EKF- and UKF-Based Estimators for Radar System

In radar, the measurements (like the range and radial velocity) are determined from the time delay and Doppler shift. Since the time delay and Doppler shift are estimated from the phase of the received echo, the concerned estimation problem is nonlinear. Consequently, the conventional estimator based on the fast Fourier transform (FFT) is prone to yield high estimation errors. Recently, nonlinear estimators based on kernel least mean square (KLMS) are introduced and found to outperform the conventional estimator. However, estimators based on KLMS are susceptible to incorrect choice of various system parameters. Thus, to mitigate the limitation of existing estimators, in this paper, two efficient low-complexity nonlinear estimators, namely, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are proposed. The EKF is advantageous due to its implementation simplicity; however, it suffers from the poor representation of the nonlinear functions by the first-order linearization, whereas UKF outperforms the EKF and offers better stability due to exact consideration of the system nonlinearity. Simulation results reveal improved accuracy achieved by the proposed EKF- and UKF-based estimators.

Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method

Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method