Cast correction term to float in LCCUpdater

[ekhunter123]

TLDR: Gaussian components updated using the LCCUpdater have weights which are Probability objects. This in turn causes some component state vectors to be made of Probabilities instead of floats. To fix this, we can cast the l1 correction term from a Probability to a float.

Problem:
When using the GM-LCC filter, sometimes an updated component's state vector is filled with Probability types, instead of floats. For example, an updated component may have state vector
[Probability(15.0), Probability(0.5), 8.0, Probability(0.3)]
On its own, this is not a big problem. But it isn't the proper use of a Probability object and none of the other filters behave this way.

Cause:
I traced the problem back and found that it was caused by two things:

The LCCUpdater calculates an l1 correction factor. As seen in the code below, that correction factor will be a Probability object (I have checked this).

Stone-Soup/stonesoup/updater/pointprocess.py

Lines 164 to 187 in d38a196

	def _calculate_update_terms(self, updated_sum_list, hypotheses):
	"""
	Calculate the higher order terms used in the LCC Filter
	"""
	# Get the predicted weight sum
	predicted_weight_sum =\
	Probability.sum(hypothesis.prediction.weight for hypothesis in
	hypotheses[-1]) * self.prob_survival
	# Second order predicted cumulant c(2)
	predicted_c2 = self.second_order_cumulant * self.prob_survival**2
	# Detected predicted weight mu_d
	detected_weight_sum = self.prob_detection*predicted_weight_sum
	# Detected predicted weight mu_phi
	misdetected_weight_sum = (1-self.prob_detection)*predicted_weight_sum
	# Calculate the alpha of the predicted Panjer process
	alpha_pred = ((predicted_weight_sum +
	self.mean_number_of_false_alarms)**2)\
	/ (predicted_c2+self.second_order_false_alarm_cumulant+1e-26)
	# Calculate l1 and l2 correction factors
	denominator = alpha_pred + detected_weight_sum \
	+ self.mean_number_of_false_alarms
	number_of_measurements = len(hypotheses)-1
	numerator = alpha_pred + number_of_measurements
	l1 = numerator/denominator

Later, the correction factor is used as a factor in the weight calculation for updated components. Thus, the calculated weight will be a Probability. This means that updated components in a GM-LCC (other than the birth component) will have Probability weights.

Stone-Soup/stonesoup/updater/pointprocess.py

Lines 99 to 112 in d38a196

	l1 = self._calculate_update_terms(weight_sum_list, hypotheses)
	for missed_detected_hypotheses in hypotheses[-1]:
	# Add all active components except birth component back into
	# mixture as miss detected components
	if missed_detected_hypotheses.prediction.tag != "birth":
	component = TaggedWeightedGaussianState(
	tag=missed_detected_hypotheses.prediction.tag,
	weight=missed_detected_hypotheses.prediction.weight
	* (1-self.prob_detection) * l1,
	state_vector=missed_detected_hypotheses.prediction.mean,
	covar=missed_detected_hypotheses.prediction.covar,
	timestamp=missed_detected_hypotheses.prediction.timestamp)
	updated_components.append(component)

This Probability weight causes problems further down the line in the GaussianMixtureReducer. When merging two components, the state vector of each original component is multiplied by its weight. If that weight is a Probability, it will make the merged component mean have Probability elements. It is also true that a Probability weight will perpetuate the problem in the next timesteps even if the component is not merged with another.

Proposed Solution:
In the LCCUpdater function _calculate_update_terms(), simply cast l1 as a numpy float64 before returning it. Note that it is cast as a numpy 64 float so that the weights are also numpy64, thus matching the result from a PHDUpdater.

[codecov]

Codecov Report

Merging #627 (fa46ed4) into main (d38a196) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main     #627   +/-   ##
=======================================
  Coverage   94.22%   94.22%           
=======================================
  Files         158      158           
  Lines        7832     7833    +1     
  Branches     1506     1506           
=======================================
+ Hits         7380     7381    +1     
  Misses        343      343           
  Partials      109      109           

Flag	Coverage Δ
integration	67.80% <50.00%> (+<0.01%)	⬆️
unittests	91.98% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
stonesoup/updater/pointprocess.py	97.18% <100.00%> (+0.04%)	⬆️

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