diff --git a/gtsam/navigation/Scenario.h b/gtsam/navigation/Scenario.h
index e4b380ff9..acb8f46f5 100644
--- a/gtsam/navigation/Scenario.h
+++ b/gtsam/navigation/Scenario.h
@@ -57,10 +57,13 @@ class Scenario {
 class ConstantTwistScenario : public Scenario {
  public:
   /// Construct scenario with constant twist [w,v]
-  ConstantTwistScenario(const Vector3& w, const Vector3& v)
-      : twist_((Vector6() << w, v).finished()), a_b_(w.cross(v)) {}
+  ConstantTwistScenario(const Vector3& w, const Vector3& v,
+                        const Pose3& nTb0 = Pose3())
+      : twist_((Vector6() << w, v).finished()), a_b_(w.cross(v)), nTb0_(nTb0) {}
 
-  Pose3 pose(double t) const override { return Pose3::Expmap(twist_ * t); }
+  Pose3 pose(double t) const override {
+    return nTb0_ * Pose3::Expmap(twist_ * t);
+  }
   Vector3 omega_b(double t) const override { return twist_.head<3>(); }
   Vector3 velocity_n(double t) const override {
     return rotation(t).matrix() * twist_.tail<3>();
@@ -70,6 +73,7 @@ class ConstantTwistScenario : public Scenario {
  private:
   const Vector6 twist_;
   const Vector3 a_b_;  // constant centripetal acceleration in body = w_b * v_b
+  const Pose3 nTb0_;
 };
 
 /// Accelerating from an arbitrary initial state, with optional rotation
diff --git a/gtsam/navigation/tests/testScenario.cpp b/gtsam/navigation/tests/testScenario.cpp
index bc965b058..ef30552ea 100644
--- a/gtsam/navigation/tests/testScenario.cpp
+++ b/gtsam/navigation/tests/testScenario.cpp
@@ -15,8 +15,8 @@
  * @author  Frank Dellaert
  */
 
-#include <gtsam/navigation/Scenario.h>
 #include <gtsam/base/numericalDerivative.h>
+#include <gtsam/navigation/Scenario.h>
 
 #include <CppUnitLite/TestHarness.h>
 #include <boost/bind.hpp>
@@ -99,6 +99,29 @@ TEST(Scenario, Loop) {
   EXPECT(assert_equal(Point3(0, 0, 2 * R), T30.translation(), 1e-9));
 }
 
+/* ************************************************************************* */
+TEST(Scenario, LoopWithInitialPose) {
+  // Forward velocity 2m/s
+  // Pitch up with angular velocity 6 kDegree/sec (negative in FLU)
+  const double v = 2, w = 6 * kDegree;
+  const Vector3 W(0, -w, 0), V(v, 0, 0);
+  const Rot3 nRb0 = Rot3::yaw(M_PI);
+  const Pose3 nTb0(nRb0, Point3(1, 2, 3));
+  const ConstantTwistScenario scenario(W, V, nTb0);
+
+  const double T = 30;
+  EXPECT(assert_equal(W, scenario.omega_b(T), 1e-9));
+  EXPECT(assert_equal(V, scenario.velocity_b(T), 1e-9));
+  EXPECT(assert_equal(W.cross(V), scenario.acceleration_b(T), 1e-9));
+
+  // R = v/w, so test if loop crests at 2*R
+  const double R = v / w;
+  const Pose3 T30 = scenario.pose(30);
+  EXPECT(
+      assert_equal(nRb0 * Rot3::Rodrigues(0, M_PI, 0), T30.rotation(), 1e-9));
+  EXPECT(assert_equal(Point3(1, 2, 3 + 2 * R), T30.translation(), 1e-9));
+}
+
 /* ************************************************************************* */
 TEST(Scenario, Accelerating) {
   // Set up body pointing towards y axis, and start at 10,20,0 with velocity