This investigation is concerned with effective state estimation of a system driven by an unknown nonGaussian input with additive white Gaussian noise, and observed by measurements containing feedthrough of the same nonGaussian input and corrupted by additional white Gaussian noise. A Gaussian sum (GS) approach has previously been developed [6-8] which can cope with the non Gaussian nature of the input signal. Due to a serious growing memory problem in this approach, a modified Gaussian sum (MGS) estimation technique is developed that avoids the growing memory problem while providing effective state estimation. Several differences between the MGS and GS algorithms are examined. An MGS adaptive filter is derived for a general system and a modal system, with simulation examples performed using a non Gaussian input signal. The modal system simulation results are compared to those produced from an augmented Kalman filter based on an augmented modal system model assuming a narrowband Gaussian input signal. A necessary condition for effective MGS estimation is derived. Alternate estimation procedures are developed to compensate for situations when this condition is not met. Several configurations are simulated and their performance results are analyzed and compared. Two methods of monitoring and updating key parameters of the MGS filter are developed. Simulation results are analyzed to investigate the performance of these methods. / Ph. D.