Cigarette smoking is a major global public health issue and the leading cause of preventable death in the United States. Toward a goal of designing better smoking cessation treatments, system identification techniques are applied to intervention data to describe smoking cessation as a process of behavior change. System identification problems that draw from two modeling paradigms in quantitative psychology (statistical mediation and self-regulation) are considered, consisting of a series of continuous-time estimation problems. A continuous-time dynamic modeling approach is employed to describe the response of craving and smoking rates during a quit attempt, as captured in data from a smoking cessation clinical trial. The use of continuous-time models provide benefits of parsimony, ease of interpretation, and the opportunity to work with uneven or missing data.

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Quantization is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantized observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantized realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a , , quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the minimization in terms of the sparsity of the induced solution.