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In this paper we propose an approach that enables mobile clients to determine the validity of previous queries based on their current locations. In order to make this possible, the server returns in addition to the query result, a validity region around the client's location within which the result remains the same. We focus on two of the most common spatial query types, namely nearest neighbor and window queries, define the validity region in each case and propose the corresponding query processing algorithms. In addition, we provide analytical models for estimating the expected size of the validity region. Our techniques can significantly reduce the number of queries issued to the server, while introducing minimal computational and network overhead compared to traditional spatial queries.

Filter degeneracy is the main obstacle for the implementation of particle filters in nonlinear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced, in which samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction.We test and explore the properties of the new scheme using a 1000 dimensional simple linear model and the 1000 dimensional nonlinear Lorenz96 model and compare the performance of the scheme with that of a local ensemble transformed Kalman filter (LETKF). The new scheme is never degenerate and shows good and consistent performance in all experiments. The LETKF has lower root-mean-square errors at observed grid points, but its ensemble spread is too low at unobserved grid points, where the IEWPF performs better. Furthermore, the IEWPF has a consistent spread in all experiments.This new filter opens up a new class of particle filters that, by construction, do not suffer from the curse of dimensionality.