In certain frequency estimation applications one or more of the underlying frequencies are known. For example, in rotary machines the known frequency may be a strong network frequency masking important closely spaced frequencies. Being able to include this information in the design of the estimator can be expected to improve the performance when estimating such closely spaced frequencies. We present a framework to include such prior information in a class of subspace-based estimators. Through

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... nte Carlo simulations and real-data applications we show the usefulness of our approach.