Nowadays, the location information of people and objects is a necessity for indoor environments. Therefore, many technologies, methods, and algorithms have been employed in recent years to estimate the positions of people and objects. Although there has been much research into different methods, none of these methods has yet been accepted as a common solution for accurate indoor positioning. Therefore, there is still a lot of work to be done in this area of research. WiFi-based indoor positioning applications are one of the most popular research topics due to not requiring any additional hardware or cost. However, WiFi signals are influenced by many environmental effects, and thus, they show unstable behaviors in indoor environments. Because of the fluctuation of WiFi signal behavior, WiFi-based systems cannot provide sub-meter level accurate solutions. In this paper, we aimed at two main contributions. First, we analyzed and compared the 2.4 and 5 GHz WiFi signal behaviors based on the distance. For this purpose, we conducted an experiment using access points along a 27.83 m corridor with 0.605 m intervals in an indoor environment. This experiment showed that the 5 GHz WiFi signal behaviors are more stable than the 2.4 GHz signals. For this reason, it is expected that 5 GHz WiFi signals enable more accurate distance and position information as compared to the 2.4 GHz signals. Secondly, we performed six real-time kinematic experiments on two different trajectories with two main objectives. The first objective was to compare the positioning performances of 2.4 and 5 GHz WiFi signals. As expected from the first experiment results, positioning accuracies obtained from 5 GHz signals are significantly better than 2.4 GHz signals. In the second objective, we proposed a new algorithm that mainly consists of a fusion of the Bilateration and extended Kalman filter (EKF) algorithms. The main purpose of this algorithm is to diminish the effects of faulty received signal strength values on positioning, and therefore, improve the positioning accuracy of the mobile devices. It concluded that the proposed algorithm dramatically improves the positioning accuracy as compared to the Bilateration and EKF algorithms.