General cone classes for signal modeling and detection

The article describes a deterministic signal model, cone classes and intersections of cone classes, with applications to both signal detection and estimation. Cone classes include a variety of different types of signal models. Two examples are linear subspaces with mismatch, and time and/or frequency concentrated classes. Other examples with applications to array processing and periodic sequences are given. The classes explored are classes using different operators with the same eigenvectors. The procedure for the maximum likelihood estimation of an unknown signal in the class in additive Gaussian noise is derived. The procedure provides a way of estimating and detecting unknown signals. A practical example of the detection of quasi-periodic finback whale pulses in noise is included.