Celestial navigation using time delay measurement is an innovative autonomous navigation method. To calculate the equivalent measurement, the numerical method needs to be applied, which is time-consuming. The event-triggered mechanism intermittently and aperiodically processes measurements by judging if the update error has changed drastically. However, its performance is greatly affected by the constant threshold. To solve this problem, a parameter-independent event-triggered implicit unscented Kalman filter (UKF) is proposed and applied to the celestial navigation using time delay measurement. The innovation at the current moment and the updated estimate covariance at the last moment are compared with the previous value instead of the constant threshold. The event is automatically triggered when the accuracy of the state estimate is low. Simulation results indicate that the proposed parameter-independent event-triggered implicit UKF can reduce the running time by reducing unnecessary measurement updates, whose performance will not be affected by any parameter or window size. In a word, the proposed method substitutes the dynamic threshold for the constant threshold, ensuring that its performance will not be affected by any parameter or window size.