Systems and methods for navigation using cross correlation on evidence grids are provided. In one embodiment, a system for using cross-correlated evidence grids to acquire navigation information comprises: a navigation processor coupled to an inertial measurement unit, the navigation processor configured to generate a navigation solution; a sensor configured to scan an environment; an evidence grid creator coupled to the sensor and the navigation processor, wherein the evidence grid creator is configured to generate a current evidence grid based on data received from the sensor and the navigation solution; a correlator configured to correlate the current evidence grid against a historical evidence grid stored in a memory to produce displacement information; and where the navigation processor receives correction data derived from correlation of evidence grids and adjusts the navigation solution based on the correction data.