2. Related work

Global navigation satellite systems (GNSS) such as GLONASS (Russia's version of GPS), GALI-LEO, and GPS work well in outdoor environments, but their accuracy can significantly decrease in indoor environments due to many factors, such as penetration loss, refraction, multipath propagation, and absorption. Therefore, it is important to develop a system that can work in indoor environments with high accuracy. To this end, many techniques have been proposed for IPS in the last decade. In model-based techniques, the location is estimated based on a geometrical model, such as the log-distance path loss (LDPL) model, in which a semi-statistical function is built on the relationship between the RF propagation function and the RSS value. Several approaches have been proposed that are trade-offs between accuracy and cost, such as TOA, TDOA, AOA, and multidimensional scaling (MDS). MDS is a set of statistical techniques that are used to visualize the information in order to find similarities/dissimilarities in the data. The matrix in MDS begins with item-item dissimilarities, and AP-AP distances are determined by a radio attenuation model [9]. The fingerprinting-based technique depends on matching algorithms (e.g., kNN) that have been used in RADAR [14], which is one of the first Wi-Fi signal strength-based IPS and is considered the basis of WLAN fingerprinting IPS. Many developed kNN algorithms have been proposed for determining the similarity/dissimilarity in metrics, which is usually done using the Manhattan or Euclidean distance, such as in [11–18]. Ref. [19] proposed a new version of kNN that is more efficient than the probabilistic methods, neural networks, and traditional kNN, as it relies upon the decision tree of the training phases and takes into account the average of reference point (RP) measurements instead of needing the entire dataset to estimate the object's location. Ref. [20] performed a modified deterministic kNN technique with Mahalanobis, Manhattan, and Euclidian distances and found the Manhattan distance to be the most accurate. Recently, the use of probabilistic distribution measurements in many IPS applications has increased. The authors in [21] pioneered the use of the probabilistic distribution measurement in IPS and proposed a probabilistic framework by using the Bayesian network to estimate the location. In [22] the authors used a modified probability neural network (MPNN) to estimate the coordinates of the object and found that it outperformed the triangulation method. In [23], a kernel method was proposed to estimate the object's location using a histogram of the RSSI at the unknown location. In [24], the probability density function (PDF) was estimated using the Kullback-Leibler divergence (KLD) framework for composite hypothesis testing between the fingerprinting database and the test point, whereas in [25], the authors assumed that the RSSI distribution was multivariate Gaussian and used the KLD to estimate the impacts of the RPs on the test point in order to estimate the probability of the closest one and to identify the coordinates of the test point.

In [26], the RSS-based Bluetooth low-energy localization technique was used to establish the fingerprint, after which the KLD was used in probabilistic kernel regression to estimate the object's location. The results showed this method to be accurate to approximately 1 m in an office environment. In general, the KLD kernel regression performs better in a multimodal distribution. In [27], the KLD was used to estimate the probabilistic kernel of both Gaussian and non-Gaussian distributions in order to compare them and to determine their limitations.
