From d2915df15dceadfa45fd6775c2f60d31ddf4a788 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Thu, 6 Aug 2026 13:10:22 +0800
Subject: [PATCH 1/3] Reject undefined axial Kalman mean updates

---
 src/pyrecest/filters/axial_kalman_filter.py | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/src/pyrecest/filters/axial_kalman_filter.py b/src/pyrecest/filters/axial_kalman_filter.py
index 8f8df3542..4c877213f 100644
--- a/src/pyrecest/filters/axial_kalman_filter.py
+++ b/src/pyrecest/filters/axial_kalman_filter.py
@@ -8,6 +8,9 @@
 from .abstract_axial_filter import AbstractAxialFilter
 
 
+_MIN_NORMALIZABLE_MEAN_NORM = 1e-12
+
+
 def _is_complex_array(value):
     """Return whether a NumPy/JAX array or PyTorch tensor has complex dtype."""
     dtype = getattr(value, "dtype", None)
@@ -128,7 +131,14 @@ def update_identity(self, gauss_v, z):
         mu_new = self._filter_state.mu + K @ (z - self._filter_state.mu)
         C_new = (eye(d) - K) @ self._filter_state.C
 
-        mu_new = mu_new / linalg.norm(mu_new)  # enforce unit vector
+        mu_new_norm = linalg.norm(mu_new)
+        if not bool(isfinite(mu_new_norm)):
+            raise ValueError("Axial Kalman update produced a non-finite posterior mean.")
+        if not bool(mu_new_norm > _MIN_NORMALIZABLE_MEAN_NORM):
+            raise ValueError(
+                "Axial Kalman update produced an undefined zero-length posterior mean."
+            )
+        mu_new = mu_new / mu_new_norm  # enforce unit vector
         self._filter_state = GaussianDistribution(mu_new, C_new, check_validity=False)
 
     def get_point_estimate(self):

From 4e8a2e2db0ea50c85a513d1cf1efc751670a676c Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Thu, 6 Aug 2026 13:10:35 +0800
Subject: [PATCH 2/3] Test zero-length axial Kalman update handling

---
 .../test_axial_kalman_filter_zero_mean.py     | 43 +++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 tests/filters/test_axial_kalman_filter_zero_mean.py

diff --git a/tests/filters/test_axial_kalman_filter_zero_mean.py b/tests/filters/test_axial_kalman_filter_zero_mean.py
new file mode 100644
index 000000000..67f8a689d
--- /dev/null
+++ b/tests/filters/test_axial_kalman_filter_zero_mean.py
@@ -0,0 +1,43 @@
+import unittest
+
+import numpy.testing as npt
+
+import pyrecest.backend
+from pyrecest.backend import array
+from pyrecest.distributions import GaussianDistribution
+from pyrecest.filters.axial_kalman_filter import AxialKalmanFilter
+
+
+class TestAxialKalmanFilterZeroMean(unittest.TestCase):
+    @unittest.skipIf(
+        pyrecest.backend.__backend_name__ == "pytorch",
+        reason="Not supported on this backend",  # pylint: disable=no-member
+    )
+    def test_update_rejects_zero_length_posterior_mean_atomically(self):
+        inv_sqrt_two = 2.0**-0.5
+        state_cov = array([[5.0, 2.0], [2.0, 1.0]])
+        noise_cov = array(
+            [
+                [2.0 - inv_sqrt_two, 1.0],
+                [1.0, (1.0 + inv_sqrt_two) / 2.0],
+            ]
+        )
+
+        axial_filter = AxialKalmanFilter()
+        axial_filter.filter_state = GaussianDistribution(
+            array([1.0, 0.0]), state_cov
+        )
+        prior_mu = axial_filter.filter_state.mu.copy()
+        prior_cov = axial_filter.filter_state.C.copy()
+        noise = GaussianDistribution(array([1.0, 0.0]), noise_cov)
+        measurement = array([inv_sqrt_two, inv_sqrt_two])
+
+        with self.assertRaisesRegex(ValueError, "zero-length posterior mean"):
+            axial_filter.update_identity(noise, measurement)
+
+        npt.assert_array_equal(axial_filter.filter_state.mu, prior_mu)
+        npt.assert_array_equal(axial_filter.filter_state.C, prior_cov)
+
+
+if __name__ == "__main__":
+    unittest.main()

From eb627170895253beb2d7e26da238c7db0ddc572f Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Thu, 6 Aug 2026 13:12:39 +0800
Subject: [PATCH 3/3] Format axial Kalman validation guard

---
 src/pyrecest/filters/axial_kalman_filter.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/pyrecest/filters/axial_kalman_filter.py b/src/pyrecest/filters/axial_kalman_filter.py
index 4c877213f..f21fc65e3 100644
--- a/src/pyrecest/filters/axial_kalman_filter.py
+++ b/src/pyrecest/filters/axial_kalman_filter.py
@@ -133,7 +133,9 @@ def update_identity(self, gauss_v, z):
 
         mu_new_norm = linalg.norm(mu_new)
         if not bool(isfinite(mu_new_norm)):
-            raise ValueError("Axial Kalman update produced a non-finite posterior mean.")
+            raise ValueError(
+                "Axial Kalman update produced a non-finite posterior mean."
+            )
         if not bool(mu_new_norm > _MIN_NORMALIZABLE_MEAN_NORM):
             raise ValueError(
                 "Axial Kalman update produced an undefined zero-length posterior mean."