Joint and Dual Estimation of States and Parameters with Extended and Unscented Kalman Filters

Switching Kalman filter for damage estimation in the presence of sensor faults

“…From past experience with JEKF [40], the state and parameter covariances are selected as, Q v = 10 10 × I, and Q θ = 10 3 × I, and have been maintained throughout the article unless mentioned otherwise. However existing methods [41][42][43] that identify and quantify Q u , Q v , and Q θ can also be opted.…”

How Not to Make the Joint Extended Kalman Filter Fail with Unstructured Mechanistic Models

“…It is composed of a process model and a measurement model along with error covariance matrices of the process ( Q ), measurement ( R ), and state ( P ) [ 3 , 4 ]. The EKF, beyond state estimation, is also used for the parameter estimation (parameter evolution [ 5 ]) of nonlinear systems (process models) considering a single joint state variable vector, which includes both the states and parameters of the process model [ 6 , 7 , 8 ]. This approach is called the j oint estimation of states and parameters with an e xtended K alman f ilter (JEKF).…”

“…The first discussions and applications of the JEKF approach started in the 1960s for the estimation of linear systems (in which there is a bilinear relation between the states and parameters) [ 6 , 7 , 8 , 9 , 10 ]. However, the JEKF is still very popular, with several new applications in different areas [ 5 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ], and with unsolved problems [ 22 , 23 ]. Furthermore, the JEKF has been established as the least expensive nonlinear estimator for moderate-size systems in terms of computational cost because the practical implementation of adaptive controllers using microcontrollers (and/or minicomputers and/or microprocessors) requires numerically economical and robust algorithms, such as the JEKF [ 11 , 24 ].…”

“…In JEKF, the system states and the set of model parameters for the dynamical system are simultaneously corrected based only on the observed noisy signal . It is essential to point out that we consider JEKF as an approach for parameter evolution [ 5 ], because it cannot guarantee convergence in some cases [ 6 ]. However, it can guarantee the evolution of the parameters based on the following equation [ 5 ] where the parameters are defined as random variables with perturbation (noise) added at each time step.…”

“…It is essential to point out that we consider JEKF as an approach for parameter evolution [ 5 ], because it cannot guarantee convergence in some cases [ 6 ]. However, it can guarantee the evolution of the parameters based on the following equation [ 5 ] where the parameters are defined as random variables with perturbation (noise) added at each time step. This parameter evolution can be enough to update the process model parameters when we are near the optimal parameters regarding a specific condition.…”