Summary With the advancement of global positioning systems and communication technologies, location‐based services (LBS) have become widely used. However, user location privacy is vulnerable during service exchange, and location‐related queries may result in serious privacy disclosure issues. In this article, considering that attackers may make use of auxiliary information to track a mobile user, we propose a real‐time privacy‐preserving scheme based on the grouping of queries in continuous LBS. In this scheme, we first design the probability density functions to select virtual locations. Then, we group these virtual locations and the query location of the user into several queries. Simultaneously, we send these grouping queries to the LBS server. Following the steps outlined above, grouping queries can be used to conceal the true query. Moreover, the results of security analyses and performance evaluations show that the proposed scheme is effective and secure.

This paper investigates the mean square consensus problem for continuous-time multiagent systems with randomly switching topologies and noises. The switching is governed by a time-homogeneous Markov process, and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of the Markov process. Then, necessary and sufficient conditions can be obtained under a control protocol with time-varying gain. Moreover, we extend our result to the cases where the topological structure is semi-Markovian switching and the elements of transition rate matrix are partly unknown. Finally, we give an example to illustrate the validity of our results.