Laser scan matching with grid-based maps is a promising tool for real-time indoor positioning of mobile Unmanned Ground Vehicles (UGVs). While there are critical implementation problems, such as the ability to estimate the position by sensing the unknown indoor environment with sufficient accuracy and low enough latency for stable vehicle control, further development work is necessary. Unfortunately, most of the existing methods employ heuristics for quick positioning in which numerous accumulated errors easily lead to loss of positioning accuracy. This severely restricts its applications in large areas and over lengthy periods of time. This paper introduces an efficient real-time mobile UGV indoor positioning system for large-area applications using laser scan matching with an improved probabilistically-motivated Maximum Likelihood Estimation (IMLE) algorithm, which is based on a multi-resolution patch-divided grid likelihood map. Compared with traditional methods, the improvements embodied in IMLE include: (a) Iterative Closed Point (ICP) preprocessing, which adaptively decreases the search scope; (b) a totally brute search matching method on multi-resolution map layers, based on the likelihood value between current laser scan and the grid map within refined search scope, adopted to obtain the global optimum position at each scan matching; and (c) a patch-divided likelihood map supporting a large indoor area. A UGV platform called NAVIS was designed, manufactured, and tested based on a low-cost robot integrating a LiDAR and an odometer sensor to verify the IMLE algorithm. A series of experiments based on simulated data and field tests with NAVIS proved that the proposed IMEL algorithm is a better way to perform local scan matching that can offer a quick and stable positioning solution with high accuracy so it can be part of a large area localization/mapping, application. The NAVIS platform can reach an updating rate of 12 Hz in a feature-rich environment and 2 Hz even in a feature-poor environment, respectively. Therefore, it can be utilized in a real-time application.