scholarly journals An extended Kalman filter with a computed mean square error bound

2014 ◽  
Author(s):  
G. Hexner ◽  
H. Weiss
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Error Bound ◽  
Extended Kalman Filter ◽  
Mean Square

scholarly journals Iterated extended Kalman filter based state estimation of diode circuit

2021 ◽  
Vol 2070 (1) ◽  
pp. 012092
Author(s):  
Amit Kumar Gautam ◽  
Sudipta Majumdar
Keyword(s):  
Performance Evaluation ◽  
Kalman Filter ◽  
Root Mean Square Error ◽  
State Estimation ◽  
Mean Square Error ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Mean Square ◽  
Extended Kalman Filtering ◽  
Iterated Extended Kalman Filter

Abstract This paper presents the state estimation of diode circuit using iterated extended Kalman filter (IEKF). The root mean square error (RMSE) based performance evaluation gives the superiority of the IEKF based estimation over extended Kalman filtering (EKF) based method.

Two-layer structure algorithm for estimation of commercial vehicle mass

2019 ◽  
Vol 234 (2-3) ◽  
pp. 378-389
Author(s):  
Liuliu Cai ◽  
Hongliang Wang ◽  
Tianle Jia ◽  
Pai Peng ◽  
Dawei Pi ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Extended Kalman Filter ◽  
Commercial Vehicle ◽  
Layer Structure ◽  
Estimation Algorithm ◽  
Mean Square ◽  
Mass Estimation ◽  
Grade Estimation

Aiming at the problem of mass estimation for commercial vehicle, a two-layer structure mass estimation algorithm was proposed. The first layer was the grade estimation algorithm based on recursive least squares method and the second layer was a mass estimation algorithm using the extended Kalman filter. The estimated grade was introduced as the observation quantity of the second layer. The influence of the suspension deformation on grade estimation was considered in the first layer algorithm, which was corrected in real time according to the mass and road grade estimated by the second layer algorithm. The proposed estimation algorithm was validated via a co-simulation platform involving TruckSim and MATLAB/Simulink. Finally, a road test was carried out, and the evaluation method using the root mean square error was proposed. According to the test, the average value of the root mean square error reduces from 871.65 to 772.52, grade estimation is more accurate, and the convergence speed of mass estimation is faster, compared with estimation results of the extended Kalman filter method.

Adaptive and augmented nonlinear filters : theory and applications

2018 ◽  
Author(s):  
◽  
Tao Sun
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Gaussian Approximation ◽  
Adaptive Strategy ◽  
Nonlinear Filters ◽  
Nonlinear Transformation ◽  
Mean Square ◽  
Gaussian Filters ◽  
Non Gaussian ◽  
Gaussian Estimation

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Nonlinear estimation and filtering have been intensively studied for decades since it has been widely used in engineering and science such as navigation, radar signal processing and target tracking systems. Because the posterior density function is not a Gaussian distribution, then the optimal solution is intractable. The nonlinear/non-Gaussian estimation problem is more challenging than the linear/Gaussian case, which has an optimal closed form solution, i.e. the celebrated Kalman filter. Many nonlinear filters including the extended Kalman filter, the unscented Kalman filter and the Gaussian-approximation filters, have been proposed to address nonlinear/non-Gaussian estimation problems in the past decades. Although the estimate yield by Gaussian-approximation filters such as cubature Kalman filters and Gaussian-Hermite quadrature filters is satisfied in many applications, there are two obvious drawbacks embedded in the use of Gaussian filters. On the one hand, with the increase of the quadrature points, much computational effort is devoted to approximate Gaussian integrals, which is not worthy sometimes. On the other hand, by the use of the update rule, the estimate constrains to be a linear function of the observation. In this dissertation, we aim to address this two shortcoming associated with the conventional nonlinear filters. We propose two nonlinear filters in the dissertation. Based on an adaptive strategy, the first one tries to reduce the computation cost during filtering without sacrificing much accuracy, because when the system is close to be linear, the lower level Gaussian quadrature filter is sufficient to provide accurate estimate. The adaptive strategy is used to evaluate the nonlinearity of the system at current time first and then utilize different quadrature rule for filtering. Another filter aims to modify the conventional update rule, i.e. the linear minimum mean square error (LMMSE) rule, to involve a nonlinear transformation of the observation, which is proven to be an efficient way to exploit more information from the original observation. According to the orthogonal property, we propose a novel approach to construct the nonlinear transformation systematically. The augmented nonlinear filter outperforms Gaussian filters and other conventional augmented filters in terms of the root mean square error and onsistency. Furthermore, we also extend the work to the more general case. The higher order moments can be utilized to construct the nonlinear transformation and in turn, the measurement space can be expand efficiently. Without the Gaussian assumption, the construction of the nonlinear transformation only demand the existence of a finite number of moments. Finally, the simulation results validate and demonstrate the superiority of the adaptive and augmented nonlinear filters.

scholarly journals Studi Analisa Kalman Filter Sebagai State Estimator Untuk Meningkatkan Akurasi Pengukuran Kecepatan Motor DC

2021 ◽  
Vol 3 (01) ◽  
pp. 9-18
Author(s):  
Ivan Sutresno Hadi Sujoto ◽  
Hari Sutiksno
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
State Estimator

State estimator merupakan sebuah teknik yang digunakan untuk mengestimasi besarnya suatu sinyal dari suatu data yang telah tercampur dengan noise. Noise tersebut dapat terjadi pada proses di dalam suatu plant (motor DC) maupun pada pembacaan oleh sensor, yang menyebabkan nilai yang sesungguhnya dari suatu sinyal tidak dapat diketahui dengan akurat. Sinyal yang tercampur dengan noise tersebut dapat direduksi dengan berbagai cara, di antaranya adalah dengan menggunakan Kalman Filter. Kalman Filter merupakan sebuah state estimator yang merupakan filter linier terbaik (bila semua syarat terpenuhi) dengan menggunakan konsep Minimum Mean Square Error (MMSE). Dalam tugas akhir ini akan diuji coba dan diamati manfaat Kalman Filter untuk mengestimasi nilai kecepatan motor DC yang sesungguhnya bila sistem tersebut bekerja pada kondisi yang bernoise. Sebagai pembanding, dalam tugas akhir ini akan diuji coba juga teknik pemfilteran data yang lain untuk dibandingkan performansinya terhadap Kalman Filter. Pengujian dilakukan dengan menggunakan program Matlab dengan cara memberikan noise ke dalam sistem. Hasil uji coba menunjukkan bahwa Kalman Filter mampu mereduksi error pada pengukuran kecepatan motor DC hingga kurang dari 0.5 rad/sec hanya dalam waktu 0.025 detik.

EEG ENHANCEMENT USING EXTENDED KALMAN FILTER TO TRAIN MULTI-LAYER PERCEPTRON

2019 ◽  
Vol 31 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Manel Yakoubi ◽  
Rachid Hamdi ◽  
Mounir Bousbia Salah
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Brain Activity ◽  
Activation Function ◽  
Eeg Signal ◽  
Mean Square ◽  
Least Mean Square ◽  
Multi Layer Perceptron ◽  
Non Stationary Signal

In many applications of signal processing, especially in biomedicine, electroencephalogram (EEG) is the recording of electrophysiological brain activity along the scalp over a small interval of time and it is a biological non stationary signal which contains important information. Analysis of EEG signal is useful to identify physiological situations of the human as normal and epileptic subject. EEG signal becomes more complicated to be analyzed by the introduction of the noise. In this paper, a nonlinear Kalman Filter scheme where an extended Kalman filter (EKF) based Multi-layer perceptron (MLP) model is proposed to remove white and colored Gaussian noises from EEG recordings in physiological and pathological states (normal and epileptic). The MLP is one of the artificial neural network (ANN) models that has great track of impacts at solving a variety of problems. Activation function is one of the elements in MLP neural network. Selection of the activation function as sigmoid in the MLP network plays an essential role on the network performance. Thus, the MLP parameters as weights, and outputs are trained by an EKF in order to minimize the difference between the output of the neural network and the desired outputs. The results comparison studies are evaluated with root mean square difference (RMSD) and signal to noise ratio (SNR). The elapsed time is decreased using this method compared to normalised least mean square (NLMS) and Meyer wavelet methods. These parameters applied to EEG signals show the validity and effectiveness of the proposed approach.

scholarly journals Estimasi Lintasan AUV 3 Dimensi (3D) Dengan Ensemble Kalman Filter

2019 ◽  
Vol 4 (1) ◽  
pp. 12
Author(s):  
Ngatini Ngatini ◽  
Hendro Nurhadi
Keyword(s):  
Kalman Filter ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Ensemble Kalman Filter ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Mean Square ◽  
Guidance Control ◽  
Non Linear

AUV (Autonomous Underwater Vehicle) merupakan kapal selam tanpa awak yang sistem geraknya dikemudikan (dikendalikan) oleh perangkat komputer. Sistem gerak dari AUV membutuhkan sebuah navigasi dan guidance control yang mampu mengarahkan gerak AUV, sehingga dibutuhkan sebuah estimasi posisi AUV sesuai dengan lintasan yang diberikan. Penelitian ini mengembangkan estimasi posisi dari AUV Segorogeni ITS menggunakan metode atau algoritma Ensemble Kalman Filter (EnKF) karena EnKF mampu mengestimasi persoalan berbentuk model sistem non linier dimana persamaan gerak dari AUV berbentuk non linear. Estimasi posisi dilakukan pada lintasan atau trayektori 3 dimensi (3D) yang dibangun dengan bantuan program Octave. Simulasi menampilkan hasil estimasi posisi AUV menggunakan algoritma EnKF dengan beberapa jumlah ensemble yang berbeda yaitu 50, 100, 200 dan 300 ensemble. Akurasi dari estimasi tersebut diukur dari nilai error hasil estimasi yaitu nilai RMSE (Root Mean Square Error). Hasil simulasi menunjukan rata-rata error estimasi yaitu 0.4 m posisi-x, 0.46 m posisi-y, 0.08 m posisi-z dan 0.1 m error sudut.

scholarly journals Estimasi Kelajuan dan Volume Kendaraan Berdasarkan Model Makroskopik Arus Lalu Lintas Jalan Tol dengan Metode Extended Kalman Filter

2019 ◽  
Vol 2 (2) ◽  
pp. 51-60
Author(s):  
Febriana Prihatiningsih ◽  
Sigit Pancahayani ◽  
Subchan Subchan
Keyword(s):  
Kalman Filter ◽  
Traffic Flow ◽  
Extended Kalman Filter ◽  
Flow Rate ◽  
Mean Square ◽  
Relative Speed ◽  
Traffic Jam ◽  
Forward Difference ◽  
Approach Time

In this thesis, the analysis of vehicles' determination of speed and volume in the traffic flow will be discussed by approach time. The analyzation of vehicles' speed and volume done by estimated on macroscopic term of traffic flow in the traffic jam with Extended Kalman Filter (EKF) method. The term of macroscopic views with measured the traffic variable by density the flow rate the flow rate of vehicle and also the vehicle speed's average. In the estimating process, forward difference scheme is implemented to the model and error are measured by Root Mean Square Error. The result showed that the estimation the average of the vehicle’s relative speed in a segment decreased when its volume of vehicle is increased and vice versa.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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