# Dynamic Indoor Localization Using Maximum Likelihood Particle Filtering
## 1 Introduction  
Wireless positioning is the most popular approach for indoor location-based services. It finds applications in emergency rescue, smart home, security monitoring and many other areas. In contrast to outdoor positioning, whose dominant approach is based on the global positioning system (GPS), indoor positioning is hindered by multiple sources of interference and multipath effects in time-varying environments. In view of this, multiple techniques for indoor positioning are currently being investigated. The most popular ones are based on radio frequency identification [1, 2], Bluetooth signals [3, 4], ultra-wideband signals [5, 6] and WiFi signals [7, 8]. Due to their large coverage, low implementation cost and availability in existing mobile devices, WiFi-based indoor positioning is the most promising technique. A broad classification of indoor localization methods can be done in two categories, namely, geometric mapping and fingerprinting [9]. In geometric mapping, the target's position is estimated using geometric information like distances and angles from the target to a set of access points (APs) [10]. Typical techniques for obtaining geometric information are time of flight (ToF) [11] and angle of arrival (AoA) [12]. This approach typically requires obtaining information from more than three APs. The resulting methods are based on line of sight (LOS) signals, and therefore are easily influenced by obstacles. Strict synchronization is also needed between different devices. The above limitations are overcome by the fingerprinting method [13]. It consists of building a database containing the values of certain received signal features at a given set of known locations. Localization is then done by comparing the features obtained at the target's location with those of the database. Localization based on fingerprinting is more immune to distortions caused by the environment, since the latter are coded in the feature database. However, it suffers from poor positioning accuracy when the target is in a position far from anyone in the database. The most commonly WiFi signal feature used for indoor localization is its received signal strength (RSS) [14]. It measures the signal power strength at the receiver side. Although RSS measurements are easy to obtain, only a very rough estimation of the receiver's position can be obtained from it. This is due to the fading and distortion suffered by signals propagating through multipaths. To tackle this problem, in recent years channel state information (CSI) has been used instead of RSS [9]. CSI contains information of the phase and amplitude value of each subcarrier of an orthogonal frequency division multiplexing (OFDM) channel. It can be readily obtained from any OFDM system based on the 802.11n protocol. Since multipath and fading information is represented in the CSI, its use for indoor localization leads to more accurate and stable results in comparison to RSS. To improve the accuracy of any given localization method, extra information can be obtained from a motion model of the target. The common solution for fusing the information from the motion model with that from measurements consists of using some Bayesian tracking technique. We refer to resulting techniques as dynamic localization methods [15]. One such techniques is the Kalman filter [16; 17; 18]. While being optimal and having a closed-form, it only applies to linear Gaussian model. This assumption can be relaxed using the extended Kalman filter [19]. However, since this method is simply based on linearizing a non-linear model, it often leads to inaccurate results. This can be overcome by using particle filtering [20; 21; 22; 23]. This essentially consists of approximating non-Gaussian probability distributions using a number of samples (particles) multiplied by their associated weights. As it is known, a Bayesian tracking method consists of alternating two steps called prediction and update.