## 1 Introduction
The idea behind the integration of INS and infrastructure-based solutions arises from different error models [14], and the capability of mutual error correction based on systems' characteristics. INS has small but accumulative error, while infrastructure-based systems have significant but constant error. There are, however, shortcomings of these methods of error correction. A GPS signal is, in most cases, not received indoors. The radio beacons must be present before a fire starts in a building. Preparing the radio beacon infrastructure just in case of a fire is economically debatable because of the rare occurrence of fire and the special operational requirements--fire resistance and an alternative source of power. During search and rescue operations, exploiting this type of positioning system could be limited due to electricity loss or temperature damage. The other set of approaches for error correction becomes available when the layout of a building is accessible [15; 16; 17]. Progress in building design means that the majority of buildings are currently designed in Building Information Modeling technology ([[https://en.wikipedia.org/wiki/Building_information_modeling](https://en.wikipedia.org/wiki/Building_information_modeling)]([https://en.wikipedia.org/wiki/Building_information_modeling](https://en.wikipedia.org/wiki/Building_information_modeling))). Having such a vast source of information related to the building (where the navigation takes place), we can create a set of rules and constraints to better navigate the firefighter in the building. The algorithms that match a sequence of observed user positions to a digital map of the building or, in general, the real world, are grouped under a common umbrella called Map-Aided navigation. The task of map-matching is to determine a correspondence between sequences of previously obtained user position points (e.g., from GPS) and a given map. The main application of Map-Aided algorithms is fixing data obtained from a Global Navigation Satellite System, into a spatial road network for car navigation. However, the idea of using building geometry for heading errors in positioning systems is also extensively exploited. In the case of pedestrian indoor navigation, building floor plans are transformed into a representation that expresses traversable areas. For example, people cannot walk through wallsand floor changes can occur only via staircases or elevators. There are currently three approaches to map-aided navigation indoors [18]: (a) probabilistic map matching based on particle filtering using wall constraints, (b) topological map matching based on link-node representation of a building plan and (c) reduction of heading error by comparison with building cardinal heading. In this article, we propose an algorithm for map-aiding which uses wall constraints. However, due to the fact that most of the error pruning in our INS is angular rate estimation, we decided to apply a velocity-based correction approach instead of particle filtering. The core of the concepts in our approach is velocity obstacle and collision avoidance velocity. This paper contributes to the domain by proposing a new approach for INS error correction, based on collision avoidance velocity. The approach can be beneficial for the problem of moving an individual who is close to building obstacles. Close proximity to building obstacles is encountered in firefighting during search and rescue operations in smoky compartments [19]. Thus, the main goal of the algorithm is to improve the indoor navigation system for firefighters. Map-aided correction techniques were invented for vehicle dead reckoning in 1984 [20]. Since then, a substantial amount of research has been conducted in order to address problems of map-matching for vehicle navigation. The majority of the available solutions focus on correcting routes from GPS.