diff --git a/src/pyrecest/filters/hyperhemispherical_grid_filter.py b/src/pyrecest/filters/hyperhemispherical_grid_filter.py
index 44ee345f6..9f45ad215 100644
--- a/src/pyrecest/filters/hyperhemispherical_grid_filter.py
+++ b/src/pyrecest/filters/hyperhemispherical_grid_filter.py
@@ -196,7 +196,8 @@ def update_identity(self, meas_noise, z):
 
         Supported noise: :class:`HyperhemisphericalWatsonDistribution`,
         :class:`WatsonDistribution`, :class:`VonMisesFisherDistribution`
-        for measurements on the equator, symmetric :class:`HypersphericalMixture`.
+        for measurements on the equator, symmetric two-component
+        :class:`HypersphericalMixture` of VMF distributions.
 
         Parameters
         ----------
@@ -233,9 +234,22 @@ def update_identity(self, meas_noise, z):
             isinstance(meas_noise, HypersphericalMixture)
             and len(meas_noise.dists) == 2
             and all(abs(w - 0.5) < 1e-12 for w in meas_noise.w)
+            and all(
+                isinstance(dist, VonMisesFisherDistribution)
+                for dist in meas_noise.dists
+            )
+            and allclose(
+                meas_noise.dists[0].mu, -meas_noise.dists[1].mu, atol=1e-12
+            )
+            and meas_noise.dists[0].kappa == meas_noise.dists[1].kappa
         ):
-            meas_noise.dists[0].mu = z
-            meas_noise.dists[1].mu = -z
+            meas_noise = HypersphericalMixture(
+                [
+                    meas_noise.dists[0].set_mode(z),
+                    meas_noise.dists[1].set_mode(-z),
+                ],
+                meas_noise.w,
+            )
         else:
             raise ValueError(
                 "UpdateIdentity:UnsupportedNoise: unsupported measurement noise type."
@@ -283,7 +297,8 @@ def sys_noise_to_transition_density(d_sys, no_grid_points):
         ----------
         d_sys : AbstractDistribution
             Supported: :class:`HyperhemisphericalWatsonDistribution`,
-            :class:`WatsonDistribution`, symmetric :class:`HypersphericalMixture`.
+            :class:`WatsonDistribution`, symmetric two-component
+            :class:`HypersphericalMixture` of VMF distributions.
         no_grid_points : int
             Number of grid points on the hemisphere.
 
@@ -309,6 +324,10 @@ def trans_cp(grid, _grid):
             isinstance(d_sys, HypersphericalMixture)
             and len(d_sys.dists) == 2
             and all(abs(w - 0.5) < 1e-12 for w in d_sys.w)
+            and all(
+                isinstance(dist, VonMisesFisherDistribution)
+                for dist in d_sys.dists
+            )
             and allclose(d_sys.dists[0].mu, -d_sys.dists[1].mu, atol=1e-12)
             and d_sys.dists[0].kappa == d_sys.dists[1].kappa
         ):
diff --git a/tests/filters/test_hyperhemispherical_grid_filter_mixture_update.py b/tests/filters/test_hyperhemispherical_grid_filter_mixture_update.py
new file mode 100644
index 000000000..006cd101c
--- /dev/null
+++ b/tests/filters/test_hyperhemispherical_grid_filter_mixture_update.py
@@ -0,0 +1,93 @@
+import unittest
+
+import pyrecest.backend
+from pyrecest.backend import allclose, array
+from pyrecest.distributions.hypersphere_subset.hyperspherical_mixture import (
+    HypersphericalMixture,
+)
+from pyrecest.distributions.hypersphere_subset.von_mises_fisher_distribution import (
+    VonMisesFisherDistribution,
+)
+from pyrecest.distributions.hypersphere_subset.watson_distribution import (
+    WatsonDistribution,
+)
+from pyrecest.filters.hyperhemispherical_grid_filter import (
+    HyperhemisphericalGridFilter,
+)
+
+
+@unittest.skipIf(
+    pyrecest.backend.__backend_name__ == "jax",  # pylint: disable=no-member
+    reason="HyperhemisphericalGridFilter is not supported on the JAX backend",
+)
+class TestHyperhemisphericalGridFilterMixtureUpdate(unittest.TestCase):
+    def setUp(self):
+        self.pole = array([0.0, 0.0, 1.0])
+        self.measurement = array([1.0, 0.0, 0.0])
+
+    def _symmetric_vmf_mixture(self, kappa=3.0):
+        return HypersphericalMixture(
+            [
+                VonMisesFisherDistribution(self.pole, kappa),
+                VonMisesFisherDistribution(-self.pole, kappa),
+            ],
+            array([0.5, 0.5]),
+        )
+
+    def test_update_identity_does_not_mutate_measurement_noise(self):
+        filt = HyperhemisphericalGridFilter(20, 2)
+        meas_noise = self._symmetric_vmf_mixture()
+
+        filt.update_identity(meas_noise, self.measurement)
+
+        self.assertTrue(bool(allclose(meas_noise.dists[0].mu, self.pole)))
+        self.assertTrue(bool(allclose(meas_noise.dists[1].mu, -self.pole)))
+
+    def test_update_identity_rejects_unequal_vmf_concentrations(self):
+        filt = HyperhemisphericalGridFilter(20, 2)
+        meas_noise = HypersphericalMixture(
+            [
+                VonMisesFisherDistribution(self.pole, 2.0),
+                VonMisesFisherDistribution(-self.pole, 3.0),
+            ],
+            array([0.5, 0.5]),
+        )
+
+        with self.assertRaisesRegex(ValueError, "UnsupportedNoise"):
+            filt.update_identity(meas_noise, self.measurement)
+
+    def test_update_identity_rejects_nonantipodal_vmf_components(self):
+        filt = HyperhemisphericalGridFilter(20, 2)
+        meas_noise = HypersphericalMixture(
+            [
+                VonMisesFisherDistribution(self.pole, 3.0),
+                VonMisesFisherDistribution(array([1.0, 0.0, 0.0]), 3.0),
+            ],
+            array([0.5, 0.5]),
+        )
+
+        with self.assertRaisesRegex(ValueError, "UnsupportedNoise"):
+            filt.update_identity(meas_noise, self.measurement)
+
+    def test_update_identity_rejects_nonunit_measurement_for_mixture(self):
+        filt = HyperhemisphericalGridFilter(20, 2)
+        meas_noise = self._symmetric_vmf_mixture()
+
+        with self.assertRaisesRegex(ValueError, "normalized"):
+            filt.update_identity(meas_noise, array([2.0, 0.0, 0.0]))
+
+    def test_prediction_rejects_non_vmf_symmetric_mixture(self):
+        d_sys = HypersphericalMixture(
+            [
+                WatsonDistribution(self.pole, 3.0),
+                WatsonDistribution(-self.pole, 3.0),
+            ],
+            array([0.5, 0.5]),
+        )
+
+        with self.assertRaisesRegex(ValueError, "unsupported distribution"):
+            HyperhemisphericalGridFilter.sys_noise_to_transition_density(d_sys, 20)
+
+
+if __name__ == "__main__":
+    unittest.main()