonesia in 2017-2021 can use the application of the stochastic frontier analysis model of the Cobb-Douglas function. And for the value of the highest efficiency level obtained by PT. Sequis Financial with a value of 0.9996, and for the lowest efficiency value obtained by PT. Sequis Financial with an efficient value of 0.0845.&#x0D; Abstrak. Stochastic frontier memiliki dua komponen galat yaitu galat yang berasal dari kesalahan acak dan galat yang berasal dari faktor-faktor lain ang bisa dikendalikan yaitu galat inefisiensi. Model Stochastic Frontier Analysis merupakan perkembangan dari model deterministic frontier yang dikembangkan oleh Aigner dan Chu (1968) dalam Coelli et al (1998). Stochastic Frontier Analysis (SFA) adalah salah satu teknik yang paling dikenal untuk menentukan efisiensi. Maka untuk menanggulangi tingkat efisiensi suatu perusahaan peneliti akan menggunakan stochastic frontier dengan model fungsi produksi cobb-douglas. Fungsi keuntungan (profit) merupakan pendekatan dua arah, dan sering digunakan untuk mengukur tingkat efisiensi produksi. Mengukur tingkat efisiensi produksi, baik efisiensi teknis maupun alokatif, dengan menggunakan fungsi profit yang umum digunakan hanya bersifat relative. Penelitian ini bertujuan untuk mengurutkan tingkat efisiensi perusahaan di Indonesia. Hasil penelitian berdasarkan dari 10 perusahaan asuransi jiwa di Indonesia pada tahun 2017-2021 dapat menggunakan penerapan model stochastic frontier analysis fungsi cobb-douglas. Dan untuk nilai tingkat efisiensi tertinggi didapatkan oleh PT. Sequis Financial dengan nilai 0.9996, dan untuk nilai efisiensi terendah didapatkan oleh PT. Sequis Financial dengan nilai efisien 0.0845.
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32

Zhao, Yan, Jing Zhang, Gaoge Hu, and Yongmin Zhong. "Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty." Sensors 20, no. 3 (2020): 627. http://dx.doi.org/10.3390/s20030627.

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This paper presents a new set-membership based hybrid Kalman filter (SM-HKF) by combining the Kalman filtering (KF) framework with the set-membership concept for nonlinear state estimation under systematic uncertainty consisted of both stochastic error and unknown but bounded (UBB) error. Upon the linearization of the nonlinear system model via a Taylor series expansion, this method introduces a new UBB error term by combining the linearization error with systematic UBB error through the Minkowski sum. Subsequently, an optimal Kalman gain is derived to minimize the mean squared error of the state estimate in the KF framework by taking both stochastic and UBB errors into account. The proposed SM-HKF handles the systematic UBB error, stochastic error as well as the linearization error simultaneously, thus overcoming the limitations of the extended Kalman filter (EKF). The effectiveness and superiority of the proposed SM-HKF have been verified through simulations and comparison analysis with EKF. It is shown that the SM-HKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.
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33

Lewy, P., and A. Nielsen. "Modelling stochastic fish stock dynamics using Markov Chain Monte Carlo." ICES Journal of Marine Science 60, no. 4 (2003): 743–52. http://dx.doi.org/10.1016/s1054-3139(03)00080-8.

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Abstract A new age-structured stock dynamics approach including stochastic survival and recruitment processes is developed and implemented. The model is able to analyse detailed sources of information used in standard age-based fish stock assessment such as catch-at-age and effort data from commercial fleets and research surveys. The stock numbers are treated as unobserved variables subject to process errors while the catches are observed variables subject to both sampling and process errors. Results obtained for North Sea plaice using Markov Chain Monte Carlo methods indicate that the process error by far accounts for most of the variation compared to sampling error. Comparison with results from a simpler separable model indicates that the new model provides more precise estimates with fewer parameters.
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34

Goldrick, Matthew, and Robert Daland. "Linking speech errors and phonological grammars: insights from Harmonic Grammar networks." Phonology 26, no. 1 (2009): 147–85. http://dx.doi.org/10.1017/s0952675709001742.

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AbstractPhonological grammars characterise distinctions between relatively well-formed (unmarked) and relatively ill-formed (marked) phonological structures. We review evidence that markedness influences speech-error probabilities. Specifically, although errors result in unmarked as well as marked structures, there is a markedness asymmetry: errors are more likely to produce unmarked outcomes. We show that stochastic disruption to the computational mechanisms realising a Harmonic Grammar (HG) can account for the broad empirical patterns of speech errors. We demonstrate that our proposal can account for the general markedness asymmetry. We also develop methods for linking particular HG proposals to speech-error distributions, and illustrate these methods using a simple HG and a set of initial consonant errors in English.
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35

Cheng, Qiang, Qiunan Feng, Zhifeng Liu, Peihua Gu, and Ligang Cai. "Fluctuation prediction of machining accuracy for multi-axis machine tool based on stochastic process theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 14 (2014): 2534–50. http://dx.doi.org/10.1177/0954406214562633.

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Geometric error has significant influence on the processing results and reduces machining accuracy. Machine tool geometric errors can be interpreted as a deterministic value with an uncertain fluctuation of probabilistic distribution. Although, the uncertain fluctuation can not be compensated, it has extremely profound significance on the precision and ultra-precision machining to reduce the fluctuation range of machining accuracy as far as possible. In this paper, a typical 3-axis machine tool with high precision is selected and the fluctuations in machining accuracy are studied. The volumetric error modeling of machine tool is established by multi-body system (MBS) theory, which describes the topological structure of MBS in a simple and convenient matrix form. Based on the volumetric error model, the equivalent components of the errors for the three axes are established by reducing error terms. Then, the fluctuations of equivalent errors and the machining accuracy in working planes are depicted and predicted using the theory of stochastic process, whose range should be controlled within a certain confidence interval. Furthermore, the critical geometric errors that have significant influence on the machining accuracy fluctuation are identified. Based on the analysis results, some improvement in the machine tool parts introduced and the results for the modified machine show that the prediction allow for reduction in errors for the precision and ultra-precision machining.
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36

Pellissetti, Manuel, and Roger Ghanem. "A Method for the Validation of Predictive Computations Using a Stochastic Approach." Journal of Offshore Mechanics and Arctic Engineering 126, no. 3 (2004): 227–34. http://dx.doi.org/10.1115/1.1782915.

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Stochastic finite element methods provide predictions of the behavior of mechanical systems with randomly fluctuating material properties. Limited data is typically available for the characterization of these properties, introducing errors in their representation. In the present paper, the sensitivity of the response predictions with respect to the stochastic properties is analyzed, by means of the direct differentiation method (DDM). Explicit expressions for the dependence of certain statistics of the response on the statistics of the material property are obtained. The response sensitivities are then used to estimate the error in the response predictions, caused by the error in the representation of the stochastic property. Numerical results for a simple Bernoulli beam are presented.
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37

Li, Yang, Qianhai Xu, Yifei Xin, and Yu Zhang. "New Order 2.0 Simplified Weak Itô–Taylor Symmetrical Scheme for Stochastic Delay Differential Equations." Symmetry 16, no. 6 (2024): 685. http://dx.doi.org/10.3390/sym16060685.

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In this article, we construct a new order 2.0 simplified weak Itô–Taylor symmetrical scheme for stochastic delay differential equations. By the new local weak convergence lemma and the connection inequality, we theoretically prove the global weak convergence theorem in two parts on the basis of Malliavin stochastic analysis. Meanwhile, numerical examples are presented to illustrate the error and convergence results. Furthermore, the obtained results display the influence of the delay coefficient on global errors.
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38

Clark, Todd E., Michael W. McCracken, and Elmar Mertens. "Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors." Review of Economics and Statistics 102, no. 1 (2020): 17–33. http://dx.doi.org/10.1162/rest_a_00809.

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We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to simple variance approaches, our stochastic volatility model improves the accuracy of uncertainty measures for survey forecasts.
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39

Vannitsem, Stéphane. "Stochastic modelling and predictability: analysis of a low-order coupled ocean–atmosphere model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2018 (2014): 20130282. http://dx.doi.org/10.1098/rsta.2013.0282.

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There is a growing interest in developing stochastic schemes for the description of processes that are poorly represented in atmospheric and climate models, in order to increase their variability and reduce the impact of model errors. The use of such noise could however have adverse effects by modifying in undesired ways a certain number of moments of their probability distributions. In this work, the impact of developing a stochastic scheme (based on stochastic averaging) for the ocean is explored in the context of a low-order coupled (deterministic) ocean–atmosphere system. After briefly analysing its variability, its ability in predicting the oceanic flow generated by the coupled system is investigated. Different phases in the error dynamics are found: for short lead times, an initial overdispersion of the ensemble forecast is present while the ensemble mean follows a dynamics reminiscent of the combined amplification of initial condition and model errors for deterministic systems; for longer lead times, a reliable diffusive ensemble spread is observed. These different phases are also found for ensemble-oriented skill measures like the Brier score and the rank histogram. The implications of these features on building stochastic models are then briefly discussed.
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40

Zhong, Shaopeng, Lihui Zhang, and Max Bushell. "Reliability-Based Marginal Cost Pricing Problem Case with Both Demand Uncertainty and Travelers’ Perception Errors." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/695307.

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Focusing on the first-best marginal cost pricing (MCP) in a stochastic network with both travel demand uncertainty and stochastic perception errors within the travelers’ route choice decision processes, this paper develops a perceived risk-based stochastic network marginal cost pricing (PRSN-MCP) model. Numerical examples based on an integrated method combining the moment analysis approach, the fitting distribution method, and the reliability measures are also provided to demonstrate the importance and properties of the proposed model. The main finding is that ignoring the effect of travel time reliability and travelers’ perception errors may significantly reduce the performance of the first-best MCP tolls, especially under high travelers’ confidence and network congestion levels. The analysis result could also enhance our understanding of (1) the effect of stochastic perception error (SPE) on the perceived travel time distribution and the components of road toll; (2) the effect of road toll on the actual travel time distribution and its reliability measures; (3) the effect of road toll on the total network travel time distribution and its statistics; and (4) the effect of travel demand level and the value of reliability (VoR) level on the components of road toll.
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41

Wu, Zhifeng, Bin Huang, Kong Fah Tee, and Weidong Zhang. "A Novel Stochastic Approach for Static Damage Identification of Beam Structures Using Homotopy Analysis Algorithm." Sensors 21, no. 7 (2021): 2366. http://dx.doi.org/10.3390/s21072366.

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This paper proposes a new damage identification approach for beam structures with stochastic parameters based on uncertain static measurement data. This new approach considers not only the static measurement errors, but also the modelling error of the initial beam structures as random quantities, and can also address static damage identification problems with relatively large uncertainties. First, the stochastic damage identification equations with respect to the damage indexes were established. On this basis, a new homotopy analysis algorithm was used to solve the stochastic damage identification equations. During the process of solution, a static condensation technique and a L1 regularization method were employed to address the limited measurement data and ill-posed problems, respectively. Furthermore, the definition of damage probability index is presented to evaluate the possibility of existing damages. The results of two numerical examples show that the accuracy and efficiency of the proposed damage identification approach are good. In comparison to the first-order perturbation method, the proposed method can ensure better accuracy in damage identification with relatively large measurement errors and modelling error. Finally, according to the static tests of a simply supported concrete beam, the proposed method successfully identified the damage of the beam.
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42

Jacobs, C. S., and O. J. Sovers. "An Assessment of the Accuracy of the Deep Space Network Extragalactic Reference Frame." Symposium - International Astronomical Union 156 (1993): 173–78. http://dx.doi.org/10.1017/s0074180900173152.

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The Deep Space Network (DSN) Radio Reference Frame consists of a catalog of angular positions for 281 extragalactic radio sources based on VLBI measurements made during the period from 1978 to 1992. A realistic assessment of the accuracy of these source position estimates must consider both modeled stochastic errors and systematic model deficiencies. Modeled stochastic errors include thermal noise (signal-to-noise ratio) and fluctuations in tropospheric refractivity due to the changing distribution of water vapor. These modeled errors result in a median formal position uncertainty of ≈0.3 milliarcseconds (mas). In particular, we examine the effect of changing the model for inter-observation correlations of water vapor fluctuations on estimated parameters. Next, a comparison of our radio source positions with independently determined positions is presented as evidence of systematic errors at ≤ 0.5 mas. We discuss several aspects of VLBI model accuracy focussing on tidal effects, antenna thermal expansion, pressure loading, source structure, precession and nutation. Prospects for reducing these errors are also discussed. We conclude by combining these estimates of modeled stochastic errors and systematic errors into an overall assessment of &lt; 1.0 mas for the current accuracy of the DSN extragalactic radio frame.
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43

Green, Amy C., Chris Kilsby, and András Bárdossy. "Assessing rainfall radar errors with an inverse stochastic modelling framework." Hydrology and Earth System Sciences 28, no. 20 (2024): 4539–58. http://dx.doi.org/10.5194/hess-28-4539-2024.

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Abstract. Weather radar is a crucial tool for rainfall observation and forecasting, providing high-resolution estimates in both space and time. Despite this, radar rainfall estimates are subject to many error sources – including attenuation, ground clutter, beam blockage and drop-size distribution – with the true rainfall field unknown. A flexible stochastic model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard weather radar processing methods and imposing path-integrated attenuation effects, a stochastic drop-size-distribution field, and sampling and random errors. This can provide realistic weather radar images, of which we know the true rainfall field and the corrected “best-guess” rainfall field which would be obtained if they were observed in a real-world case. The structure of these errors is then investigated, with a focus on the frequency and behaviour of “rainfall shadows”. Half of the simulated weather radar images have at least 3 % of their significant rainfall rates shadowed, and 25 % have at least 45 km2 containing rainfall shadows, resulting in underestimation of the potential impacts of flooding. A model framework for investigating the behaviour of errors relating to the radar rainfall estimation process is demonstrated, with the flexible and efficient tool performing well in generating realistic weather radar images visually for a large range of event types.
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44

Hoteit, I., D. T. Pham, M. E. Gharamti, and X. Luo. "Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF." Monthly Weather Review 143, no. 7 (2015): 2918–36. http://dx.doi.org/10.1175/mwr-d-14-00088.1.

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Abstract The stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of the observational error covariance, which is often the case in real oceanic and atmospheric data assimilation applications. This work introduces an efficient serial scheme to mitigate the impact of observations’ perturbations sampling in the analysis step of the EnKF, which should provide more accurate ensemble estimates of the analysis error covariance matrices. The new scheme is simple to implement within the serial EnKF algorithm, requiring only the approximation of the EnKF sample forecast error covariance matrix by a matrix with one rank less. The new EnKF scheme is implemented and tested with the Lorenz-96 model. Results from numerical experiments are conducted to compare its performance with the EnKF and two standard deterministic EnKFs. This study shows that the new scheme enhances the behavior of the EnKF and may lead to better performance than the deterministic EnKFs even when implemented with relatively small ensembles.
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45

HANSEN, LARS PETER, and RAVI JAGANNATHAN. "Assessing Specification Errors in Stochastic Discount Factor Models." Journal of Finance 52, no. 2 (1997): 557–90. http://dx.doi.org/10.1111/j.1540-6261.1997.tb04813.x.

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46

Bernal, D. "Analytical minimization of synchronicity errors in stochastic identification." Mechanical Systems and Signal Processing 98 (January 2018): 415–24. http://dx.doi.org/10.1016/j.ymssp.2017.04.043.

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47

Fluck, Manuel, and Curran Crawford. "Minimizing errors in interpolated discrete stochastic wind fields." Journal of Wind Engineering and Industrial Aerodynamics 152 (May 2016): 15–22. http://dx.doi.org/10.1016/j.jweia.2016.02.007.

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48

Zhu, Yunmin. "STOCHASTIC APPROXIMATION UNDER A CLASS OF MEASUREMENT ERRORS." Acta Mathematica Scientia 5, no. 1 (1985): 105–17. http://dx.doi.org/10.1016/s0252-9602(18)30694-5.

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49

Tsyrulnikov, M. D. "Stochastic modelling of model errors: A simulation study." Quarterly Journal of the Royal Meteorological Society 131, no. 613 (2005): 3345–71. http://dx.doi.org/10.1256/qj.05.19.

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50

Tamazin, M., A. Noureldin, and M. J. Korenberg. "Robust Modeling of Low-Cost MEMS Sensor Errors in Mobile Devices Using Fast Orthogonal Search." Journal of Sensors 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/101820.

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Accessibility to inertial navigation systems (INS) has been severely limited by cost in the past. The introduction of low-cost microelectromechanical system-based INS to be integrated with GPS in order to provide a reliable positioning solution has provided more wide spread use in mobile devices. The random errors of the MEMS inertial sensors may deteriorate the overall system accuracy in mobile devices. These errors are modeled stochastically and are included in the error model of the estimated techniques used such as Kalman filter or Particle filter. First-order Gauss-Markov model is usually used to describe the stochastic nature of these errors. However, if the autocorrelation sequences of these random components are examined, it can be determined that first-order Gauss-Markov model is not adequate to describe such stochastic behavior. A robust modeling technique based on fast orthogonal search is introduced to remove MEMS-based inertial sensor errors inside mobile devices that are used for several location-based services. The proposed method is applied to MEMS-based gyroscopes and accelerometers. Results show that the proposed method models low-cost MEMS sensors errors with no need for denoising techniques and using smaller model order and less computation, outperforming traditional methods by two orders of magnitude.
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