The penetration rate is one of the most important factors that affects the effectiveness of the mobile phonebased traffic state estimation. This article thoroughly investigates the influence of the penetration rate on the traffic state estimation using mobile phones as traffic probes and proposes reasonable solutions to minimize such influence. In this research, the so-called "acceptable" penetration rate, at which the estimation accuracy is kept as an "acceptable" level, is identified. This recognition is important to bring the mobile phone-based traffic state estimation systems into realization. In addition, two novel "velocity-density inference" models, namely the "adaptive" and the "adaptive feedback" velocity-density inference circuits, are proposed to improve the effectiveness of the traffic state estimation. Furthermore, an artificial neural network-based prediction approach is introduced to a the effectiveness of the velocity and the density estimation when the penetration rate degrades to 0%. These improvements are practically meaningful since they help to guarantee a high accurate traffic state estimation, even in cases of very low penetration rate. The experimental evaluations reveal the effectiveness as well as the robustness of the proposed solutions.
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