Unscented Kalman Filter Using Augmented State in the Presence of Additive Noise

The article presents an approach for combining methods of recursive Bayesian estimation with models of dynamical systems with varying differentiation order. The work addresses the problem of explicit fractional order estimation and tracking by constructing an efficient Unscented Kalman filter, where the model order is directly estimated within an augmented state along with the variables of interest. The feasibility of the estimation method is assessed using a benchmark problem based on a simplified fractional neuron firing rate model and time-dependent differentiation order. The proposed technique is compared to an implicit method based on Interacting Multiple Model filtering and a computationally efficient method using a modification of the Ensemble Kalman filter. The performance with respect to different parameters and filter settings is analyzed and a corresponding discussion is provided.

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Estimation of Forcing Function, Mistuning and Modal Damping in a Bladed Rotor

Volume 7A: Structures and Dynamics ◽

10.1115/gt2019-90262 ◽

2019 ◽

Author(s):

Arjun Singh Chauhan ◽

Alok Sinha

Keyword(s):

Kalman Filter ◽

State Space ◽

Unscented Kalman Filter ◽

State Space Model ◽

Space Model ◽

Vibration Data ◽

Forcing Function ◽

Modal Damping ◽

Bladed Rotor ◽

Augmented State

Abstract This paper deals with the estimation of forcing function, modal damping and mistuned modal stiffnesses in a bladed rotor. Previous research on parameter estimation in a mistuned bladed rotor relies on the knowledge of the forcing function as well as the vibration data. This paper presents two novel approaches. The first approach relies on knowledge of both the forcing and vibration data. The parameters are treated as states of the system and an augmented state space model is created. Unscented Kalman Filter is then used on the steady state data to estimate the parameters. The second approach eliminates the dependence on forcing data. Both the forcing and parameters are now treated as states of the system to construct an augmented state space model. Unscented Kalman Filter is then used on transient vibration data for estimation. Numerical results are presented for a simple model of a mistuned bladed rotor which considers a single mode of vibration per blade.

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A Novel Bilateral Fuzzy Adaptive Unscented Kalman Filter and its Implementation to Nonlinear Systems with Additive Noise

2020 IEEE Industry Applications Society Annual Meeting ◽

10.1109/ias44978.2020.9334835 ◽

2020 ◽

Author(s):

Sohrab Mokhtari ◽

Kang K Yen

Keyword(s):

Kalman Filter ◽

Nonlinear Systems ◽

Additive Noise ◽

Unscented Kalman Filter ◽

Adaptive Unscented Kalman Filter ◽

Fuzzy Adaptive

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A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems with Additive Noise

International Journal of Aerospace Engineering ◽

10.1155/2015/381478 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 9

Author(s):

Yong Zhou ◽

Chao Zhang ◽

Yufeng Zhang ◽

Juzhong Zhang

Keyword(s):

Kalman Filter ◽

Nonlinear Systems ◽

Covariance Matrix ◽

Adaptive Filtering ◽

Additive Noise ◽

Unscented Kalman Filter ◽

Square Root ◽

Noise Covariance Matrix ◽

Highly Nonlinear ◽

Noise Covariance

The Kalman filter (KF), extended KF, and unscented KF all lack a self-adaptive capacity to deal with system noise. This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on the square-root unscented KF (SRUKF), traditional Maybeck’s estimator is modified and extended to nonlinear systems. The square root of the process noise covariance matrixQor that of the measurement noise covariance matrixRis estimated straightforwardly. Because positive semidefiniteness ofQorRis guaranteed, several shortcomings of traditional Maybeck’s algorithm are overcome. Thus, the stability and accuracy of the filter are greatly improved. In addition, based on three different nonlinear systems, a new adaptive filtering technique is described in detail. Specifically, simulation results are presented, where the new filter was applied to a highly nonlinear model (i.e., the univariate nonstationary growth model (UNGM)). The UNGM is compared with the standard SRUKF to demonstrate its superior filtering performance. The adaptive SRUKF (ASRUKF) algorithm can complete direct recursion and calculate the square roots of the variance matrixes of the system state and noise, which ensures the symmetry and nonnegative definiteness of the matrixes and greatly improves the accuracy, stability, and self-adaptability of the filter.

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