The Kalman filter based recursive algorithm: windup and its avoidance

2001 ◽  
Author(s):  
Liyu Cao ◽  
H.M. Schwartz
Keyword(s):  
Kalman Filter ◽  
Recursive Algorithm

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

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.

Kalman Filter Algorithm for Adaptive Digital Predistortion

2013 ◽  
Vol 347-350 ◽  
pp. 2385-2389
Author(s):  
Xiao Wei Kong ◽  
Jin Zheng Li ◽  
Wei Xia ◽  
Zi Shu He
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
State Space ◽  
Recursive Algorithm ◽  
Digital Predistortion ◽  
Parameters Extraction ◽  
Kalman Filter Algorithm ◽  
Digital Predistorter ◽  
Space Equation ◽  
Accuracy And Stability

This paper introduces a recursive algorithm of Kalman filter for digital predistorter parameters extraction based on memory polynomials predistorter model. The predistorter model is firstly formulated as linear regression expression. Then we derive the state-space equation of the model and attain the steps of the algorithm. Finally, the accuracy and stability of the algorithm is proved by simulation.

scholarly journals Assessment of bias-adjusted PM<sub>2.5</sub> air quality forecasts over the continental United States during 2007

2009 ◽  
Vol 2 (2) ◽  
pp. 1375-1406 ◽  
Author(s):  
D. Kang ◽  
R. Mathur ◽  
S. Trivikrama Rao
Keyword(s):  
United States ◽  
Kalman Filter ◽  
Air Quality ◽  
Recursive Algorithm ◽  
Warm Season ◽  
Correlation Coefficients ◽  
Rocky Mountain ◽  
Meteorological Model ◽  
Bias Adjustment ◽  
Air Quality Forecast

Abstract. To develop fine particular matter (PM2.5) air quality forecasts, a National Air Quality Forecast Capability (NAQFC) system, which linked NOAA's North American Mesoscale (NAM) meteorological model with EPA's Community Multiscale Air Quality (CMAQ) model, was deployed in the developmental mode over the continental United States during 2007. This study investigates the operational use of a bias-adjustment technique called the Kalman Filter Predictor approach for improving the accuracy of the PM2.5 forecasts at monitoring locations. The Kalman Filter Predictor bias-adjustment technique is a recursive algorithm designed to optimally estimate bias-adjustment terms using the information extracted from previous measurements and forecasts. The bias-adjustment technique is found to improve PM2.5 forecasts (i.e. reduced errors and increased correlation coefficients) for the entire year at almost all locations. The NAQFC tends to overestimate PM2.5 during the cool season and underestimate during the warm season in the eastern part of the continental US domain, but the opposite is true for the pacific coast. In the Rocky Mountain region, the NAQFC system overestimates PM2.5 for the whole year. The bias-adjustment forecasts can quickly (after 2–3 days' lag) adjust to reflect the transition from one regime to the other. The modest computational requirements and systematical improvements in forecast results across all seasons suggest that this technique can be easily adapted to perform bias-adjustment for real-time PM2.5 air quality forecasts.

Prediction of Track Geometry Status Based on Gray Forecast-Kalman Filter Analysis

2011 ◽  
Author(s):  
Chaolong Jia ◽  
Weixiang Xu ◽  
Hanning Wang
Keyword(s):  
Kalman Filter ◽  
Prediction Model ◽  
Recursive Algorithm ◽  
Status Change ◽  
Track Geometry ◽  
Real Change ◽  
The Status ◽  
Change Tendency ◽  
Filter Analysis ◽  
Track Status

Excellent condition of track geometry status is the foundation to ensure train travel security. The detection data of track inspection car contains many valuable features of the track status. The technique of gray forecast and Kalman filtering can be used to investigate the problem and predict the status change of the track geometry. In this paper, gray forecast is used in qualitative analysis of track geometry status changes, and we predict the development of track geometry status change using the Kalman filter prediction model and specific recursive algorithm, established prediction model of the track geometry to make an emulation experiment to analyze the data that track inspection car has detected, and predict changing trends of track geometry the state. Experiment results show that the application model of improved Kalman filter to predict the track geometry status changes gets a higher accuracy, and it can reflect the real change tendency of the track status.

scholarly journals Assessment of bias-adjusted PM<sub>2.5</sub> air quality forecasts over the continental United States during 2007

2010 ◽  
Vol 3 (1) ◽  
pp. 309-320 ◽  
Author(s):  
D. Kang ◽  
R. Mathur ◽  
S. Trivikrama Rao
Keyword(s):  
United States ◽  
Kalman Filter ◽  
Air Quality ◽  
Recursive Algorithm ◽  
Fine Particulate Matter ◽  
Warm Season ◽  
Correlation Coefficients ◽  
Meteorological Model ◽  
Bias Adjustment ◽  
Air Quality Forecast

Abstract. To develop fine particulate matter (PM2.5) air quality forecasts for the US, a National Air Quality Forecast Capability (NAQFC) system, which linked NOAA's North American Mesoscale (NAM) meteorological model with EPA's Community Multiscale Air Quality (CMAQ) model, was deployed in the developmental mode over the continental United States during 2007. This study investigates the operational use of a bias-adjustment technique called the Kalman Filter Predictor approach for improving the accuracy of the PM2.5 forecasts at monitoring locations. The Kalman Filter Predictor bias-adjustment technique is a recursive algorithm designed to optimally estimate bias-adjustment terms using the information extracted from previous measurements and forecasts. The bias-adjustment technique is found to improve PM2.5 forecasts (i.e. reduced errors and increased correlation coefficients) for the entire year at almost all locations. The NAQFC tends to overestimate PM2.5 during the cool season and underestimate during the warm season in the eastern part of the continental US domain, but the opposite is true for the Pacific Coast. In the Rocky Mountain region, the NAQFC system overestimates PM2.5 for the whole year. The bias-adjusted forecasts can quickly (after 2–3 days' lag) adjust to reflect the transition from one regime to the other. The modest computational requirements and systematic improvements in forecast outputs across all seasons suggest that this technique can be easily adapted to perform bias adjustment for real-time PM2.5 air quality forecasts.

scholarly journals Ground-level ozone concentration over Spain: an application of Kalman Filter post-processing to reduce model uncertainties

2011 ◽  
Vol 4 (1) ◽  
pp. 343-384 ◽  
Author(s):  
V. Sicardi ◽  
J. Ortiz ◽  
A. Rincón ◽  
O. Jorba ◽  
M. T. Pay ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Recursive Algorithm ◽  
Ground Level ◽  
Accurate Estimate ◽  
Post Processing ◽  
Bias Adjustment ◽  
Ground Level Ozone ◽  
Gross Error ◽  
Suitable Technique ◽  
Modelling System

Abstract. The CALIOPE air quality modelling system, namely WRF-ARW/HERMES-EMEP/CMAQ/BSC-DREAM8b, has been used to perform the simulation of ground level O3 concentration for the year 2004, over the Iberian Peninsula. We use this system to study the daily ground-level O3 maximum. We investigate the use of a post-processing such as the Kalman Filter bias-adjustment technique to improve the simulated O3 maximum. The Kalman Filter bias-adjustment technique is a recursive algorithm to optimally estimate bias-adjustment terms from previous measurements and model results. The bias-adjustment technique is found to improve the simulated O3 maximum for the entire year and the whole domain. The corrected simulation presents improvements in statistical indicators such as correlation, root mean square error, mean bias, standard deviation, and gross error. After the post-processing the exceedances of O3 concentration limits, as established by the European Directive 2008/50/CE, are better reproduced and the uncertainty of the modelling system is reduced from 20% to 7.5%. Such uncertainty in the model results is under the established EU limit of the 50%. Significant improvements in the O3 average daily cycle and in its amplitude are also observed after the post-processing. The systematic improvements in the O3 maximum simulations suggest that the Kalman Filter post-processing method is a suitable technique to reproduce accurate estimate of ground-level O3 concentration.

scholarly journals An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 240
Author(s):  
Cristian Busu ◽  
Mihail Busu
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Kalman Filter ◽  
Loss Function ◽  
Kalman Filtering ◽  
Kinetic Models ◽  
Applied Mathematics ◽  
Recursive Algorithm ◽  
Linear Quadratic ◽  
Symmetric Loss

Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

Spacecraft attitude estimation based on matrix Kalman filter and recursive cubature Kalman filter

2017 ◽  
Vol 232 (16) ◽  
pp. 3024-3033
Author(s):  
Tao Zhang ◽  
Xiang Xu ◽  
Zhicheng Wang
Keyword(s):  
Kalman Filter ◽  
Recursive Algorithm ◽  
Estimation Method ◽  
Attitude Estimation ◽  
Previous Method ◽  
Spacecraft Attitude ◽  
Original Matrix ◽  
Cubature Kalman Filter ◽  
The Matrix ◽  
Gyro Drift

An interlaced matrix Kalman filter, which is based on vector observations and gyro measurements, is proposed for spacecraft attitude estimation in this paper. It combines the matrix Kalman filter and cubature Kalman filter to estimate spacecraft attitude and gyro drift bias, respectively. The defects of the original matrix Kalman filter, which could only estimate the attitude parameters of spacecraft, are addressed by the proposed interlaced matrix Kalman filter. In addition, the dimensions of cubature Kalman filter for conventional attitude estimation method are reduced by the designed recursive algorithm. It is noted that the two filters are not independent with each other. Firstly, the attitude quaternion of spacecraft is estimated by the modified matrix Kalman filter. Then, the estimated quaternion is input for the recursive cubature Kalman filter, which is used to estimate the gyro drift bias. Finally, the estimated gyro drift bias is compensated for the measurements of the gyros. Therefore, the precision of the estimated attitude of spacecraft is improved by the interacting process of the modified matrix Kalman filter and recursive cubature Kalman filter. A simulation test is designed to verify the advantage of the proposed method by comparing with the previous method, and the results indicate that the proposed algorithm has better performance on convergence rate and stability.

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