This paper introduces a new method of estimating Shannon entropy. The proposed method can be successfully used for large data samples and enables fast computations to rank the data samples according to their Shannon entropy. Original definitions of positional entropy and integer entropy are discussed in details to explain the theoretical concepts that underpin the proposed approach. Relations between positional entropy, integer entropy and Shannon entropy were demonstrated through computational experiments. The usefulness of the introduced method was experimentally verified for various data samples of different type and size. The experimental results clearly show that the proposed approach can be successfully used for fast entropy estimation. The analysis was also focused on quality of the entropy estimation. Several possible implementations of the proposed method were discussed. The presented algorithms were compared with the existing solutions. It was demonstrated that the algorithms presented in this paper estimate the Shannon entropy faster and more accurately than the state-of-the-art algorithms.

This paper introduces a method to detect malicious data in urban vehicular networks, where vehicles report their locations to road-side units controlling traffic signals at intersections. The malicious data can be injected by a selfish vehicle approaching a signalized intersection to get the green light immediately. Another source of malicious data are vehicles with malfunctioning sensors. Detection of the malicious data is conducted using a traffic model based on cellular automata, which determines intervals representing possible positions of vehicles. A credibility score algorithm is introduced to decide if positions reported by particular vehicles are reliable and should be taken into account for controlling traffic signals. Extensive simulation experiments were conducted to verify effectiveness of the proposed approach in realistic scenarios. The experimental results show that the proposed method detects the malicious data with higher accuracy than compared state-of-the-art methods. The improved accuracy of detecting malicious data has enabled mitigation of their negative impact on the performance of traffic signal control.