scholarly journals A generalized Kalman filter with its precision in recursive form when the stochastic model is misspecified

2021 ◽  
Vol 95 (9) ◽  
Author(s):  
P. J. G. Teunissen ◽  
A. Khodabandeh ◽  
D. Psychas
Keyword(s):  
Quality Control ◽  
Kalman Filter ◽  
Stochastic Model ◽  
Dynamic Model ◽  
State Vector ◽  
Error Variance ◽  
Precision Analysis ◽  
Actual Error ◽  
Generalized Kalman Filter

AbstractIn this contribution, we introduce a generalized Kalman filter with precision in recursive form when the stochastic model is misspecified. The filter allows for a relaxed dynamic model in which not all state vector elements are connected in time. The filter is equipped with a recursion of the actual error-variance matrices so as to provide an easy-to-use tool for the efficient and rigorous precision analysis of the filter in case the underlying stochastic model is misspecified. Different mechanizations of the filter are presented, including a generalization of the concept of predicted residuals as needed for the recursive quality control of the filter.

Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

2011 ◽  
Vol 139 (6) ◽  
pp. 2008-2024 ◽  
Author(s):  
Brian C. Ancell ◽  
Clifford F. Mass ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Complex Terrain ◽  
Error Variance ◽  
Small Scale ◽  
Observation Error ◽  
Grid Spacing ◽  
Background Error

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

scholarly journals Assimilation of GOSAT Methane in the Hemispheric CMAQ; Part II: Results Using Optimal Error Statistics

2022 ◽  
Vol 14 (2) ◽  
pp. 375
Author(s):  
Sina Voshtani ◽  
Richard Ménard ◽  
Thomas W. Walker ◽  
Amir Hakami
Keyword(s):  
Kalman Filter ◽  
Cross Validation ◽  
Error Variance ◽  
Error Statistics ◽  
Optimal Error ◽  
Meaningful Improvement ◽  
Aircraft Observations ◽  
Variance Parameters ◽  
Analysis Error ◽  
Or Modelling

We applied the parametric variance Kalman filter (PvKF) data assimilation designed in Part I of this two-part paper to GOSAT methane observations with the hemispheric version of CMAQ to obtain the methane field (i.e., optimized analysis) with its error variance. Although the Kalman filter computes error covariances, the optimality depends on how these covariances reflect the true error statistics. To achieve more accurate representation, we optimize the global variance parameters, including correlation length scales and observation errors, based on a cross-validation cost function. The model and the initial error are then estimated according to the normalized variance matching diagnostic, also to maintain a stable analysis error variance over time. The assimilation results in April 2010 are validated against independent surface and aircraft observations. The statistics of the comparison of the model and analysis show a meaningful improvement against all four types of available observations. Having the advantage of continuous assimilation, we showed that the analysis also aims at pursuing the temporal variation of independent measurements, as opposed to the model. Finally, the performance of the PvKF assimilation in capturing the spatial structure of bias and uncertainty reduction across the Northern Hemisphere is examined, indicating the capability of analysis in addressing those biases originated, whether from inaccurate emissions or modelling error.

Changing Income Risk across the US Skill Distribution: Evidence from a Generalized Kalman Filter

2021 ◽  
Author(s):  
J. Carter Braxton ◽  
Kyle Herkenhoff ◽  
Jonathan Rothbaum ◽  
Lawrence Schmidt
Keyword(s):  
Kalman Filter ◽  
Income Risk ◽  
The Us ◽  
Generalized Kalman Filter

scholarly journals Soc Estimation of the Lithium-Ion Battery Pack using a Sigma Point Kalman Filter Based on a Cell’s Second Order Dynamic Model

2020 ◽  
Vol 10 (5) ◽  
pp. 1896 ◽  
Author(s):  
Chi Nguyen Van ◽  
Thuy Nguyen Vinh
Keyword(s):  
Kalman Filter ◽  
Lithium Ion Battery ◽  
Dynamic Model ◽  
Dynamic Models ◽  
Lithium Ion ◽  
Second Order ◽  
Battery Pack ◽  
Sigma Point ◽  
Soc Estimation ◽  
Cell Modules

This paper deals with the state of charge (SoC) estimation of a lithium-ion battery pack (LiBP) connected by some cells in series and parallel. The voltage noise, noise and current bias of current through the LiBP are taken into account in the SoC estimation problem. In order to describe the cell dynamic more accurately, especially for practical applications with charge and discharge amplitude varying suddenly, in this paper we use the second dynamic order model of the cell to estimate the SoC of the LiBP. By applying the sigma point Kalman filter (SPKF), the average SoC of the pack and bias current of current measurement are estimated by first estimator; the second estimator estimates the SoC differences of the cell modules from average SoC of the pack. The SoC of the cell modules are the sum of average SoCs of the pack and the SoC differences. By only using two estimators, the calculation complexity for SoC estimation is more reduced; this is very useful for the LiBP, which has the number of cells connected in a large series. This method was applied for the pack of SAMSUNG ICR18650-22P connected by seven cell modules; the cell modules were connected by nine cells in parallel; the LiBP was charged and discharged with amplitude varying suddenly. The estimated SoC of seven cell modules is smaller than 2% for a temperature operating range typically −5 °C to 45 °C. The comparison of the accuracy of SoC estimation based on the first and the second order dynamic models is made; the result shows that the SoC estimation used the second order dynamic model is more exact.

Investigation of Ensemble Variance as a Measure of True Forecast Variance

2011 ◽  
Vol 139 (12) ◽  
pp. 3954-3963 ◽  
Author(s):  
Walter C. Kolczynski ◽  
David R. Stauffer ◽  
Sue Ellen Haupt ◽  
Naomi S. Altman ◽  
Aijun Deng
Keyword(s):  
Stochastic Model ◽  
Error Variance ◽  
Reliable Estimate ◽  
Ensemble Size ◽  
Adjustment Factor ◽  
Simple Method ◽  
Ensemble Data ◽  
Fair Comparison ◽  
Measure Of Uncertainty ◽  
The Ideal

Abstract The uncertainty in meteorological predictions is of interest for applications ranging from economic to recreational to public safety. One common method to estimate uncertainty is by using meteorological ensembles. These ensembles provide an easily quantifiable measure of the uncertainty in the forecast in the form of the ensemble variance. However, ensemble variance may not accurately reflect the actual uncertainty, so any measure of uncertainty derived from the ensemble should be calibrated to provide a more reliable estimate of the actual uncertainty in the forecast. A previous study introduced the linear variance calibration (LVC) as a simple method to determine the ensemble variance to error variance relationship and demonstrated this technique on real ensemble data. The LVC parameters, the slopes, and y intercepts, however, are generally different from the ideal values. This current study uses a stochastic model to examine the LVC in a controlled setting. The stochastic model is capable of simulating underdispersive and overdispersive ensembles as well as perfectly reliable ensembles. Because the underlying relationship is specified, LVC results can be compared to theoretical values of the slope and y intercept. Results indicate that all types of ensembles produce calibration slopes that are smaller than their theoretical values for ensemble sizes less than several hundred members, with corresponding y intercepts greater than their theoretical values. This indicates that all ensembles, even otherwise perfect ensembles, should be calibrated if the ensemble size is less than several hundred. In addition, it is shown that an adjustment factor can be computed for inadequate ensemble size. This adjustment factor is independent of the stochastic model and is applicable to any linear regression of error variance on ensemble variance. When applied to experiments using the stochastic model, the adjustment produces LVC parameters near their theoretical values for all ensemble sizes. Although the adjustment is unnecessary when applying LVC, it allows for a more accurate assessment of the reliability of ensembles, and a fair comparison of the reliability for differently sized ensembles.

Extracting Rolling Element Bearing Faults From Noisy Vibration Signal Using Kalman Filter

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Sidra Khanam ◽  
J. K. Dutt ◽  
N. Tandon
Keyword(s):  
Kalman Filter ◽  
Signal To Noise Ratio ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Vibration Signal ◽  
Error Variance ◽  
Rolling Element Bearing ◽  
Measured Signal ◽  
Process Noise ◽  
Bearing Faults

Vibration analysis has been widely accepted as a common and reliable method for bearing fault identification, however, the presence of noise in the measured signal poses the maximum amount of difficulty. Therefore, for the clearer detection of defect frequencies related to bearing faults, a denoising technique based on the Kalman filtering algorithm is presented in this paper. The Kalman filter yields a linear, unbiased, and minimum mean error variance recursive algorithm to optimally estimate the unknown states of a dynamic system from noisy data taken at discrete real time intervals. The dynamics of a rotor bearing system is presented through a linear model, where displacement and velocity vectors are chosen as states of the system. Process noise and measurement noise in the equations of motion take into account the modeling inaccuracies and vibration from other sources, respectively. The covariance matrix of the process noise has been obtained through the transfer function approach. The efficiency of the proposed technique is validated through experiments. Periodic noise and random noises obeying the white Gaussian, colored Gaussian and non-Gaussian distribution have been simulated and mixed with a clean experimental signal in order to study the efficiency of the standard Kalman filter under various noisy environments. Additionally, external vibrations to the test rig have been imparted through an electromechanical shaker. The results indicate an improvement in the signal to noise ratio, resulting in the clear identification of characteristic defect frequencies after passing the signal through the Kalman filter. The authors find that there is sufficient potential in using the Kalman filter as an effective tool to denoise the bearing vibration signal.

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