This paper considers constant bias injection attacks on the glucose sensor deployed in an artificial pancreas system. The main challenge with such apparently simple attacks is that they are detectable for only a limited duration if the system is linear and has an integrator. More formally put, such attacks are steady-state stealthy. To address this issue, we propose a method to design a bias-sensitive Kalman filter based on the Kullback-Leibler divergence metric. The resulting filter outperforms the nominal Kalman filter for attack detection as illustrated by numerical simulations on a realistic model.