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 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.

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.

scholarly journals A Study on Minimum Sigma Set SRUKF Based GPS/INS Tightly-Coupled System

2017 ◽  
Author(s):  
Maosong Wang ◽  
Xiaofeng He ◽  
Wenqi Wu ◽  
Zhenbo Liu
Keyword(s):  
Kalman Filter ◽  
Kalman Filters ◽  
Unscented Kalman Filter ◽  
Coupled System ◽  
The State ◽  
Computational Time ◽  
Square Root ◽  
Unscented Transformation ◽  
Tightly Coupled ◽  
The Stability

In this paper, firstly, some questionable formulas and conceptual oversights of previous reduced sigma set unscented transformation (UT) methods are revised through theoretical analysis. Then the revised UT methods based Kalman filters are used in a GPS/INS tightly-coupled system. The Kalman filter flows are the kind of square-root, since the square-root unscented Kalman filters (SRUKFs) can guarantee the stability of the system. By using the reduced sigma set SRUKFs (which contain simplex sigma set square-root unscented Kalman filter (S-SRUKF), spherical simplex sigma set square-root unscented Kalman filter (SS-SRUKF) and minimum sigma set square-root unscented Kalman filter (M-SRUKF)), the computation cost is greatly saved compared with the standard SRUKF, while the accuracy of the GPS/INS tightly-coupled system still maintained. The structure of the GPS/INS tightly-coupled system is in the form of error state, and the time updates of the state and the state covariance of SRUKFs are directly estimated without using UT, thus the computational time is also greatly saved. The pseudo-satellite is introduced to aid the system when the observation information is deficient, for example, when the GPS signal is deficient in the maneuver environment. By using the pseudo-satellite, the optimal performance of the system is guaranteed. Experiment of unmanned aerial vehicle (UAV) showed that the pseudo-satellite aided mechanism worked well.

scholarly journals A square root unscented Kalman filter for multiple view geometry based stereo cameras/inertial navigation

2016 ◽  
Vol 13 (5) ◽  
pp. 172988141666485 ◽  
Author(s):  
Zhiwen Xian ◽  
Junxiang Lian ◽  
Mao Shan ◽  
Lilian Zhang ◽  
Xiaofeng He ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Inertial Navigation ◽  
Square Root ◽  
Multiple View Geometry ◽  
Multiple View ◽  
Stereo Cameras
Sign in / Sign up

Export Citation Format

Share Document