## 1 Introduction
According to a previous survey [21], we can categorise general approaches for map-matching algorithms presented in the literature into four groups: geometric, topological, probabilistic and other advanced method. In this domain, the problems faced are not only related to the algorithm itself but also data structure to store the map in a computationally effective manner [21]. The most commonly used geometric map-matching algorithm is a simple search algorithm. In this approach, each position fix is matched to the closest 'node' or'shape point' of a road segment. This is known as point-to-point matching [22]. More general approaches exploit 'point-to-curve' or 'curve-to-curve' matching [22; 23; 24] using trajectory estimated from consecutive GPS fixes as the candidate route. In [25; 26] the development of the path is computed by INS/GPS combination. Those techniques exploit the general idea of mapping a path obtained by different systems (with possible accumulative and constant error) with possible route shapes encoded by a map. Unfortunately, in indoor environments, the number of possible routes is unbounded; therefore, the possibility of direct application of those techniques in individual navigation systems is substantially limited. Map-Aided Pedestrian/Individual Navigation (MAPN) is more challenging than vehicle map-aided navigation. Most of the time, we cannot assume constraints on a path--humans can take sudden turns and accidental stops, whereas a car needs to be bounded with maneuvering constraints. Moreover, since the acceleration characteristics of vehicles are less rapid, the error of these INSs is more bounded, which eventually results in better path estimation. Simple derivation of the 'curve-to-curve' matching technique for MAPN is illustrated in [15]. To compensate for the inaccuracies in step detection and heading estimation, the authors matched the detected step series onto the expected route using a sequence alignment algorithm outputting the 'best fit'. This method is convenient only when a mobile device is navigating a pedestrian over the path (therefore, we know the expected route). A substantial amount of research exploits Particle Filters for MAPN to address high non-linearity in human movement [16; 17; 27; 28; 29; 30]. For example, ref. [7] uses an on-line technique for particle weighting which is based on a transition map between hexagonal map division 'cells'. Nevertheless, this approach assumes frequent re-visiting of 'cells' to achieve a bounded positioning error. The authors of [31] introduce the Cardinal Heading Aided Inertial Navigation (CHAIN)--a technique in which particles are weighted or 'killed', eliminating impossible states based on building walls. CHAIN uses four cardinal moves and heuristics based on the building structure to obtain the most possible heading correction (it is important to note that heading error is crucial in pedestrian INS). In [32], the authors exploit a similar technique but instead of assuming heading based on the wall structure, the authors trained a Hidden Markov Model to express 'human behavior' in movement. In [33], the authors introduce substantial optimization for particle filters exploiting indoor maps in this specific application. The particle filter is most commonly used for MAPN because it provides a straight-forward, formally clean method of exploiting the error covariance matrix from the Kalman Filter--the particles reflect possible paths in which the probability is inherited from error modelling. Nevertheless, when the path does not cross any obstacles, a great number of possible paths (particles) need to be maintained for longer periods and the whole technique becomes a computationally demanding algorithm. Consequently, exploiting it on mobile devices can be limited by power supplies. Our work is very similar to that of [31; 32] but instead of maintaining all possible paths, we assumed very specific path traversal behaviour of firefighters.