Change in sound intensity is but one source of information for specifying motion parameters of a sound-emitting object in space. This model is based on Bayesian data-fusion techniques that have been developed in the field of passive sonar. Although these measurement equations are nonlinear, they can be linearized sufficiently to utilize standard Kalman filtering techniques as recursive estimators of motion-state variables. Theoretical lower bounds can be established using the Cramer-Rao lower bound on the recursive estimators, which gives the minimum variance that an unbiased estimator can achieve from a series of noisy measurements. Bob Savit, Department of Physics, University of Michigan.
Time series generated by complex, nonlinear systems are notoriously difficult to analyze.
One important problem that must be addressed early on, is whether the underlying dynamics driving the process is time independent. This question is related to, but not the same as, the question of stationarity. In this talk I will describe a new method for analyzing time series from complex systems that is designed to uncover time dependence in the underlying dynamics. In addition to addressing the question of whether the underlying dynamics is time dependent or not, the approach provides insight into the nature of the time dependence, if it exists. I will discuss applications of the method to the analysis of intracranial EEG recordings from patients with temporal lobe epilepsy, to a problem in mechanical vibration analysis, as well as to some examples of simulated data.