In data communication, limited communication resources often lead to measurement bias, which adversely affects subsequent system estimation if not effectively handled. This paper proposes a novel bias calibration algorithm under communication constraints to achieve accurate system states of the interested system. An output-based event-triggered scheme is first employed to alleviate transmission burden. Accounting for the limited-communication-induced measurement bias, a novel bias calibration algorithm following the Kalman filtering line is developed to restrain the effect of the measurement bias on system estimation, thereby achieving accurate system state estimates. Subsequently, the Field Programmable Gate Array (FPGA) implementation of the proposed algorithm is also realized with the hope of providing fast bias calibration in practical scenarios. A simulation about a numerical example and a practical example (for gyroscope’s angular velocity bias calibration) on MATLAB is provided to demonstrate the feasibility and effectiveness of the proposed algorithm.