On the Performance Similarity Between Exponential Moving Average and Discrete Linear Kalman Filter

2019 ◽  
Author(s):  
Muhammad Fikri ◽  
Samiadji Herdjunanto ◽  
Adha Cahyadi
Keyword(s):  
Kalman Filter ◽  
Moving Average

Improved exponential weighted moving average based measurement noise estimation for strapdown inertial navigation system/doppler velocity log integrated system

2020 ◽  
pp. 1-21
Author(s):  
Lanhua Hou ◽  
Xiaosu Xu ◽  
Yiqing Yao ◽  
Di Wang ◽  
Jinwu Tong
Keyword(s):  
Kalman Filter ◽  
Inertial Navigation System ◽  
Moving Average ◽  
Integrated System ◽  
Measurement Noise ◽  
Noise Estimation ◽  
Doppler Velocity ◽  
Forgetting Factor ◽  
Exponential Weighted Moving Average ◽  
Weighted Moving Average

Abstract The strapdown inertial navigation system (SINS) with integrated Doppler velocity log (DVL) is widely utilised in underwater navigation. In the complex underwater environment, however, the DVL information may be corrupted, and as a result the accuracy of the Kalman filter in the SINS/DVL integrated system degrades. To solve this, an adaptive Kalman filter (AKF) with measurement noise estimator to provide noise statistical characteristics is generally applied. However, existing methods like moving windows (MW) and exponential weighted moving average (EWMA) cannot adapt to a dynamic environment, which results in unsatisfactory noise estimation performance. Moreover, the forgetting factor has to be determined empirically. Therefore, this paper proposes an improved EWMA (IEWMA) method with adaptive forgetting factor for measurement noise estimation. First, the model for a SINS/DVL integrated system is established, then the MW and EWMA based measurement noise estimators are illustrated. Subsequently, the proposed IEWMA method which is adaptive to the various environments without experience is introduced. Finally, simulation and vehicle tests are conducted to evaluate the effectiveness of the proposed method. Results show that the proposed method outperforms the MW and EWMA methods in terms of measurement noise estimation and navigation accuracy.

Estimation of Steady-State Optimal Filter Gain From Nonoptimal Kalman Filter Residuals

1994 ◽  
Vol 116 (3) ◽  
pp. 550-553 ◽  
Author(s):  
Chung-Wen Chen ◽  
Jen-Kuang Huang
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Finite Number ◽  
Discrete Time ◽  
Stochastic System ◽  
Moving Average ◽  
Ar Model ◽  
Numerical Example ◽  
Measurement Noises ◽  
Time Invariant

This paper proposes a new algorithm to estimate the optimal steady-state Kalman filter gain of a linear, discrete-time, time-invariant stochastic system from nonoptimal Kalman filter residuals. The system matrices are known, but the covariances of the white process and measurement noises are unknown. The algorithm first derives a moving average (MA) model which relates the optimal and nonoptimal residuals. The MA model is then approximated by inverting a long autoregressive (AR) model. From the MA parameters the Kalman filter gain is calculated. The estimated gain in general is suboptimal due to the approximations involved in the method and a finite number of data. However, the numerical example shows that the estimated gain could be near optimal.

A Bayesian Approach to Kalman Filter for Elliptically Contoured Distribution and its Application in Time Series Models

1994 ◽  
Vol 44 (1-2) ◽  
pp. 11-28 ◽  
Author(s):  
A. K. Basu ◽  
J. K. Das
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Moving Average ◽  
State Equation ◽  
Autoregressive Moving Average ◽  
Missing Observations ◽  
Estimation Of Parameters ◽  
Bayesian Formulation ◽  
Set Up ◽  
Elliptically Contoured

This paper develops a Bayesian formulation of Kalman filter under the errors having elliptically contoured distributions in both observation equation and system (or state) equation, using some recent results in multivariate analysis. Estimation of parameters in case of missing observations and prediction of missing observations as well are dealt with under the above set up of autoregressive-moving average process in time series. Two illustrative examples are presented with the help of AR(1) model and ARMA (1, 1) model.

Self-Tuning Fusion Kalman Filter for ARMA Signals

2012 ◽  
Vol 229-231 ◽  
pp. 1768-1771
Author(s):  
Wen Qiang Liu ◽  
Na Han ◽  
Man Yan ◽  
Gui Li Tao
Keyword(s):  
Kalman Filter ◽  
Instrumental Variable ◽  
Single Channel ◽  
Moving Average ◽  
Correlation Method ◽  
Autoregressive Moving Average ◽  
Model Parameters ◽  
Self Tuning ◽  
Optimal Fusion

For the single-channel autoregressive moving average (ARMA) signals with multisensor, and with unknown model parameters and noise variances, the local estimators of unknown model parameters and noise variances are obtained by the recursive instrumental variable (RIV) algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. Substituting them into the optimal fusion Kalman filter, a self-tuning fusion Kalman filter for single-channel ARMA signals is presented. A simulation example shows its effectiveness.

Application of Kalman Filtering for Natural Gray Image Denoising

2011 ◽  
Vol 187 ◽  
pp. 92-96 ◽  
Author(s):  
Zhi Kai Huang ◽  
De Hui Liu ◽  
Xing Wang Zhang ◽  
Ling Ying Hou
Keyword(s):  
Kalman Filter ◽  
Image Denoising ◽  
Kalman Filtering ◽  
Moving Average ◽  
Arma Model ◽  
Adaptive Method ◽  
Natural Image ◽  
Autoregressive Moving Average ◽  
Processing Step ◽  
Reduction Methods

Image denoising is one of the classical problems in digital image processing, and has been studied for nearly half a century due to its important role as a pre-processing step in various image applications. In this work, a denoising algorithm based on Kalman filtering was used to improve natural image quality. We have studied noise reduction methods using a hybrid Kalman filter with an autoregressive moving average (ARMA) model that the coefficients of the AR models for the Kalman filter are calculated by solving for the minimum square error solutions of over-determined linear systems. Experimental results show that as an adaptive method, the algorithm reduces the noise while retaining the image details much better than conventional algorithms.

GNSS/IMU/Odometer based Train Positioning

2020 ◽  
Author(s):  
Qing Li ◽  
Robert Weber
Keyword(s):  
Kalman Filter ◽  
Urban Areas ◽  
Moving Average ◽  
Accurate Determination ◽  
Integrated System ◽  
Single Frequency ◽  
Integration Algorithm ◽  
Speed Sensor ◽  
Train Positioning ◽  
Train Tracks

<p>Usually train positioning is realized via counting wheel rotations (Odometer), and correcting at fixed locations known as balises. A balise is an electronic beacon or transponder placed between the rails of a railway as part of an automatic train protection (ATP) system. Balises constitute an integral part of the European Train Control System, where they serve as “beacons” giving the exact location of a train. Unfortunately, balises are expensive sensors which need to be placed over about 250 000 km of train tracks in Europe.</p><p>Therefore, recently tremendous efforts aim on the development of satellite-based techniques in combination with further sensors to ensure precise train positioning. A fusion of GNSS receiver and Inertial Navigation Unit (IMU) observations processed within a Kalman Filter proved to be one of potential optimal solutions for train traction vehicles positioning.</p><p>Today several hundreds of trains in Austria are equipped with a single-frequency GPS/GLONASS unit. However, when the GNSS signal fails (e.g. tunnels and urban areas), we expect an outage or at least a limited positioning quality. To yet ensure availability of a reliable trajectory in these areas, the GNSS sensor is complemented by a strapdown IMU platform and a wheel speed sensor (odometer).</p><p>In this study a filtering algorithm based on the fusion of three sensors GPS, IMU and odometer is presented, which enables a reliable train positioning performance in post-processing. Odometer data are counts of impulses, which relate the wheel’s circumference to the velocity and the distance traveled by the train. This odometer data provides non-holonomic constraints as one-dimensional velocity updates and complements the basic IMU/GPS navigation system. These updates improve the velocity and attitude estimates of the train at high update rates while GPS data is used to provide accurate determination in position with low rates. In case of GNSS outages, the integrated system can switch to IMU/odometer mode. Using the exponentially weighted moving average method to estimate of measurement noise for odometer velocity helps to construct measurement covariance matrices. In the presented examples an IMU device, a GPS receiver and an Odometer provide the data input for the loosely coupled Kalman Filter integration algorithm. The quality of our solution was tested against trajectories obtained with the software iXCOM-CMD (iMAR) as reference.</p>

scholarly journals Rainfall Forecasting Model Using ARIMA and Kalman Filter in Makassar, Indonesia

2021 ◽  
Vol 2123 (1) ◽  
pp. 012044
Author(s):  
Sukarna ◽  
Elma Yulia Putri Ananda ◽  
Maya Sari Wahyuni
Keyword(s):  
Kalman Filter ◽  
Moving Average ◽  
Arima Model ◽  
Rainfall Data ◽  
Percentage Error ◽  
Filter Method ◽  
Rainfall Forecasting ◽  
Forecasting Methods ◽  
Filter Methods ◽  
Kalman Filter Method

Abstract Many forecasting methods have been used for forecasting rainfall data. Kalman Filter is one of the forecasting methods that could give better forecasts. To our knowledge, the Kalman Filter method has not been used to forecast rainfall data in Makassar, Indonesia. This study aims to provide more precise forecasts for rainfall data in Makassar, Indonesia by using Autoregressive Integrated Moving Average (ARIMA) and Kalman Filter methods. Rainfall data from January 2010 to December 2020 were used. The best model selection is based on the smallest Mean Absolute Percentage Error (MAPE) value. The results showed that the best ARIMA model is ARIMA(0,1,1)(0,1,1)12 with MAPE is 111.48, while MAPE value by using the Kalman Filter algorithm is 47.00 indicating that Kalman Filter has better prediction than ARIMA model.

scholarly journals Machine Intelligent Hybrid Methods Based on Kalman Filter and Wavelet Transform for Short-Term Wind Speed Prediction

Wind ◽  
2022 ◽  
Vol 2 (1) ◽  
pp. 37-50
Author(s):  
Yug Patel ◽  
Dipankar Deb
Keyword(s):  
Kalman Filter ◽  
Wavelet Transform ◽  
Wind Speed ◽  
Hybrid Methods ◽  
Moving Average ◽  
Offshore Wind ◽  
Electricity Grid ◽  
Wind Speed Prediction ◽  
Speed Prediction ◽  
Hybrid Forecasting

Wind power’s increasing penetration into the electricity grid poses several challenges for power system operators, primarily due to variability and unpredictability. Highly accurate wind predictions are needed to address this concern. Therefore, the performance of hybrid forecasting approaches combining autoregressive integrated moving average (ARIMA), machine learning models (SVR, RF), wavelet transform (WT), and Kalman filter (KF) techniques is essential to examine. Comparing the proposed hybrid methods with available state-of-the-art algorithms shows that the proposed approach provides more accurate prediction results. The best model is a hybrid of KF-WT-ML with an average R2 score of 0.99967 and RMSE of 0.03874, followed by ARIMA-WT-ML with an average R2 of 0.99796 and RMSE of 0.05863 over different datasets. Moreover, the KF-WT-ML model evaluated on different terrains, including offshore and hilly regions, reveals that the proposed KF based hybrid provides accurate wind speed forecasts for both onshore and offshore wind data.

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