A parallel approach is being proposed for the construction of a nonlinear-based state estimator for closed-loop systems failing the Hurwitz criteria during finite time intervals. The instability originates from sensor errors, and it is assumed that a Kalman-Bucy/Luenberger estimator is being processed in closed loop. It is shown that a bounded nonlinear state estimator can be constructed via nonlinear state transforms over a finite time interval, and makes use of the control input and the measured output of the destabilised closed-loop system. The filter presented provides an interesting new approach for the correction of state estimation due to sensor bias. In cases where the closed-loop plant remains stable, this approach is useful for dealing with pure sensor bias without the need for high gain filtering. The original uncontrolled open-loop system is assumed stable as a preemptive criterion throughout this study.