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One interesting scenario in personal positioning involves an energy-conscious mobile user who tries to obtain estimates about his positions with sufficiently high confidence while consuming as little battery energy as possible. Besides obtaining estimates directly from a position measuring device, the user can rely on extrapolative calculations based on a user movement model and a known initial estimate. Because each measuring probe usually incurs a substantially higher cost than the extrapolative calculation, the objective is to minimize the overall cost of the measurement probes.Assuming that the user moves at a normally-distributed velocity, we consider two scenarios which differ in the probing devices used. In the first scenario, only one probing device is used. In this case, the aim is to minimize the total number of probes required. In the second scenario, two types of positioning devices are given, where one type of devices offers a higher positioning precision, but also at a greater probing cost. In this case, the aim is to choose an optimal combination of probes from the two types of devices.For both scenarios, we present algorithms for determining the minimum-cost probing sequences. The algorithms are computationally efficient in reducing the searching space of all possible probing sequences. Our approach is based on Kalman Filtering theory which allows to integrate estimates obtained from the measurements and the extrapolative calculations. The variances in the estimates can provably stay below the specified level throughout the journey.To the best of our knowledge, these results appear to be the first that uses a mathematically rigorous approach to minimize the probing cost while guaranteeing the quality of estimates in personal positioning.

Controlling Uncertainty in Personal Positioning at Minimal Measurement Cost