Basic Example

import numpy as np

Formulating the possible associations between targets and measurements

Both EHM and EHM2 operate on a validation_matrix and a likelihood_matrix. The validation_matrix is an indicator matrix that represents the possible associations between different targets and measurements, while the likelihood_matrix contains the respective likelihoods/probabilities of these associations. Both matrices have a shape (N_T, N_M+1), where N_T is the number of targets and N_M is the numer of measurements.

For example, assume we have the following scenario of 4 targets and 4 measurements (taken from Section 4.4 of [EHM2]):

Target index	Gated measurement indices
0	0, 1
1	0, 1, 2, 3
2	0, 1, 2
3	0, 3, 4

where the null measurement hypothesis is given the index of 0. Then the validation_matrix would be a (4, 5) numpy array of the following form:

validation_matrix = np.array([[1, 1, 0, 0, 0],   # 0 -> 0,1
                              [1, 1, 1, 1, 0],   # 1 -> 0,1,2,3
                              [1, 1, 1, 0, 0],   # 2 -> 0,1,2
                              [1, 0, 0, 1, 1]])  # 3 -> 0,3,4

The likelihood_matrix is such that each element likelihood_matrix[i, j] contains the respective likelihood of target i being associated to measurement j. Therefore, based on the above example, the likelihood_matrix could be the following:

likelihood_matrix = np.array([[0.1, 0.9, 0, 0, 0],
                              [0.1, 0.3, 0.2, 0.4, 0],
                              [0.7, 0.1, 0.2, 0, 0],
                              [0.2, 0, 0, 0.75, 0.05]])

Computing joint association probabilities

Based on the above, we can use EHM or EHM2 to compute the joint association probabilities matrix assoc_matrix as follows:

from pyehm.core import EHM, EHM2

assoc_matrix_ehm = EHM.run(validation_matrix, likelihood_matrix)
print('assoc_matrix_ehm =\n {}\n'.format(assoc_matrix_ehm))
# or
assoc_matrix_ehm2 = EHM2.run(validation_matrix, likelihood_matrix)
print('assoc_matrix_ehm2 =\n {}'.format(assoc_matrix_ehm2))

assoc_matrix_ehm =
 [[0.17948718 0.82051282 0.         0.         0.        ]
 [0.25925926 0.07692308 0.4045584  0.25925926 0.        ]
 [0.85754986 0.01139601 0.13105413 0.         0.        ]
 [0.35555556 0.         0.         0.55555556 0.08888889]]

assoc_matrix_ehm2 =
 [[0.17948718 0.82051282 0.         0.         0.        ]
 [0.25925926 0.07692308 0.4045584  0.25925926 0.        ]
 [0.85754986 0.01139601 0.13105413 0.         0.        ]
 [0.35555556 0.         0.         0.55555556 0.08888889]]

Note that both EHM and EHM2 should produce the same results, although EHM2 should, in principle, be significantly faster for large numbers of targets and measurements.

# Check if the probability matrices produced by EHM and EHM2 are equal
print(np.allclose(assoc_matrix_ehm, assoc_matrix_ehm2))

True