| This dissertation introduces a technique for detection of a class of transient signals that are produced by time warping of sinusoidal signals. The technique combines classical detection theory with two approaches of recent interest within the signal processing research community: unitary axis warping and physics-based signal modeling. Using the fact that a unitary operator maps orthonormal bases to orthonormal bases in , the unitary axis warping approach maps a “standard” set of orthonormal analysis functions, such as sinusoids, to form new sets of analysis functions having characteristics well-matched to the signals of interest. In many applications, it is desirable to detect sinusoids in noise after they have been subjected to a distortion by some physical process that is described by a physical model having only a few unknown parameters. The technique introduced here addresses the situation in which the parametric distortion model gives rise to a parametric unitary axis warping operator, thereby allowing signal processing methods based on unitary operator theory to be used in computation of optimal detection statistics suggested by classical detection theory.; The dissertation introduces the technique in a general setting and then proceeds to apply it to two real-world examples: motor spin-up and closest point of approach of a constant velocity signal source to a sensor. In each case, both simulated and actual sensor data are used to demonstrate the technique, examine its performance, and investigate practical issues such as parameter mismatch. |
