Add ESS Resampler to particle filter tutorial

docs/tutorials/04_ParticleFilter.py

@@ -144,10 +144,26 @@
 # many resampling schemes, and almost as many choices as to when to undertake resampling. The
 # systematic resampler is described in [#]_, and in what follows below resampling is undertaken
 # at each time-step.
+
+# %%
+# Use of Effective Sample Size resampler (ESS)
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+# Resampling removes particles with a low weight and duplicates particles with a high weight.
+# A side-effect of this is that additional variance is added. Use of `~.SystematicResampler`
+# at each time-step means that additional variance is being introduced when it may not necessarily
+# be required. To reduce the additional variance, it may be optimal to resample less frequently.
+#
+# The Effective Sample Size resampler (`~.ESSResampler`) compares the variance of the unnormalised weights
+# of the particles to a pre-specified threshold, and only resamples when the variance is greater than this threshold.
+# This threshold is often calculated by the ESS criterion (at time n) given by:
+#
+# .. math::
+#           ESS = \left(\sum_{i=1}^{N} (W_{n}^i)^2\right)^{-1}
+
 from stonesoup.predictor.particle import ParticlePredictor
 predictor = ParticlePredictor(transition_model)
-from stonesoup.resampler.particle import SystematicResampler
-resampler = SystematicResampler()
+from stonesoup.resampler.particle import ESSResampler
+resampler = ESSResampler()
 from stonesoup.updater.particle import ParticleUpdater
 updater = ParticleUpdater(measurement_model, resampler)