Hidden Markov modeling for radar electronic warfare

A method for classifying source models in dependence upon an electromagnetic signal emitted from a source of electromagnetic signals comprising the steps of:

• receiving the electromagnetic signal emitted from the source;
• providing a plurality of L source models λ such that the L source models λ have L different observation alphabets or continuous distributions comprising symbols or multivariate observations being integer multiples of L different time periods, the source models λ being hidden Markov modeled finite state automatons;
• transforming the received electromagnetic signal into L sequences of observation symbols or multivariate observations O using the L different observation alphabets or continuous distributions;
• and,
• determining for each combination of a source model λ of the L source models with a sequence of observation symbols or multivariate observations O(l) of the L sequences of observation symbols or multivariate observations an observation probability P└λ(l)|O(l)┘, 1≦l≦L of the source model λ for producing the sequence of observation symbols or multivariate observations O(l).

A method for decoding an electromagnetic signal emitted from a source of electromagnetic signals comprising the steps of:

• receiving the electromagnetic signal emitted from the source;
• determining a sequence of observation symbols or multivariate observations O in dependence upon the received electromagnetic signal;
• providing a source model λ, the source model λ being a hidden Markov modeled finite state automaton;
• determining a plurality of sequences of state transitions Q of the hidden Markov modeled finite state automaton;
• and,
• determining for each of the sequences of state transitions Q a probability of occurrence P[Q|O, λ] with respect to the sequence of observation symbols or multivariate observations O.

A method for predicting a second portion of an electromagnetic signal based upon a first portion of the electromagnetic signal emitted from a source of electromagnetic signals comprising the steps of:

• receiving the first portion of the electromagnetic signal;
• determining a partial sequence of observation symbols or multivariate observations Ot in dependence upon the received first portion of the signal;
• providing a source model, the source model being a hidden Markov modeled finite state automaton;
• determining for each observation symbol or multivariate observation of an observation alphabet or continuous distribution of the source model a probability for being the next symbol or multivariate observation at time t+1 in the sequence of observation symbols or multivariate observations O based on a state transition probability distribution at time t of the source model and an observation symbol or multivariate observation probability distribution of the source model at time t;
• and,
• determining a most probable observation symbol or multivariate observation.

A method for training a source model of a source emitting electromagnetic signals comprising the steps of:

• receiving an electromagnetic signal emitted from the source;
• determining a sequence of observation symbols or multivariate observations in dependence upon the received signal emitted from the source;
• providing the source model, the source model being a hidden Markov modeled finite state automaton;
• and,
• estimating a new source model based upon the probability ξt(i,j) of the source model being in state i at time t and in state j at time t+1 for the sequence of observation symbols or multivariate observations and the probability γt(i) of the source model being in state i at time t for the sequence of observation symbols or multivariate observations.