diff --git a/src/roboticstoolbox/mobile/ParticleFilter.py b/src/roboticstoolbox/mobile/ParticleFilter.py
index bee0e69c0..9e84361f0 100644
--- a/src/roboticstoolbox/mobile/ParticleFilter.py
+++ b/src/roboticstoolbox/mobile/ParticleFilter.py
@@ -15,7 +15,6 @@
 
 import matplotlib.pyplot as plt
 import numpy as np
-import scipy as sp
 import spatialmath.base as smb
 from matplotlib import animation
 from matplotlib.axes import Axes
@@ -696,21 +695,15 @@ def _select(self) -> None:
         #
         # particles with large weights will occupy a greater percentage of the
         # y axis in a cummulative plot
-        cdf = np.cumsum(self.weight) / self.weight.sum()
+        cdf = np.cumsum(self.weight)
+        cdf = cdf / cdf[-1]
 
         # so randomly (uniform) choosing y values is more likely to correspond to
         # better particles...
         iselect = self.random.uniform(0, 1, size=(self.nparticles,))
 
         # find the particle that corresponds to each y value (just a look up)
-        interpfun = sp.interpolate.interp1d(
-            cdf,
-            np.arange(self.nparticles),
-            assume_sorted=True,
-            kind="nearest",
-            fill_value="extrapolate",
-        )
-        inextgen = interpfun(iselect).astype(int)
+        inextgen = np.searchsorted(cdf, iselect, side="right")
 
         # copy selected particles for next generation..
         self.x = self.x[inextgen, :]
diff --git a/tests/test_particle_filter_api.py b/tests/test_particle_filter_api.py
index f94c8ebfc..3dfa57d52 100644
--- a/tests/test_particle_filter_api.py
+++ b/tests/test_particle_filter_api.py
@@ -32,6 +32,24 @@ def test_map_is_the_map_of_the_sensor() -> None:
     assert pf.map is pf.sensor.map
 
 
+@pytest.mark.parametrize("first_weight", [0.2, 0.8])
+def test_resampling_uses_weighted_cdf_intervals(first_weight: float) -> None:
+    pf = _filter()
+    particles = np.column_stack(
+        (np.arange(pf.nparticles), np.zeros((pf.nparticles, 2)))
+    )
+    pf.x = particles.copy()
+    pf.weight = np.zeros(pf.nparticles)
+    pf.weight[[0, -1]] = [first_weight, 1 - first_weight]
+    pf._random = np.random.default_rng(47)
+    draws = np.random.default_rng(47).uniform(0, 1, size=pf.nparticles)
+    expected_indices = np.where(draws < first_weight, 0, pf.nparticles - 1)
+
+    pf._select()
+
+    np.testing.assert_array_equal(pf.x, particles[expected_indices])
+
+
 @pytest.mark.parametrize("verbose", [False, True])
 def test_verbose_is_what_was_asked(verbose: bool) -> None:
     assert _filter(verbose=verbose).verbose is verbose