Electric vehicles (EVs) have emerged as a promising solution for sustainable transportation. The high energy density, long cycle life, and low self-discharge rate of lithium-ion batteries make them an ideal choice for EVs. Recently, these batteries have been prone to faster decay in life span, leading to sudden failure of the battery. To avoid uncertainty among EV users with sudden battery failures, a robust health monitoring and prediction scheme is required for the EV battery management system. In this regard, the Unscented Kalman Filter (UKF)-based technique has been developed for accurate and reliable prediction of battery health status. The UKF approximates nonlinearity using a set of sigma points and propagates them via the nonlinear function to enhance battery health estimation accuracy. Furthermore, the UKF-based health estimation scheme considers the state of charge (SOC) and internal resistance of the battery. Here, the UKF-based health prediction technique is compared with the Extended Kalman filter (EKF) scheme. The robustness of the UKF and EKF-based health prognostic techniques were studied under varying initial SOC values. Under these abrupt changing conditions, the proposed UKF technique performed effectively in terms of state of health (SOH) prediction. Accurate SOH determination can help EV users to decide when the battery needs to be replaced or if adjustments need to be made to extend its life. Ultimately, accurate and reliable battery health estimation is essential in vehicular applications and plays a pivotal role in ensuring lithium-ion battery sustainability and minimizing environmental impacts.