diff --git a/src/pyrecest/filters/ekf_spline_tracker.py b/src/pyrecest/filters/ekf_spline_tracker.py
index b9ddd48de..b9d24e031 100644
--- a/src/pyrecest/filters/ekf_spline_tracker.py
+++ b/src/pyrecest/filters/ekf_spline_tracker.py
@@ -1,4 +1,5 @@
 # pylint: disable=duplicate-code,no-member,no-name-in-module,too-many-lines
+from math import isfinite
 from numbers import Integral
 
 from pyrecest.backend import (
@@ -125,8 +126,8 @@ def __init__(
             "closest_point_iterations",
             0,
         )
-        if self.finite_difference_step <= 0.0:
-            raise ValueError("finite_difference_step must be positive")
+        if not isfinite(self.finite_difference_step) or self.finite_difference_step <= 0.0:
+            raise ValueError("finite_difference_step must be finite and positive")
         self.last_quadratic_form = None
         self._sync_state_views()
 
@@ -585,4 +586,4 @@ def get_bounding_box(self, n=100):
         }
 
 
-EkfSplineTracker = EKFSplineTracker
+EkfSplineTracker = EKFSplineTracker
\ No newline at end of file
diff --git a/src/pyrecest/filters/mem_soekf_tracker.py b/src/pyrecest/filters/mem_soekf_tracker.py
index 0e69834d7..3ede7f99a 100644
--- a/src/pyrecest/filters/mem_soekf_tracker.py
+++ b/src/pyrecest/filters/mem_soekf_tracker.py
@@ -1,5 +1,7 @@
 from __future__ import annotations
 
+from math import isfinite
+
 # pylint: disable=no-name-in-module,no-member,duplicate-code,too-many-locals
 from pyrecest.backend import (
     array,
@@ -29,8 +31,8 @@ class MEMSOEKFTracker(MEMEKFTracker):
     def __init__(self, *args, finite_difference_step=1e-5, **kwargs):
         super().__init__(*args, **kwargs)
         self.finite_difference_step = float(finite_difference_step)
-        if self.finite_difference_step <= 0.0:
-            raise ValueError("finite_difference_step must be positive")
+        if not isfinite(self.finite_difference_step) or self.finite_difference_step <= 0.0:
+            raise ValueError("finite_difference_step must be finite and positive")
 
     @staticmethod
     def _extent_transform_from_shape(shape_state):
diff --git a/tests/filters/test_finite_difference_step_validation.py b/tests/filters/test_finite_difference_step_validation.py
new file mode 100644
index 000000000..451d865d6
--- /dev/null
+++ b/tests/filters/test_finite_difference_step_validation.py
@@ -0,0 +1,48 @@
+import unittest
+
+# pylint: disable=no-name-in-module,no-member
+import pyrecest.backend
+from pyrecest.backend import array, diag
+from pyrecest.filters import EKFSplineTracker, MEMSOEKFTracker
+
+
+@unittest.skipIf(
+    pyrecest.backend.__backend_name__ != "numpy",
+    reason="Finite-difference tracker validation tests use the NumPy backend.",
+)
+class TestFiniteDifferenceStepValidation(unittest.TestCase):
+    @staticmethod
+    def _make_mem_soekf(finite_difference_step):
+        return MEMSOEKFTracker(
+            array([0.0, 0.0, 1.0, -1.0]),
+            diag(array([0.1, 0.1, 0.01, 0.01])),
+            array([0.0, 2.0, 1.0]),
+            diag(array([0.01, 0.1, 0.2])),
+            measurement_matrix=array(
+                [
+                    [1.0, 0.0, 0.0, 0.0],
+                    [0.0, 1.0, 0.0, 0.0],
+                ]
+            ),
+            finite_difference_step=finite_difference_step,
+        )
+
+    def test_mem_soekf_rejects_nonfinite_step(self):
+        for invalid_step in (float("nan"), float("inf"), float("-inf")):
+            with self.subTest(step=invalid_step), self.assertRaisesRegex(
+                ValueError,
+                "finite_difference_step",
+            ):
+                self._make_mem_soekf(invalid_step)
+
+    def test_ekf_spline_rejects_nonfinite_step(self):
+        for invalid_step in (float("nan"), float("inf"), float("-inf")):
+            with self.subTest(step=invalid_step), self.assertRaisesRegex(
+                ValueError,
+                "finite_difference_step",
+            ):
+                EKFSplineTracker(finite_difference_step=invalid_step)
+
+
+if __name__ == "__main__":
+    unittest.main()