diff --git a/cartographer/mapping/imu_tracker.cc b/cartographer/mapping/imu_tracker.cc
index a6df73e..39cac08 100644
--- a/cartographer/mapping/imu_tracker.cc
+++ b/cartographer/mapping/imu_tracker.cc
@@ -42,7 +42,7 @@ void ImuTracker::Advance(const common::Time time) {
       transform::AngleAxisVectorToRotationQuaternion(
           Eigen::Vector3d(imu_angular_velocity_ * delta_t));
   orientation_ = (orientation_ * rotation).normalized();
-  gravity_vector_ = rotation.inverse() * gravity_vector_;
+  gravity_vector_ = rotation.conjugate() * gravity_vector_;
   time_ = time;
 }
 
@@ -61,7 +61,7 @@ void ImuTracker::AddImuLinearAccelerationObservation(
   // Change the 'orientation_' so that it agrees with the current
   // 'gravity_vector_'.
   const Eigen::Quaterniond rotation = Eigen::Quaterniond::FromTwoVectors(
-      gravity_vector_, orientation_.inverse() * Eigen::Vector3d::UnitZ());
+      gravity_vector_, orientation_.conjugate() * Eigen::Vector3d::UnitZ());
   orientation_ = (orientation_ * rotation).normalized();
   CHECK_GT((orientation_ * gravity_vector_).z(), 0.);
   CHECK_GT((orientation_ * gravity_vector_).normalized().z(), 0.99);