diff --git a/src/pyrecest/filters/candidate_mixture.py b/src/pyrecest/filters/candidate_mixture.py
index a5f2f5d6a..2ed8021a9 100644
--- a/src/pyrecest/filters/candidate_mixture.py
+++ b/src/pyrecest/filters/candidate_mixture.py
@@ -99,6 +99,17 @@ def __post_init__(self) -> None:
             covariances = covariances.copy()
         if not np.all(np.isfinite(covariances)):
             raise ValueError("covariances must contain only finite values")
+        covariance_transposes = np.swapaxes(covariances, -1, -2)
+        covariance_scale = np.maximum(
+            np.maximum(np.abs(covariances), np.abs(covariance_transposes)), 1.0
+        )
+        with np.errstate(over="ignore", under="ignore", invalid="ignore"):
+            relative_asymmetry = np.abs(
+                covariances / covariance_scale
+                - covariance_transposes / covariance_scale
+            )
+        if np.any(relative_asymmetry > 1e-12):
+            raise ValueError("covariances must be symmetric")
         covariances = np.stack([_symmetrize(value) for value in covariances])
         try:
             cholesky = np.linalg.cholesky(covariances)
diff --git a/tests/filters/test_candidate_mixture_covariance_symmetry.py b/tests/filters/test_candidate_mixture_covariance_symmetry.py
new file mode 100644
index 000000000..d3f217590
--- /dev/null
+++ b/tests/filters/test_candidate_mixture_covariance_symmetry.py
@@ -0,0 +1,48 @@
+import unittest
+
+import numpy as np
+from pyrecest.filters.candidate_mixture import GaussianMixtureMeasurementFactor
+
+
+class GaussianMixtureMeasurementCovarianceSymmetryTest(unittest.TestCase):
+    def test_rejects_nonsymmetric_shared_covariance(self):
+        nonsymmetric = np.array([[2.0, 1.0], [0.0, 2.0]])
+
+        with self.assertRaisesRegex(ValueError, "covariances must be symmetric"):
+            GaussianMixtureMeasurementFactor(
+                means=np.zeros((2, 2)),
+                covariances=nonsymmetric,
+            )
+
+    def test_rejects_nonsymmetric_component_covariance(self):
+        covariances = np.array(
+            [
+                np.eye(2),
+                [[2.0, 1.0], [0.0, 2.0]],
+            ]
+        )
+
+        with self.assertRaisesRegex(ValueError, "covariances must be symmetric"):
+            GaussianMixtureMeasurementFactor(
+                means=np.zeros((2, 2)),
+                covariances=covariances,
+            )
+
+    def test_tolerates_roundoff_scale_asymmetry(self):
+        covariance = np.array([[2.0, 1.0 + 1e-13], [1.0, 2.0]])
+
+        factor = GaussianMixtureMeasurementFactor(
+            means=np.zeros((1, 2)),
+            covariances=covariance,
+        )
+
+        np.testing.assert_allclose(
+            factor.covariances[0],
+            0.5 * (covariance + covariance.T),
+            rtol=0.0,
+            atol=0.0,
+        )
+
+
+if __name__ == "__main__":
+    unittest.main()