diff --git a/src/pyrecest/filters/mem_rbpf_tracker.py b/src/pyrecest/filters/mem_rbpf_tracker.py
index 056ec5f9c..47e94d2c5 100644
--- a/src/pyrecest/filters/mem_rbpf_tracker.py
+++ b/src/pyrecest/filters/mem_rbpf_tracker.py
@@ -463,13 +463,16 @@ def _update_particle_weights(self, centered, meas_noise_cov, mult_var):
             marginal_cov = self._symmetrize(marginal_cov)
             if self.covariance_regularization > 0.0:
                 marginal_cov = marginal_cov + self.covariance_regularization * eye(2)
-            determinant = linalg.det(marginal_cov)
-            if float(determinant) <= 0.0:
+            covariance_eigenvalues = linalg.eigvalsh(marginal_cov)
+            if bool(backend_any(~isfinite(covariance_eigenvalues))) or bool(
+                backend_any(covariance_eigenvalues <= 0.0)
+            ):
                 log_likelihoods.append(array(-float("inf")))
                 continue
+            log_determinant = backend_sum(log(covariance_eigenvalues))
             inverse_cov = linalg.pinv(marginal_cov)
             quad = einsum("ma,ab,mb->m", centered, inverse_cov, centered)
-            log_likelihoods.append(-0.5 * backend_sum(log(determinant) + quad))
+            log_likelihoods.append(-0.5 * backend_sum(log_determinant + quad))
         log_likelihoods = array(log_likelihoods)
         log_weights = log(maximum(self.weights, 1e-300))
         self.weights = self._normalize_log_weights(log_weights + log_likelihoods)
diff --git a/tests/filters/test_mem_rbpf_log_weight_stability.py b/tests/filters/test_mem_rbpf_log_weight_stability.py
new file mode 100644
index 000000000..1e2e591d1
--- /dev/null
+++ b/tests/filters/test_mem_rbpf_log_weight_stability.py
@@ -0,0 +1,38 @@
+import numpy as np
+import pytest
+from pyrecest import backend
+from pyrecest.backend import array, diag, eye, zeros
+from pyrecest.filters.mem_rbpf_tracker import MEMRBPFTracker
+
+
+pytestmark = pytest.mark.skipif(
+    backend.__backend_name__ != "numpy",
+    reason="MEM-RBPF particle-weight stability is currently exercised on NumPy only",
+)
+
+
+def test_mem_rbpf_particle_weights_preserve_tiny_covariance_information():
+    tracker = MEMRBPFTracker(
+        kinematic_state=array([0.0, 0.0, 0.0, 0.0]),
+        covariance=eye(4),
+        shape_state=array([0.0, 1.0, 1.0]),
+        shape_covariance=diag(array([1e-3, 1e-3, 1e-3])),
+        meas_noise_cov=zeros((2, 2)),
+        sys_noise=zeros((4, 4)),
+        shape_sys_noise=zeros((3, 3)),
+        multiplicative_noise_cov=1e-200 * eye(2),
+        n_particles=2,
+        resampling_threshold=0,
+    )
+    tracker.theta = array([0.0, 0.0])
+    tracker.axis = array([[1.0, 1.0], [np.sqrt(2.0), np.sqrt(2.0)]])
+    tracker.axis_covariances = zeros((2, 2, 2))
+    tracker.weights = array([0.5, 0.5])
+
+    tracker._update_particle_weights(
+        centered=zeros((1, 2)),
+        meas_noise_cov=zeros((2, 2)),
+        mult_var=1e-200,
+    )
+
+    np.testing.assert_allclose(np.asarray(tracker.weights), [2.0 / 3.0, 1.0 / 3.0])