scholarly journals A Possibilistic Kalman Filter for the Reduction of the Final Measurement Uncertainty, in Presence of Unknown Systematic Errors

Metrology ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 39-51
Author(s):  
Harsha Vardhana Jetti ◽  
Simona Salicone
Keyword(s):  
Kalman Filter ◽  
Measurement Uncertainty ◽  
Systematic Error ◽  
Kalman Filters ◽  
Systematic Errors ◽  
The State ◽  
Fuzzy Variables ◽  
Final Measurement ◽  
Random Fuzzy Variables ◽  
System States

A Kalman filter is a concept that has been in existence for decades now and it is widely used in numerous areas. It provides a prediction of the system states as well as the uncertainty associated to it. The original Kalman filter can not propagate uncertainty in a correct way when the variables are not distributed normally or when there is a correlation in the measurements or when there is a systematic error in the measurements. For these reasons, there have been numerous variations of the original Kalman filter, most of them mathematically based (like the original one) on the theory of probability. Some of the variations indeed introduce some improvements, but without being completely successful. To deal with these problems, more recently, Kalman filters have also been defined using random-fuzzy variables (RFVs). These filters are capable of also propagating distributions that are not normal and propagating systematic contributions to uncertainty, thus providing the overall measurement uncertainty associated to the state predictions. In this paper, the authors make another step forward, by defining a possibilistic Kalman filter using random-fuzzy variables which not only considers and propagates both random and systematic contributions to uncertainty, but also reduces the overall uncertainty associated to the state predictions by compensating for the unknown residual systematic contributions.

Accommodating the multi-state constraint Kalman filter for visual-inertial navigation in a moving and stationary flight

2022 ◽  
pp. 095441002110297
Author(s):  
Arshiya Mahmoudi ◽  
Mahdi Mortazavi ◽  
Mehdi Sabzehparvar
Keyword(s):  
Kalman Filter ◽  
Kalman Filters ◽  
Inertial Navigation ◽  
State Constraint ◽  
The State ◽  
Light Weight ◽  
Minor Error ◽  
State Augmentation ◽  
Low Speeds

For more than a decade, the multi-state constraint Kalman filter is used for visual-inertial navigation. Its advantages are the light-weight calculations, consistency, and similarity to the current mature GPS/INS Kalman filters. For using it in an airborne platform, an important deficiency exists. It diverges while the object stops moving. In this work, this deficiency is accounted for, by changing the state augmentation and measurement update policy from a time-based to horizontal travel-based scheme, and by reusing the oldest tracked point over and over. Besides the computational savings, it works infinitely with no extra errors in full-stops and with minor error build up in very low speeds.

scholarly journals Study on the Initial Value Problem for Fractional-order Cubature Kalman Filters of Nonlinear Continuous-time Fractional-order Systems

2021 ◽  
Author(s):  
Chuang Yang ◽  
Zhe Gao ◽  
Yue Miao ◽  
Tao Kan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
The State ◽  
Order System ◽  
Initial Value ◽  
Cubature Kalman Filter ◽  
Augmented State

Abstract To realize the state estimation of a nonlinear continuous-time fractional-order system, two types of fractional-order cubature Kalman filters (FOCKFs) designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system are also regarded as the augmented state, the augmented state equation is constructed to obtain the CKF based on Grünwald-Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter (HECKF) is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can effectively reduce the influence of initial value on the state estimation. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.

Position Sensorless Control Based on Augmented Extended Kalman Filter for Permanent Magnet Linear Synchronous Motor

2011 ◽  
Vol 88-89 ◽  
pp. 350-354
Author(s):  
Hua Cai Lu ◽  
Ming Jiang ◽  
Li Sheng Wei ◽  
Bing You Liu
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Sensorless Control ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
The State ◽  
State Variable ◽  
Detailed Explanation ◽  
System States ◽  
Position Sensorless

In order to achieve position sensorless control for PMLSM drive system, speed and position of the motor must be estimated. A novel sensorless position and speed estimation algorithm was designed for PMLSM drive by measuring terminal voltages and currents. That was state augmented extended Kalman filter (AEKF) estimation method. The resistance of the motor was augmented to the state variable. Then, the speed, position and the resistance were estimated simultaneously through extended Kalman filter (EKF). The influence of the resistance on the state estimation results could be reduced. As well as giving a detailed explanation of the new algorithm, experimental results were presented. It shows that the AEKF is capable of estimating system states accurately and reliability, and the proposed sensorless control system has a good dynamic response.

Study on Random-Fuzzy Variables Method for ADC Measurement Uncertainty Evaluation

2014 ◽  
Vol 568-570 ◽  
pp. 76-81
Author(s):  
Wei Jiang ◽  
Qi Zhang
Keyword(s):  
Measurement Uncertainty ◽  
Random Effects ◽  
Uncertainty Propagation ◽  
Uncertainty Evaluation ◽  
Fuzzy Variables ◽  
Measurement Result ◽  
Random Fuzzy Variables ◽  
Theory Of Evidence ◽  
Power Measurements ◽  
Measurement Uncertainty Evaluation

The random-fuzzy variables (RFVs) method based on the theory of evidence is studied, for the need of ADC uncertainty evaluation and the limitations of existing approaches. The connotation of RFVs adopted for expression of measurement result together with its associated uncertainty is discussed, and the RFVs mathematics for uncertainty propagation is analyzed. RFVs can naturally separate the contributions to the measurement uncertainty of the systematic and random effects. Taking power measurements as an example, RFVs method is applied to the presentation and propagation of the measurement uncertainty of ADC, and the results are compared with those obtained by GUM, which shows the RFVs method can be effectively employed in evaluating uncertainty of ADC, and is capable of providing the interval of confidence for all possible levels of confidence, within which the measurement result is supposed to lie.

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