This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.

The tracking of multiple targets becomes more challenging in complex environments due to the additional degrees of nonlinearity in the measurement model. In urban terrain, for example, there are multiple reflection path measurements that need to be exploited since line-of-sight observations are not always available. Multiple target tracking in urban terrain environments is traditionally implemented using sequential Monte Carlo filtering algorithms and data association techniques. However, data association techniques can be computationally intensive and require very strict conditions for efficient performance. This thesis investigates the probability hypothesis density (PHD) method for tracking multiple targets in urban environments. The PHD is based on the theory of random finite sets and it is implemented using the particle filter. Unlike data association methods, it can be used to estimate the number of targets as well as their corresponding tracks. A modified maximum-likelihood version of the PHD (MPHD) is proposed to automatically and adaptively estimate the measurement types available at each time step. Specifically, the MPHD allows measurement-to-nonlinearity associations such that the best matched measurement can be used at each time step, resulting in improved radar coverage and scene visibility. Numerical simulations demonstrate the effectiveness of the MPHD in improving tracking performance, both for tracking multiple targets and targets in clutter.