API Reference

Core API

The core components of PyEHM are the EHM and EHM2 classes, that constitute implementations of the EHM [EHM1] and EHM2 [EHM2] algorithms for data association.

The interfaces of these classes are documented below.

class pyehm.core.EHM

Efficient Hypothesis Management (EHM)

An implementation of the EHM algorithm, as documented in [EHM1].

static compute_association_probabilities(net: EHMNet, likelihood_matrix: numpy.ndarray) → numpy.ndarray

Compute the joint association weights, as described in Section 3.3 of [EHM1]

Parameters:

  • net (EHMNet) – A net object representing the valid joint association hypotheses

  • likelihood_matrix (numpy.ndarray) – A matrix of shape (num_tracks, num_detections + 1) containing the unnormalised likelihoods for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Returns:

A matrix of shape (num_tracks, num_detections + 1) containing the normalised association probabilities for all combinations of tracks and detecrtons. The first column corresponds to the null hypothesis.

Return type:

numpy.ndarray

static construct_net(validation_matrix: numpy.ndarray) → EHMNet

Construct the EHM net as per Section 3.1 of [EHM1]

Parameters:

validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

Returns:

The constructed net object

Return type:

EHMNet

static run(validation_matrix: numpy.ndarray, likelihood_matrix: numpy.ndarray) → numpy.ndarray

Run EHM to compute and return association probabilities

Parameters:

  • validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

  • likelihood_matrix (numpy.ndarray) – A matrix of shape (num_tracks, num_detections + 1) containing the unnormalised likelihoods for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Returns:

A matrix of shape (num_tracks, num_detections + 1) containing the normalised association probabilities for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Return type:

numpy.ndarray

class pyehm.core.EHM2

Efficient Hypothesis Management 2 (EHM2)

An implementation of the EHM2 algorithm, as documented in [EHM2].

static compute_association_probabilities(net: EHM2Net, likelihood_matrix: numpy.ndarray) → numpy.ndarray

Compute the joint association weights, as described in Section 4.2 of [EHM2]

Parameters:

  • net (EHMNet) – A net object representing the valid joint association hypotheses

  • likelihood_matrix (numpy.ndarray) – A matrix of shape (num_tracks, num_detections + 1) containing the unnormalised likelihoods for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Returns:

A matrix of shape (num_tracks, num_detections + 1) containing the normalised association probabilities for all combinations of tracks and detecrtons. The first column corresponds to the null hypothesis.

Return type:

numpy.ndarray

static construct_net(validation_matrix: numpy.ndarray) → EHM2Net

Construct the EHM2 net as per Section 4 of [EHM2]

Parameters:

validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

Returns:

The constructed net object

Return type:

EHM2Net

static construct_tree(validation_matrix: numpy.ndarray) → EHM2Tree

Construct the EHM2 tree as per section 4.3 of [EHM2]

Parameters:

validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

Returns:

The constructed tree object

Return type:

EHM2Tree

static run(validation_matrix: numpy.ndarray, likelihood_matrix: numpy.ndarray) → numpy.ndarray

Run EHM2 to compute and return association probabilities

Parameters:

  • validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

  • likelihood_matrix (numpy.ndarray) – A matrix of shape (num_tracks, num_detections + 1) containing the unnormalised likelihoods for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Returns:

A matrix of shape (num_tracks, num_detections + 1) containing the normalised association probabilities for all combinations of tracks and detections. The first column corresponds to the null hypothesis.

Return type:

numpy.ndarray

Net API

The pyehm.net module contains classes that implement the structures (nets, nodes, trees) constructed by the EHM and EHM2 classes.

class pyehm.net.EHMNetNode(layer: int, identity: Set[int])

A node in the EHMNet constructed by EHM.

Parameters:

  • layer (int) – Index of the network layer in which the node is placed. Since a different layer in the network is built for each track, this also represented the index of the track this node relates to.

  • identity (set of int) – The identity of the node. As per Section 3.1 of [EHM1], “the identity for each node is an indication of how measurement assignments made for tracks already considered affect assignments for tracks remaining to be considered”.

class pyehm.net.EHM2NetNode(layer: int, track: int, subnet: int, identity: Set[int])

A node in the EHM2Net constructed by EHM2.

Parameters:

  • layer (int) – Index of the network layer in which the node is placed.

  • track (int) – Index of track this node relates to.

  • subnet (int) – Index of subnet to which the node belongs.

  • identity (set of int) – The identity of the node. As per Section 3.1 of [EHM1], “the identity for each node is an indication of how measurement assignments made for tracks already considered affect assignments for tracks remaining to be considered”.

class pyehm.net.EHMNet(root: EHMNetNode, validation_matrix: numpy.ndarray)

Represents the nets constructed by EHM.

Parameters:

  • root (EHMNetNode) – The net root node.

  • validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

add_edge(parent: EHMNetNode, child: EHMNetNode, detection: int)

Add edge between two nodes, or update an already existing edge by adding the detection to it.

Parameters:

  • parent (EHMNetNode) – The parent node, i.e. the source of the edge.

  • child (EHMNetNode) – The child node, i.e. the target of the edge.

  • detection (int) – Index of measurement representing the parent child relationship.

add_node(node: EHMNetNode, parent: EHMNetNode, detection: int)

Add a node to the network.

Parameters:

  • node (EHMNetNode) – The node to be added.

  • parent (EHMNetNode) – The parent of the node.

  • detection (int) – Index of measurement representing the parent child relationship.

get_children(node: EHMNetNode) → List[EHMNetNode]

Get the children of a node.

Parameters:

node (EHMNetNode) – The node whose children should be returned

Returns:

List of child nodes

Return type:

list of EHMNetNode

get_edges(parent: EHMNetNode, child: EHMNetNode) → List[int]

Get edges between two nodes.

Parameters:

  • parent (EHMNetNode) – The parent node, i.e. the source of the edge.

  • child (EHMNetNode) – The child node, i.e. the target of the edge.

Returns:

Indices of measurements representing the parent child relationship.

Return type:

list of int

get_parents(node: EHMNetNode) → List[EHMNetNode]

Get the parents of a node.

Parameters:

node (EHMNetNode) – The node whose parents should be returned

Returns:

List of parent nodes

Return type:

list of EHMNetNode

property nodes

The nodes comprising the net

property nodes_forward

The net nodes, ordered by increasing layer

property num_layers

Number of layers in the net

property num_nodes

Number of nodes in the net

property root

The root node of the net

class pyehm.net.EHM2Net(root: EHM2NetNode, validation_matrix: numpy.ndarray)

Represents the nets constructed by EHM2.

Parameters:

  • root (EHM2NetNode) – The net root node.

  • validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

add_edge(parent: EHM2NetNode, child: EHM2NetNode, detection: int)

Add edge between two nodes, or update an already existing edge by adding the detection to it.

Parameters:

  • parent (EHM2NetNode) – The parent node, i.e. the source of the edge.

  • child (EHM2NetNode) – The child node, i.e. the target of the edge.

  • detection (int) – Index of measurement representing the parent child relationship.

add_node(node: EHM2NetNode, parent: EHM2NetNode, detection: int)

Add a new node in the network.

Parameters:

  • node (EHM2NetNode) – The node to be added.

  • parent (EHM2NetNode) – The parent of the node.

  • detection (int) – Index of measurement representing the parent child relationship.

get_children_per_detection(node: EHM2NetNode, detection: int) → List[EHM2NetNode]

Get the children of a node for a particular detection.

Parameters:

  • node (EHM2NetNode) – The node whose children should be returned.

  • detection (int) – The target detection.

get_nodes_per_layer_subnet(layer: int, subnet: int) → List[EHM2NetNode]

Get nodes for a particular layer in a subnet.

Parameters:

  • layer (int) – The target layer.

  • subnet (int) – The target subnet.

Returns:

List of nodes in the target layer and subnet.

Return type:

list of EHM2NetNode

property nodes

The nodes comprising the net

property nodes_forward

The net nodes, ordered by increasing layer

property nodes_per_track

Dictionary containing the nodes per track

property num_layers

Number of layers in the net

property num_nodes

Number of nodes in the net

property root

The root node of the net

class pyehm.net.EHM2Tree(track: int, children: List[EHM2Tree], detections: Set[int], subtree: int)

Represents the track tree structure generated by construct_tree().

The EHM2Tree object represents both a tree as well as the root node in the tree.

Parameters:

  • track (int) – The index of the track represented by the root node of the tree

  • children (list of EHM2Tree) – Sub-trees that are children of the current tree

  • detections (set of int) – Set of accumulated detections

  • subtree (int) – Index of subtree the current tree belongs to.

property depth

The depth of the tree

Utils API

The pyehm.utils module contains helper classes and functions.

class pyehm.utils.Cluster(tracks: List[int], detections: List[int] = [], validation_matrix: numpy.ndarray = numpy.array([]), likelihood_matrix: numpy.ndarray = numpy.array([]))

A cluster of tracks sharing common detections.

Parameters:

  • tracks (list of int) – Indices of tracks in cluster

  • detections (list of int) – Indices of detections in cluster. Defaults to an empty list.

  • validation_matrix (numpy.ndarray) – The validation matrix for tracks and detections in the cluster. Defaults to an empty array.

  • likelihood_matrix (numpy.ndarray) – The likelihood matrix for tracks and detections in the cluster. Defaults to an empty array.

pyehm.utils.gen_clusters(validation_matrix: numpy.ndarray, likelihood_matrix: numpy.ndarray = numpy.array([])) → List[Cluster]

Cluster tracks into groups sharing detections

Parameters:

  • validation_matrix (numpy.ndarray) – An indicator matrix of shape (num_tracks, num_detections + 1) indicating the possible (aka. valid) associations between tracks and detections. The first column corresponds to the null hypothesis (hence contains all ones).

  • likelihood_matrix (numpy.ndarray) – A matrix of shape (num_tracks, num_detections + 1) containing the unnormalised likelihoods for all combinations of tracks and detections. The first column corresponds to the null hypothesis. Defaults to an empty array, in which case the likelihood matrices of the generated clusters will also be empty arrays.

pyehm.utils.to_nx_graph(obj: EHMNet | EHM2Net | EHM2Tree) → Graph[source]

Get a NetworkX representation of a net or tree. Mainly used for plotting.

Parameters:

obj (EHMNet | EHM2Net | EHM2Tree) – The object to convert to a NetworkX graph.

Returns:

The NetworkX graph representation of the object.

Return type:

networkx.Graph

Plotting API

The pyehm.plot module contains helper functions for plotting the nets and trees constructed by the EHM and EHM2 classes.

Warning

The plotting functions require Graphviz to be installed and on the PATH.

pyehm.plotting.plot_net(net: EHMNet | EHM2Net, ax: Axes = None, annotate=True)[source]

Plot the net.

Parameters:

  • net (EHMNet | EHM2Net) – The net to plot.

  • ax (matplotlib.axes.Axes) – Axes on which to plot the net. If None, a new figure and axes will be created.

  • annotate (bool) – Flag that dictates whether to draw node and edge labels on the plotted net. The default is True

pyehm.plotting.plot_tree(tree: EHM2Tree, ax: Axes = None, annotate=True)[source]

Plot the tree.

Parameters:

  • tree (EHM2Tree) – The tree to plot.

  • ax (matplotlib.axes.Axes) – Axes on which to plot the tree. If None, a new figure and axes will be created.

  • annotate (bool) – Flag that dictates whether to draw node labels on the plotted tree. The default is True

Plugins

Stone Soup

class pyehm.plugins.stonesoup.JPDAWithEHM(hypothesiser: PDAHypothesiser)[source]

Bases: JPDA

Joint Probabilistic Data Association with Efficient Hypothesis Management (EHM)

This is a faster alternative of the standard JPDA algorithm, which makes use of Efficient Hypothesis Management (EHM) to efficiently compute the joint associations. See Maskell et al. (2004) [EHM1] for more details.

associate(tracks, detections, timestamp, **kwargs)[source]

Associate tracks and detections

Parameters:
Returns:

Mapping of track to Hypothesis

Return type:

mapping of stonesoup.types.track.Track : stonesoup.types.hypothesis.Hypothesis

class pyehm.plugins.stonesoup.JPDAWithEHM2(hypothesiser: PDAHypothesiser)[source]

Bases: JPDAWithEHM

Joint Probabilistic Data Association with Efficient Hypothesis Management 2 (EHM2)

This is an enhanced version of the JPDAWithEHM algorithm, that makes use of the Efficient Hypothesis Management 2 (EHM2) algorithm to efficiently compute the joint associations. See Horridge et al. (2006) [EHM2] for more details.

associate(tracks, detections, timestamp, **kwargs)

Associate tracks and detections

Parameters:
Returns:

Mapping of track to Hypothesis

Return type:

mapping of stonesoup.types.track.Track : stonesoup.types.hypothesis.Hypothesis