Compensation of time-varying clock-offset in a long baseline navigation

In a long baseline (LBL) navigation, the range between a navigation subject and an acoustic transponder is calculated through time-of-flight (ToF) measurement. To obtain an accurate result, it is of importance that the clocks utilized in the measurements are synchronous. The presence of any offset among them would result in a pseudorange, i.e. range plus its bias(es). Since the multiplying factor in this ToF measurement is the sound speed (around 1500 m/s), even a minuscule clock-offset may result in a pseudorange with noticeable bias. This result could be further worsened when the clock-offset varies over time. If clock recalibration is not an available option, this offset has to be modeled and compensated. In this paper, the presence of clock-offset in a LBL navigation is addressed. Its main take is to consider the clock-offset as a time-varying case. Specifically, the behavior of the clock is modeled as an autoregressive filter. The dynamics of this offset is then included into the ToF measurements and kinematics of an autonomous underwater vehicle (AUV). This leads to a state-space formulation of the system. To check the system’s observability, the so-called graphic approach is implemented instead of the conventional rank test. Finally, a standard discrete Kalman filter is deployed as the state estimator. By simulation, it is demonstrated that the estimator managed to compensate the offset and provided localization with accuracies less than 1 m.