  This paper considers the safety-critical navigation problem with Signal
Temporal Logic (STL) tasks. We developed an explicit reference governor-guided
control barrier function (ERG-guided CBF) method that enables the application
of first-order CBFs to high-order linearizable systems. This method
significantly reduces the conservativeness of the existing CBF approaches for
high-order systems. Furthermore, our framework provides safety-critical
guarantees in the sense of obstacle avoidance by constructing the margin of
safety and updating direction of safe evolution in the agent's state space. To
improve control performance and enhance STL satisfaction, we employ efficient
gradient-based methods for iteratively learning optimal parameters of
ERG-guided CBF. We validate the algorithm through both high-order linear and
nonlinear systems. A video demonstration can be found on:
\url{https://youtu.be/ZRmsA2FeFR4}
