Robust Kalman-type Filtering in Positioning Applications

Positioning refers to the estimation of one’s location by combining many different sources of information. This information is usually obtained in the form of measurements, which may be, for example, pseudorange or deltarange measurements from satellites. In addition, various wireless networks on Earth, for example, cellular networks, WLAN or Bluetooth provide means for positioning in the form of range measurements, received signal strength indicators and sector information. Portable positioning devices may also contain inertial measurement units that provide information about the movements of the user. The positioning problem may be formulated as a Bayesian filtering problem. The measurements are related to the position of the user, and the relation is approximately known. In addition, there is a model that describes the process dynamics. The measurements are obtained at discrete time intervals, and the process dynamics are also discretized. The system may be described mathematically as follows. Let xk denote the stochastic state vector at time step k , and let y k be the measurement vector. The system is governed by the following equations:

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