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With high penetration of inverter-based renewable energy sources (IBRES) power system dynamics began to occur within shorter time frames. However, existing monitoring tools that rely on phasor measurements lack sufficient resolution to monitor such fast transients in the grid. To address this issue, this paper proposes a weighted least absolute value (WLAV) estimation-based monitoring tool that uses the same discrete samples of measured voltages and currents that are used by the phasor measurement units (PMU). Such samples are in general not made available to the users by the PMUs but instead they are processed for a full or fraction of a cycle to obtain the positive sequence phasors. Given that these discrete samples are readily available, there is little reason not to use them for tracking fast voltage and current transients introduced by inverter-based renewable energy sources. Performance of the proposed estimator is illustrated using a small IEEE 30-bus system modeled using appropriate discrete-time components and simulated measurements with Gaussian noise as well as gross errors.