In recent years, the development of intelligent ground vehicles (IGV), unmanned aerial vehicles (UAV) and interplanetary spacecraft has drastically increased the need for robust, precise and autonomous navigation systems. These systems need real time position, heading, and velocity information in a broad spectrum of environments with minimal error in order to successfully accomplish the complex tasks which they have been designed for. The Global Positioning System (GPS) has come to fulfill a vast amount of this need, providing global coverage with meter-level accuracy. Unfortunately, GPS is not perfect and has a few shortcomings which undermine its use in fulfilling the requirements that some systems demand. Minor obstruction of the signal by foliage, cityscape (typically called an “urban canyon”), or indoor environments block signals from the GPS satellites, greatly reducing the accuracy of the solution if not eliminating it all together. Considering that the signals from the satellites are below the noise floor, they are also very susceptible to interference, whether intentional or not. Since it is highly probable that IGV, UAV, and interplanetary spacecraft will be in such environments, there must be other sensors involved in the navigational solution that do not have the shortcomings of GPS and other similar systems. Inertial Measurement Units (IMUs) work in these environments, but have large drift errors over time. Laser ranging scanners, typically called LADAR, have been employed to solve aspects of these problems in various degrees of complexity and integration for over twenty years. The major benefits of using LADAR are low sensor noise, autonomy, its simultaneous use for obstacle avoidance, its ability to map its surroundings, and potential to bound the drift error of an IMU. Although much work has been done in localization and mapping using LADAR, the problem of creating a fully functional high integrity navigation solution has not been achieved. This thesis will not only address and improve some of the major components and methods of 2D LADAR navigation, but will also propose entirely new methods and mathematical solutions to improve its use as a navigational system. The largest of these improvements are found in object matching/tracking, and covariance calculations.