The present invention uses a map database which is created with the view of optimization in terms of size and complexity, so that it can be easily embedded into a navigation chip. The optimized map database is referred to as a “mini-map” database. The mini-map database easily integrates with the position calculation routine. The algorithm for position calculation includes a map-matching component, which is referred to as the “mini-map-matching” (MMM) algorithm, which is implemented on the navigation chip. Application of the present invention includes any navigation system for vehicles and/or pedestrians. The navigation system may include an inertial sensor, such as a dead-reckoning (DR) sensor, for further improvement in calculated positional accuracy when satellite signals are degraded due to environmental factors.