diff --git a/gtsam/linear/tests/testNoiseModel.cpp b/gtsam/linear/tests/testNoiseModel.cpp
index f1830f37f..7d2c283a6 100644
--- a/gtsam/linear/tests/testNoiseModel.cpp
+++ b/gtsam/linear/tests/testNoiseModel.cpp
@@ -14,6 +14,7 @@
  * @date Jan 13, 2010
  * @author Richard Roberts
  * @author Frank Dellaert
+ * @author Fan Jiang
  */
 
 
@@ -504,6 +505,22 @@ TEST(NoiseModel, robustFunctionCauchy)
   DOUBLES_EQUAL(0.490258914416017, cauchy->loss(error4), 1e-8);
 }
 
+TEST(NoiseModel, robustFunctionAsymmetricCauchy)
+{
+  const double k = 5.0, error1 = 1.0, error2 = 10.0, error3 = -10.0, error4 = -1.0;
+  const mEstimator::AsymmetricCauchy::shared_ptr cauchy = mEstimator::AsymmetricCauchy::Create(k);
+  DOUBLES_EQUAL(0.961538461538461, cauchy->weight(error1), 1e-8);
+  DOUBLES_EQUAL(0.2000, cauchy->weight(error2), 1e-8);
+  // Test negative value to ensure we take absolute value of error.
+  DOUBLES_EQUAL(10.0, cauchy->weight(error3), 1e-8);
+  DOUBLES_EQUAL(1.0, cauchy->weight(error4), 1e-8);
+
+  DOUBLES_EQUAL(0.490258914416017, cauchy->loss(error1), 1e-8);
+  DOUBLES_EQUAL(20.117973905426254, cauchy->loss(error2), 1e-8);
+  DOUBLES_EQUAL(50.0, cauchy->loss(error3), 1e-8);
+  DOUBLES_EQUAL(0.5, cauchy->loss(error4), 1e-8);
+}
+
 TEST(NoiseModel, robustFunctionGemanMcClure)
 {
   const double k = 1.0, error1 = 1.0, error2 = 10.0, error3 = -10.0, error4 = -1.0;
@@ -551,6 +568,22 @@ TEST(NoiseModel, robustFunctionTukey)
   DOUBLES_EQUAL(0.480266666666667, tukey->loss(error4), 1e-8);
 }
 
+TEST(NoiseModel, robustFunctionAsymmetricTukey)
+{
+  const double k = 5.0, error1 = 1.0, error2 = 10.0, error3 = -10.0, error4 = -1.0;
+  const mEstimator::AsymmetricTukey::shared_ptr tukey = mEstimator::AsymmetricTukey::Create(k);
+  DOUBLES_EQUAL(0.9216, tukey->weight(error1), 1e-8);
+  DOUBLES_EQUAL(0.0, tukey->weight(error2), 1e-8);
+  // Test negative value to ensure we take absolute value of error.
+  DOUBLES_EQUAL(10.0, tukey->weight(error3), 1e-8);
+  DOUBLES_EQUAL(1.0, tukey->weight(error4), 1e-8);
+
+  DOUBLES_EQUAL(0.480266666666667, tukey->loss(error1), 1e-8);
+  DOUBLES_EQUAL(4.166666666666667, tukey->loss(error2), 1e-8);
+  DOUBLES_EQUAL(50.0, tukey->loss(error3), 1e-8);
+  DOUBLES_EQUAL(0.5, tukey->loss(error4), 1e-8);
+}
+
 TEST(NoiseModel, robustFunctionDCS)
 {
   const double k = 1.0, error1 = 1.0, error2 = 10.0;