scholarly journals Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

Inventions ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 80
Author(s):  
Alexander A. Manin ◽  
Sergey V. Sokolov ◽  
Arthur I. Novikov ◽  
Marianna V. Polyakova ◽  
Dmitriy N. Demidov ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Vector ◽  
Stochastic Systems ◽  
Adaptive Estimation ◽  
Measuring System ◽  
Time Intervals ◽  
Estimation Process ◽  
Nonlinear Programming Methods ◽  
Interval Observers ◽  
Accuracy And Stability

Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

Application of the auxiliary performance index for automatic optimality control of discrete Kalman filter

2020 ◽  
pp. 77-87
Author(s):  
Иннокентий Васильевич Семушин ◽  
Юлия Владимировна Цыганова ◽  
Андрей Владимирович Цыганов
Keyword(s):  
Kalman Filter ◽  
Adaptive Filter ◽  
Stochastic System ◽  
Performance Index ◽  
Stochastic Systems ◽  
Joint Control ◽  
Vector Parameter ◽  
Optimal Value ◽  
Roundoff Errors ◽  
Dynamic Stochastic

Предложен новый метод автоматического контроля оптимальности дискретного фильтра Калмана, основанный на равенстве нулю градиента вспомогательного функционала качества (ВФК) по параметрам адаптивного дискретного фильтра. Для вычисления градиента ВФК применяется численно устойчивый к ошибкам машинного округления алгоритм модифицированной взвешенной ортогонализации Грама-Шмидта (MWGS-ортогонализации). Алгоритм реализован на языке Matlab. Результаты проведенных численных экспериментов подтверждают эффективность предложенного метода The paper proposes a new method for automatic control of the nominal operating mode of a dynamic stochastic system, based on a combination of two previously developed methods: the auxiliary performance index (API) method and the LD modification of an adaptive filter numerically robust to roundoff errors. The API method was previously developed to solve the problems of identification, adaptation, and control of stochastic systems with control and filtering. We suggest using the API not only as a tool for identifying the parameters of the stochastic system model from the measurement data but also for automatically monitoring the optimality of the adaptive filter, namely, the condition that the API gradient is close to zero should be satisfied (with the necessity and sufficiency) at the point corresponding to the optimal value of the vector parameter in the adaptive Kalman filter. The main result is the new eLD-KF-AC algorithm (extended LD Kalman-like adaptive filtering algorithm with automatic optimality control). The advantages of the obtained solution are as follows: 1) the choice of the adaptive filter structure in the form of an extended LD algorithm can significantly reduce the effect of machine roundoff errors on the calculation results when supplemented by the ability to calculate the sensitivity functions by the system vector parameter of the adaptive filter; 2) the application of the API method allows controlling the optimality of the adaptive filter by the condition that the API gradient is zero at the minimum point, which corresponds to the optimal value of the parameter in the adaptive filter; 3) the calculation of the API gradient in the adaptive extended LD filter does not require significant computational costs and such a control method can be carried out in real-time. The results of the work will be applied to solving problems of joint control and identification of parameters in the class of discrete-time linear stochastic systems represented by equations in the state-space form.

scholarly journals A Modified Extended Kalman Filter for a Two-Antenna GPS/INS Vehicular Navigation System

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3809 ◽  
Author(s):  
Yushi Hao ◽  
Aigong Xu ◽  
Xin Sui ◽  
Yulei Wang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Navigation System ◽  
Adaptive Estimation ◽  
Estimation Method ◽  
Measurement Noise ◽  
Model Errors ◽  
State Process ◽  
Stability And Accuracy ◽  
The Impact

Recently, the integration of an inertial navigation system (INS) and the Global Positioning System (GPS) with a two-antenna GPS receiver has been suggested to improve the stability and accuracy in harsh environments. As is well known, the statistics of state process noise and measurement noise are critical factors to avoid numerical problems and obtain stable and accurate estimates. In this paper, a modified extended Kalman filter (EKF) is proposed by properly adapting the statistics of state process and observation noises through the innovation-based adaptive estimation (IAE) method. The impact of innovation perturbation produced by measurement outliers is found to account for positive feedback and numerical issues. Measurement noise covariance is updated based on a remodification algorithm according to measurement reliability specifications. An experimental field test was performed to demonstrate the robustness of the proposed state estimation method against dynamic model errors and measurement outliers.

scholarly journals Measurement Feedback Self-Tuning Weighted Measurement Fusion Kalman Filter for Systems with Correlated Noises

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xin Wang ◽  
Shu-Li Sun
Keyword(s):  
Kalman Filter ◽  
Stochastic Systems ◽  
Tracking System ◽  
Weighted Least Squares ◽  
Full Rank ◽  
Global Optimality ◽  
Measurement Feedback ◽  
Innovation Model ◽  
Self Tuning ◽  
Noise Statistics

For the linear discrete stochastic systems with multiple sensors and unknown noise statistics, an online estimators of the noise variances and cross-covariances are designed by using measurement feedback, full-rank decomposition, and weighted least squares theory. Further, a self-tuning weighted measurement fusion Kalman filter is presented. The Fadeeva formula is used to establish ARMA innovation model with unknown noise statistics. The sampling correlated function of the stationary and reversible ARMA innovation model is used to identify the noise statistics. It is proved that the presented self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion Kalman filter, which means its asymptotic global optimality. The simulation result of radar-tracking system shows the effectiveness of the presented algorithm.

Adaptive estimation of UVs navigation parameters by irregular inertial-satellite measurements

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sergey V. Sokolov ◽  
Arthur I. Novikov
Keyword(s):  
Kalman Filter ◽  
Adaptive Estimation ◽  
Unmanned Vehicles ◽  
Dispersion Matrix ◽  
Navigation Systems ◽  
Satellite Measurements ◽  
Preliminary Calculation ◽  
Adaptation Algorithm ◽  
Estimation Errors ◽  
Content Type

PurposeThere are shortcomings of modern methods of ensuring the stability of Kalman filtration in unmanned vehicles’ (UVs) navigation systems under the condition of a priori uncertainty of the dispersion matrix of measurement interference. First, it is the absence of strict criteria for the selection of adaptation coefficients in the calculation of the a posteriori covariance matrix. Secondly, it is the impossibility of adaptive estimation in real time from the condition of minimum covariance of the updating sequence due to the necessity of its preliminary calculation.Design/methodology/approachThis paper considers a new approach to the construction of the Kalman filter adaptation algorithm. The algorithm implements the possibility of obtaining an accurate adaptive estimation of navigation parameters for integrated UVs inertial-satellite navigation systems, using the correction of non-periodic and unstable inertial estimates by high-precision satellite measurements. The problem of adaptive estimation of the noise dispersion matrix of the meter in the Kalman filter can be solved analytically using matrix methods of linear algebra. A numerical example illustrates the effectiveness of the procedure for estimating the state vector of the UVs’ navigation systems.FindingsAdaptive estimation errors are sharply reduced in comparison with the traditional scheme to the range from 2 to 7 m in latitude and from 1.5 to 4 m in longitude.Originality/valueThe simplicity and accuracy of the proposed algorithm provide the possibility of its effective application to the widest class of UVs’ navigation systems.

scholarly journals An Improved Unscented Kalman Filter Algorithm for Radar Azimuth Mutation

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dazhang You ◽  
Pan Liu ◽  
Wei Shang ◽  
Yepeng Zhang ◽  
Yawei Kang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Unscented Kalman Filter ◽  
Tracking System ◽  
Sudden Change ◽  
Singular Value ◽  
Tracking Accuracy ◽  
Kalman Filter Algorithm ◽  
Value Decomposition ◽  
Accuracy And Stability

An improved UKF (Unscented Kalman Filter) algorithm is proposed to solve the problem of radar azimuth mutation. Since the radar azimuth angle will restart to count after each revolution of the radar, and when the aircraft just passes the abrupt angle change, the radar observation measurement will have a sudden change, which has serious consequences and is solved by the proposed novel UKF based on SVD. In order to improve the tracking accuracy and stability of the radar tracking system further, the SVD-MUKF (Singular Value Decomposition-based Memory Unscented Kalman Filter) based on multiple memory fading is constructed. Furthermore, several simulation results show that the SVD-MUKF algorithm proposed in this paper is better than the SVD-UKF (Singular Value Decomposition of Unscented Kalman Filter) algorithm and classical UKF algorithm in accuracy and stability. Last but not the least, the SVD-MUKF can achieve stable tracking of targets even in the case of angle mutation.

scholarly journals Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
FengJun Hu ◽  
Qian Zhang ◽  
Gang Wu
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Stochastic System ◽  
Stochastic Systems ◽  
System Control ◽  
Time Varying ◽  
Cubature Kalman Filter ◽  
Adaptive Correction ◽  
Kalman Filter Algorithm ◽  
Control Accuracy

Standard cubature Kalman filter (CKF) algorithm has some disadvantages in stochastic system control, such as low control accuracy and poor robustness. This paper proposes a stochastic system control method based on adaptive correction CKF algorithm. Firstly, a nonlinear time-varying discrete stochastic system model with stochastic disturbances is constructed. The control model is established by using the CKF algorithm, the covariance matrix of standard CKF is optimized by square root filter, the adaptive correction of error covariance matrix is realized by adding memory factor to the filter, and the disturbance factors in nonlinear time-varying discrete stochastic systems are eliminated by multistep feedback predictive control strategy, so as to improve the robustness of the algorithm. Simulation results show that the state estimation accuracy of the proposed adaptive cubature Kalman filter algorithm is better than that of the standard cubature Kalman filter algorithm, and the proposed adaptive correction CKF algorithm has good control accuracy and robustness in the UAV control test.

scholarly journals Robust Functional Interval Observer for Multivariable Linear Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Luc Meyer
Keyword(s):  
Linear System ◽  
Linear Function ◽  
Continuous Time ◽  
State Vector ◽  
Internal State ◽  
Design Procedure ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Interval Observer ◽  
Interval Observers

The study of a continuous-time multivariable linear system may not need the knowledge of the entire internal state vector, but only of a linear function of it. In this case, instead of designing a complete observer, only a functional (also called reduced order) observer is used. In this field of research, this paper focuses on robust functional cooperative interval observers. Such an observer is proposed and its properties (in particular, its convergence) are established. Then, a design procedure is given for practical use. Finally, the theoretical contributions are illustrated in examples.

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