Accurate calibration of inertial sensor biases is critical for preventing accumulated error growth in inertial navigation systems (INS). Conventional approaches, such as Kalman filtering and its variants, often involve significant computational complexity, dependence on precise noise modeling, and require extensive parameter tuning to ensure stability and convergence. To address these challenges, this paper presents a novel online algebraic calibration method that reformulates the INS error dynamics to directly isolate and express accelerometer and gyroscope bias terms in a closed-form manner. The proposed algorithm estimates biases by solving a deterministic system of linear equations constructed from the error states between a reference and a dependent navigation system, thereby completely eliminating the need for iterative filtering or probabilistic updates. Comprehensive simulation studies under both stationary and cruise flight conditions demonstrate the method’s high accuracy, rapid convergence, and robustness against measurement noise. The results further highlight its excellent numerical stability and adaptability to time-varying sensor characteristics. Overall, the proposed approach achieves precise and consistent bias estimation with minimal computational cost, providing a fast, stable, and resource-efficient alternative for real-time implementation in safety-critical applications such as aviation, autonomous vehicles, and robotics.