Disclosed herein are methods and systems for fusion of sensor and map data using constraint based optimization. In an embodiment, a computer-implemented method may include obtaining tracking data for a tracked subject, the tracking data including data from a dead reckoning sensor; obtaining constraint data for the tracked subject; and using a convex optimization method based on the tracking data and the constraint data to obtain a navigation solution. The navigation solution may be a path and the method may further include propagating the constraint data by a motion model to produce error bounds that continue to constrain the path over time. The propagation of the constraint data may be limited by other sensor data and/or map structural data.