The square-root unscented Kalman filter for state and parameter-estimation (original) (raw)
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The unscented Kalman filter for nonlinear estimation
2000
The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network), and dual estimation (e.g., the Expectation Maximization (EM) algorithm) where both states and parameters are estimated simultaneously.
Applying the unscented Kalman filter for nonlinear state estimation
Journal of Process Control, 2008
Based on presentation of the principles of the EKF and UKF for state estimation, we discuss the differences of the two approaches. Four rather different simulation cases are considered to compare the performance. A simple procedure to include state constraints in the UKF is proposed and tested. The overall impression is that the performance of the UKF is better than the EKF in terms of robustness and speed of convergence. The computational load in applying the UKF is comparable to the EKF.
IEEE Signal Processing Letters, 2019
This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a "linear-like" regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This "linear-like" regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.
State estimation of nonlinear systems using the Unscented Kalman Filter
2010
This paper addresses the problem of estimating the state of a nonlinear system from measurements that are perturbed by a random source of noise. The Extended Kalman Filter is a type of all-purpose filter that tries to solve this problem by dealing with a linearized version of the system. A new methodology proposed in [1], named Unscented Kalman Filter, is presented. It uses the so-called unscented transformation to better describe the stochastic evolution of the state of the system. The aim of this paper is to compare and discuss the performance of each filter when applied to state estimation of a simplified model of the DELMAC autonomous surface craft.
Modified unscented Kalman Filter for nonlinear systems having linear subsystems
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2015
The Extended Kalman Filter (EKF) is the often used filtering algorithm for nonlinear systems. But it does not usually produce desirable results. Recently a new nonlinear filtering algorithm named as Unscented Kalman Filter (UKF) is introduced. In this paper, we propose a new modified Unscented Kalman Filter (MUKF) algorithm for nonlinear stochastic systems that are linear in some components. These nonlinear systems can be considered as having linear subsystems with parameters and aim is to estimate the system parameters. In simulation study, performance of the EKF, its known variant Modified Extended Kalman Filter (MEKF), UKF and the proposed MUKF is demonstrated for a nonlinear system that is linear in some components. The results show that MUKF gives the best solution for parameter identification problem.
An unscented Kalman filter method for real time input-parameter-state estimation
An unscented Kalman filter method for real time input-parameter-state estimation, 2022
The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic states and the system parameters provide an estimation of the input. Secondly, the corrected with measurements states and parameters provide a final estimation. Importantly, it is demonstrated using the perturbation analysis that, a system with at least a zero or a non-zero known input can potentially be uniquely identified. This output-only methodology allows for a better understanding of the system compared to classical output-only parameter identification strategies, given that all the dynamic states, the parameters, and the input are estimated jointly and in real-time.
IEEE Access, 2019
Unscented Kalman filter (UKF) is one type of the sigma point Kalman filters and it is based on unscented transformation. UKF is used for parameter estimation of various dynamic systems and for such purpose either joint UKF (JUKF) or dual UKF (DUKF) schemes are considered. JUKF is based on estimating states and parameters together by using only one filter. For DUKF, states and parameters are decoupled and two separate filters are considered. In this paper, a modification to standard JUKF is proposed for parameter estimation which is based on decoupling parameter vector and updating parameter estimates by considering the error transformation between measurements and transformed sigma points during measurement update into the parameter errors. A linear transformation is proposed for such a purpose. Thus, the computational complexity of the standard JUKF is reduced significantly since parameters are decoupled from the state vector while the convergence of parameter estimate(s) is guaranteed. The new modified JUKF scheme is promising to be used for the parameter estimation of dynamic systems for which a linear transformation between measurement and parameter errors can be obtained. The effectiveness of this new scheme is proven by applying it to two nonlinear dynamic systems. INDEX TERMS Kalman filter, unscented Kalman filter, joint unscented Kalman filter, parameter estimation, dynamic systems.
An Improved Unscented Kalman Filter Algorithm for Dynamic Systems Parameters Estimation
Research Square (Research Square), 2024
The high capabilities of unscented Kalman filter (UKF) for estimating the state variables of a dynamic system have led to their use for parameter estimation as well. In order to use the UKF to estimate the unknown parameters of a dynamic system, the parameters must be assumed to be in the form of virtual state variables. This paper first shows that this assumption causes some serious challenges. Then, trying to solve this problem, a modified UKF algorithm will be presented. Eventually, using the proposed algorithm, the parameters of a power plant turbine-governor system as a typical dynamic system are estimated and the efficacy of the method is investigated. The results show that the proposed method has good performance and is superior to the conventional algorithm. Purpose -This paper proposes a modified UKF algorithm to estimate the parameters of a dynamic system Design/methodology/approach -In this paper, by changing the point of view to system modeling, an improved version of the UKF-based method was presented. In the proposed version of the UKF algorithm, unlike the traditional one, the whole of the measurement signal samples is used as input in each stage of the estimation process. By doing this, throughout the entire simulation time i.e. within the entire time in which the measured signals exist, the unknown parameters are considered constant. Findings -The effectiveness of the proposed method is demonstrated through an illustrative example in parameter estimation of a TGOV1 Turbine-governor system as a case study. The proposed approach overcomes the shortcomings of the conventional method and shows high efficiency. It can be a useful substitute for the conventional UKF method. Originality/value -The proposed method is an evolutionary method whose evolution principles do not random behavior. It is based on Kalman filter rules and relations and enjoys all the advantages of this filter. It looks similar to a smoothing approach whose practical result is to filter out (in the mean sense) estimates with little physical meaning that normally arise when the number of state-variables is increased, that ultimately might lead the filter to diverge.