diff --git a/EKF/control.cpp b/EKF/control.cpp
index f6e1beebca..a3956d855f 100644
--- a/EKF/control.cpp
+++ b/EKF/control.cpp
@@ -1304,6 +1304,11 @@ void Ekf::controlFakePosFusion()
 			if (_control_status.flags.in_air && _control_status.flags.tilt_align) {
 				fake_pos_obs_var(0) = fake_pos_obs_var(1) = sq(fmaxf(_params.pos_noaid_noise, _params.gps_pos_noise));
 
+			} else if (_control_status.flags.vehicle_at_rest) {
+				// Accelerate tilt fine alignment by fusing more
+				// aggressively when the vehicle is at rest
+				fake_pos_obs_var(0) = fake_pos_obs_var(1) = sq(0.1f);
+
 			} else {
 				fake_pos_obs_var(0) = fake_pos_obs_var(1) = sq(0.5f);
 			}