Biased Kalman Filter

In wireless positioning systems, non-line-of-sight (NLOS) error represents a common challenge that significantly increases positioning inaccuracy. To address this issue, the Biased Kalman Filter provides an effective solution. This filtering algorithm, grounded in state estimation theory, leverages prior information and real-time measurements to estimate system states while performing filtering operations to minimize errors. The implementation typically involves modifying the standard Kalman filter equations to incorporate bias estimation terms, where the bias component accounts for systematic NLOS errors. Key algorithmic enhancements include bias state augmentation in the state vector and adaptive covariance matrix adjustments. Through proper tuning of process noise and measurement noise parameters, the Biased Kalman Filter effectively mitigates NLOS errors, thereby improving both precision and accuracy in wireless positioning applications. The core implementation involves iterative prediction and correction steps, with additional bias compensation mechanisms integrated into the measurement update phase.