Accurate state of charge (SOC) estimation is helpful for battery management systems to extend batteries’ lifespan and ensure the safety batteries. However, due pseudo-positive definiteness covariance matrix noise statistics error accumulation, SOC lithium-ion batteries usually inaccurate or even divergent using Kalman filters, such as unscented filter (UKF) square-root (SRUKF). To resolve this ...

Second order necessary and sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in Milyutin and Osmolovskii (1998). These conditions require the positive (semi)-definiteness of a certain quadratic form on the finite-dimensional critical cone. Using a suitable transformation via a linear matrix ODE, Maurer and Osmolovskii (2003, 2004) have dev...

Owing to several uncertainties in the modelling of a system, checking for “robust stability” is, in fact, a more practical goal for any designer. In this, instead of a single matrix A, a family of matrices (A + δA) has to be checked for negative definiteness. This led us to the question “How long does a computer take to check the sign definiteness of a family of matrices?” Mathematically, we st...

There are multiple reasons why anisotropic basis functions may be needed or be more appropriate. The most obvious is that if the basis function is to be defined on Rn × T then there is no natural norm on this space that would reflect the unique properties of time. A second reason is that function being interpolated or approximated may incorporate a directional dependence. Thirdly, differentiabi...

Contrary to most earlier claims in the literature, we demonstrate that crucial aspects of definiteness are overtly marked in classifier languages and follow recently established typological patterns of definiteness marking. Specifically, demonstrative descriptions are used for familiar definites while definite bare nouns are used only in contexts licensed by uniqueness. In classifier languages ...

Parsimonious modelling of the within-subject covariance structure while heeding its positive-definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covaria...