A method for engaging a target missile includes sensing the position of the target and of an interceptor missile, and determining time-to-go to intercept and direction of thrust of the interceptor. A one-step intercept solution is determined based on position estimates of the target and the interceptor and is used to iteratively estimate at least two components of a three-dimensional unit thrust vector, and apply updated guidance commands to the interceptor. A system for thrust vector control of an interceptor against a target missile includes a processor for receiving sensed target signals, determining a one-step initial solution to produce time-to-go and current direction of thrust of the interceptor, iteratively estimating at least two components of a three-dimensional unit thrust vector, and producing a guidance vector for application to the interceptor.
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