Iterative posterior probability estimation, optimal filtering, and object detection
This dissertation discusses three applications of statistical signal processing to estimation of signals arising from complex environments. First, a novel approach is presented for target detection and recognition in the image environment in Chapter 2 by using Bayesian networks, which can be viewed as special cases of factor graphs. Image edge probabilities are derived for the cases of known and unknown edge polarities. The edge probabilities, which relate noisy image observations to target shape information, play key roles in a Bayesian network formulation of the target detection algorithm. Using the edge probabilities, a simple but multiply-connected Bayesian network is first developed, and a probability propagation algorithm for estimation of the approximate posterior target field probability is presented. Next, a more complicated but singly-connected Bayesian network, and a probability propagation algorithm for estimation of the exact posterior probability are presented. Target detection test results and implementation methods are discussed for both Bayesian networks.
The second problem, described in Chapter 3, is the derivation of nonlinear Kalman filtering approaches for self-calibration of millimeter-wave airborne antenna arrays. Non-linear algorithms under an i.i.d. and a non-i.i.d. noise sequence assumption are derived and presented. The full required expressions for the non-linear Kalman filter, i.e. the propagation expressions and all the required inputs to the propagation equations, are described. After the theoretical derivations and analyses, simulation results and the corresponding analysis are discussed. Finally, field experiment results and analyses employing a 32-element Ku-band antenna array are presented.
The third problem, covered in Chapter 4, is the development of techniques for increasing range measurement resolution from a base station to a mobile station (or beacon) by optimal mismatched filtering. Discrete-time optimization, which is based on a minimum mean squared error (MMSE) approach, and continuous-time optimization based on variational calculus, are used to derive signal processing approaches for increasing beacon range resolution and minimizing signal-to-noise loss in an optimal sense. Simulation results and processing considerations are discussed. The derived approaches form the basis for ongoing development of a positioning system for locating and tracking a mobile station in indoor environments.