Navigation system with estimation of n-dimensional parameters while sensing fewer than n dimensions

Embodiments of the present invention provide improved systems and methods for estimating N-dimensional parameters while sensing fewer than N dimensions. In one embodiment a navigational system comprises a processor and an inertial measurement unit (IMU) that provides an output to the processor, the processor providing a navigation solution based on the output of the IMU, wherein the navigation solution includes a calculation of an n-dimensional parameter. Further, the navigational system includes at most two sensors that provide an output to the processor, wherein the processor computes an estimate of an n-dimensional parameter from the output of the at most two sensors for bounding errors in the n-dimensional parameter as calculated by the processor when the trajectory measured by the IMU satisfies movement requirements, wherein "n" is greater than the number of the at most two sensors.