Extended Kalman Filter Design for Tracking Time-of-Flight and Clock Offsets in a Two-Way Ranging System

As radio frequency (RF) hardware continues to improve, two-way ranging (TWR) has become a viable approach for high-precision ranging applications. The precision of a TWR system is fundamentally limited by estimates of the time offset T between two platforms and the time delay tau of a signal propagating between them. In previous work, we derived a family of optimal "one-shot" joint delay-offset estimators and demonstrated that they reduce to a system of linear equations under reasonable assumptions. These estimators are simple and computationally efficient but are also susceptible to channel impairments that obstruct one or more measurements. In this work, we formulate an extended Kalman filter (EKF) for this class of estimators that specifically addresses this limitation. Unlike a generic KF approach, the proposed solution specifically integrates the estimation process to minimize the computational complexity. We benchmark the proposed first- and second-order EKF solutions against the existing one-shot estimators in a MATLAB Monte Carlo simulation environment. We demonstrate that the proposed solution achieves comparable estimation performance and, in the case of the second-order solution, reduces the computation time by an order of magnitude.