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Wireless sensor networks are useful for many reasons, but they add at least two new issues to the Extended Kalman Filtering problem. First, they can be a further cause of divergence, as the information they send could not reach the filter. Second, batteries consumption must be taken into account: this leads to the need for a policy of querying, at each time instant, only a few sensors. In this paper we show how a wise sensor querying can improve the convergence rate of the filter, thus facing both the above problems. The querying criterion we suggest is simple to be implemented and adds a little computational overload to the filtering algorithm. The simulations we report, which refer to a mobile robot position estimation problem, show that it is effective in reducing the divergence rate of the filter.