IMM-UKF Versus Frequency Analysis [Past and Present

Real-Time Implementation of Nonlinear State-of-Charge Estimation Techniques for Hybrid Electric Vehicles

“…Consequently, for practical reasons the original problem is commonly relaxed to developing a model whose output can be made "as close as possible" (in some metric sense) to the output of the dynamic system. Different methods have been developed in the literature for both linear and nonlinear system identifications and [1,2,3,4,5,6]. A common characteristic of most of these methods is the use of a parameterized model where the parameters are recursively updated in real-time to minimize a performance index such as the output identification error.…”

“…During the time update, the current state and error covariance estimate are projected forward (in time) to obtain a priori estimate of the state in the next time step. Next, the new measurement is incorporated into this priori estimate value for calculating the posteriori estimate of the corresponding state during the measurement update [1,2,3,4,5,6]. However, the process to be estimated and the measurement relationship to the process can be nonlinear in practice.…”

“…The Unscented Kalman Filter (UKF) technique [2,3,4,5,6] is based on the unscented transformation (UT) and addresses the general problem of state estimation …”

“…These sample points completely capture the true mean and covariance of the Gaussian random state variable n k R x  , and are propagated through the true nonlinear system dynamics. The cloud of the transformed sample points' distribution captures the posterior mean and covariance accurately to the fourth order while the EKF only predicts with accuracy up to the second order for the posterior mean and fourth order for the covariance [2,5,6]. However, the UKF will make more accurate estimates only if the kurtosis and higher order moments in the state error distribution are significant.…”

“…However due to the high complexity, nonlinearity, time-variation, and uncertain behavior of the batteries in HEVs, it is quite difficult to achieve reliable, accurate and satisfactory estimation/prediction performance specifications using model-based approaches that rely on linear models or linearized models of the batteries of different chemistry, such as techniques that are based on Kalman filtering (KF) Extended Kalman filtering (EKF) [1]. Thus, there is a need to develop nonlinear model-based estimation techniques [1,2,3,4,5,6] that rely and are based on the true nonlinear model of the process.…”