Constrained Estimation For Gps/Digital Map Integration

Linear and nonlinear constrained estimation is investigated in this paper as an optimal method to integrate GPS fixes with digital maps so as to improve accuracy and reliability. In addition to emergency location and roadside assistance, the integration of GPS with digital maps becomes an increasingly popular application in automotives particularly for real-time routing, driving guidance, and street prompting. A position fix is obtained by a GPS receiver, which may be subject to significant errors in urban canyons due to such effects as multipath and weak signal, whereas a digital map provides the road network of a region in which a user is traveling. When the information about roads is as accurate as (or even better than) GPS measurements, it is desired naturally to incorporate such information into position solution. In this paper, roads are modeled with analytic functions and its integration (fusion) with a GPS position fix is cast as linear and/or nonlinear state constraints in an optimization procedure. Similarly, the velocity estimates and the road directions are treated as another pair of constraints. The constrained optimization is then solved with the Lagrangian multiplier, leading to a closed-form solution for linear constraints and an iterative solution for nonlinear constraints. Geometric interpretations of the solutions are provided for simple cases. Computer simulation results are presented to illustrate the algorithms.