This paper proposes an adaptive filtering framework for real-Time estimation of pathological hand tremors such as those caused by Parkinson's disease (PD) and Essential Tremor (ET). The proposed framework is designed based on Enhanced Band-limited Multiple Fourier Linear Combiner (E-BMFLC), a recently proposed state-of-The-Art tremor estimation algorithm. Conventional BMFLC-based filter (and the E-BMFLC technique) are developed based on application of recursive Least Mean Square (LMS) algorithm. There exist variations of BMFLC-based filters that replace LMS approach by the Kalman Filter (KF) to enhance the performance. However, despite the improved performance, the KF increases the computational overhead challenging real-Time implementation which is essential in several application such as robotics-Assisted tremor suppression. The proposed framework, referred to as the Reduced-order Kalman-based E-BMFLC (RKE-BMFLC), addresses this gap. In particular, we propose a two-step development. First an extension of the E-BMFLC is proposed where classical KF is incorporated in place of the LMS algorithm; then we propose a specifically-designed reduced-order KF implementation to address the computational overhead. Evaluated through experimental pathological tremor data, the proposed RKE-BMFLC technique significantly reduces computational complexity of the conventional KF (for E-BMFLC filter) while is capable of providing improved accuracy level in comparison to the recently-developed LMS-based E-BMFLC technique.