Method and system for tracking signal sources with wrapped-phase hidden markov models
View Patent ↗A method models trajectories of a signal source. Training signals generated by a signal source moving along known trajectories are acquired by each sensor in an array of sensors. Phase differences between all unique pairs of the training signals are determined. A wrapped-phase hidden Markov model is constructed from the phase differences. The wrapped-phase hidden Markov model includes multiple Gaussian distributions to model the known trajectories of the signal source.
1. A method for modeling trajectories of a signal source, comprising:
acquiring, for each sensor in an array of sensors, training signals generated by a signal source moving along a plurality of known trajectories;
determining phase differences between all unique pairs of the training signals; and
constructing a wrapped-phase hidden Markov model from the phase differences, the wrapped-phase hidden Markov model including a plurality of Gaussian distributions to model the plurality of known trajectories of the signal source.
2. The method of claim 1 , further comprising:
acquiring, for each sensor in the array of sensors, test signals generated by the signal source moving along an unknown trajectory;
determining phase differences between all pairs of test signals; and
determining, according to the wrapped-phase hidden Markov model and the phase differences of the test signal, a likelihood that the unknown trajectory is similar to one of the plurality of known trajectories.
3. The method of claim 1 , in which the signal source generates an acoustic signal.
4. The method of claim 1 , in which the signal source generates an electromagnetic signal.
5. The method of claim 1 , in which the plurality of Gaussian distributions are replicated at k phase intervals of 2π.
6. The method of claim 1 , further comprising:
summing the plurality of Gaussian distributions.
7. The method of claim 1 , further comprising:
determining parameters of the plurality of Gaussian distributions with an expectation-maximization process.
8. The method of claim 5 , in which k ∈ −1, 0, 1.
9. The method of claim 5 , in which k ∈ −2, −1, 0, 1, 2.
10. The method of claim 1 , in which the wrapped-phase hidden Markov model is a univariate model f x (x), and further comprising:
taking a product of the univariate model for each dimension i according to:
f
x
(
x
)
=
∏
i
f
x
(
x
i
)
to represent the univariate model as a multivariate model.
11. The method of claim 1 , further comprising:
determining a posteriori probabilities of the wrapped-phase hidden Markov model.
12. The method of claim 1 , in which the phase differences are determined for a predetermined frequency range.
13. The method of claim 1 , in which the constructing is performed using supervised training.
14. The method of claim 1 , in which the constructing is performed using unsupervised training using k-means clustering, and the likelihoods are distances.
15. A system for modeling trajectories of a signal source, comprising:
an array of sensors configured to acquire training signals generated by a signal source moving along a plurality of known trajectories;
means for determining phase differences between all unique pairs of the training signals; and
means for constructing a wrapped-phase hidden Markov model from the phase differences, the wrapped-phase hidden Markov model including a plurality of Gaussian distributions to model the plurality of known trajectories of the signal source.
16. The system of claim 15 , in which test signals generated by the signal source moving along an unknown trajectory are acquired, and further comprising:
means for determining phase differences between all pairs of test signals; and
means for determining, according to the wrapped-phase hidden Markov model and the phase differences of the test signal, a likelihood that the unknown trajectory is similar to one of the plurality of known trajectories.