Navigation relative to the surrounding physical structures and obstacles is an important capability for safe vehicle operation. This capability is particularly useful for unmanned vehicles operating near large marine structures such as bridges and waterside buildings or in indoor environments such as tunnels and parking lots where global positioning system (GPS) signals are restricted or unavailable due to the line-of-sight restrictions. Also, the relative navigation is a suitable approach for vehicle navigation even in open areas, because GPS is vulnerable to natural interference and malicious jamming attacks. This dissertation presents a computationally efficient approach for localization and mapping in the context of simultaneous localization and mapping (SLAM). A parameterized map-building approach is introduced and implemented to represent the surrounding environments using a small number of geometric parameters. These parameters are obtained from LIDAR or radar measurements and incorporated into an online filter to simultaneously estimate the map parameters and localize the vehicle. This approach enables high-precision navigation and memory-efficient map representation of an environment with man-made structures or coastal water with no need of GPS or external position fixes. Field experiments using various types of unmanned vehicle systems including unmanned surface vehicles (USVs) and self-driving cars in real-world environments were performed to verify and demonstrate the performance of the proposed navigation and mapping algorithms. The field test results are presented and discussed in this thesis.