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

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.

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Kalman Filter Algorithm versus Other Methods of Estimating Missing Values: Time Series Evidence

African Journal of Mathematics and Statistics Studies ◽

10.52589/ajmss-vfvnmqlx ◽

2021 ◽

Vol 4 (2) ◽

pp. 1-9

Author(s):

Adejumo O.A. ◽

Onifade O.C. ◽

Albert S.

Keyword(s):

Time Series ◽

Kalman Filter ◽

Missing Values ◽

Absolute Error ◽

Additive Models ◽

Percentage Error ◽

Sample Sizes ◽

Linear Quadratic ◽

Kalman Filter Algorithm ◽

Accuracy Measures

Ideally, we think data are carefully collected and have regular patterns with no missing values, but in reality, this does not always happen. This study examines four (4) methods—mean imputation (MI), median imputation (MDI), linear imputation (LI) and Kalman filter algorithm (KAL)—of estimating missing values in time series. The study utilized pairs of nine (9) simulated series; each pair constitutes “actual series” and “12% missingness series”. The three (3) sample sizes i.e. small (50), medium (200) and large (1000) were varied over the additive models linear, quadratic and exponential forms of trend. The 12% missingness series were estimated using MI, MDI, LI and KAL. The performances of the method were checked using the root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), while the overall performances of the estimating methods were accessed using the average of the accuracy measures (RMSE, MAE and MAPE). The results of the average-accuracy measures show that KAL outperformed other methods (MI, MDI and LI) at the three sample sizes when the trend was linear; also, MDI outperformed other methods at the three (3) sample sizes when the trend was exponential. Furthermore, MI outperformed others at small and large sample sizes when the trend was quadratic. However, the Kalman filter algorithm proved better when the sample size was medium. Hence, KAL, MI and MDI methods are recommended to estimate missing data in time series when the trend is linear, quadratic and exponential respectively, until further study proves otherwise.

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Removal of Pink Noise from Corrupted Speech Signal using Kalman Filter

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.c8578.029420 ◽

2020 ◽

Vol 9 (4) ◽

pp. 2034-2038

Keyword(s):

Signal Processing ◽

Kalman Filter ◽

Speech Enhancement ◽

Speech Signal ◽

Linear Prediction ◽

Audio Signal ◽

Pink Noise ◽

Linear Quadratic ◽

Noise Component ◽

Practical Applications

Speech enhancement has been a major challenge in the field of Signal processing. The process of filtering the noise component from the speech signal has achieved many milestones since the early 20th century. Beside many theories Linear prediction coding is one of the best methods for speech, audio signal processing which uses the algorithm of predicting the current estimates based on the past states of an LTI system. Linear prediction is usually used in Speech recognition, Speech enhancement. One of such Kalman filter was introduced and described in 1960 by Rudolf Kalman, which uses the concept of linear quadratic estimation. Kalman filtering is effectively being used in the practical applications like navigation of ships or aircraft, designing motion planning algorithms, in communication area. Kalman filters use the autoregression model of speech for the recursive equations of Kalman filter used in state space model of filter for state estimation. In this paper, we have used Kalman filter to eliminate the pink noise from the corrupted speech signal. Pink noise is very common in electronic devices and occurs in almost all devices. The Speech corrupted with pink noise has been obtained from SpEAR database. We have used MATLAB software for the simulation purpose. Finally, Spectrograms of signals are plotted for a better visual understanding of filtered results.

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Application of High Frequency Signal Injection Method in PMSM Control Using Fuzzy Kalman Filtering Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.556-562.2274 ◽

2014 ◽

Vol 556-562 ◽

pp. 2274-2278

Author(s):

Guo Lin Che ◽

Hua Lai

Keyword(s):

Signal Processing ◽

Kalman Filter ◽

Kalman Filtering ◽

High Frequency ◽

Frequency Signal ◽

High Frequency Signal ◽

Injection Method ◽

Filtering Algorithm ◽

Signal Injection ◽

Mechanical Sensor

High frequency signal injection method is the most available method to achieve low speed and zero speed operations in mechanical sensor-less control of PMSM. The difficulty in HF signal injection method is how to pick up the HF components from the measured currents. Kalman filter is an adaptive filter and has been widely used in signal detections and processing. In this paper, a HF signal injection method using fuzzy Kalman filter for signal processing is proposed to realize the low speed operation in mechanical sensor-less control of PMSM. The Kalman filtering algorithm combined with a fuzzy inference system can efficiently adjust the covariance matrix of system measurement noise. Simulations and experiments are performed on PMSM, the results show that this method is a simple and direct signal processing method for HF signal injection method with very good stability and precision.

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