Enhanced linearized location estimators with optimization-based combinations of radiolocation measurements

Popular linearized estimators such as the Extended Kalman Filter (EKF) or the one-step linearized Least Squares (LS) estimator, which have been used for years to solve positioning and tracking problems in location-enabled wireless networks, require that available observations are locally linearized (as functions of estimated variables) around the predicted state or initial optimization guess. In most of practical cases however, using measured radiolocation metrics as direct observations (e.g. Time of Arrival (TOA) or Time Differential of Arrival (TDOA)) might lead to poor linearization conditions and hence alter estimation precision and robustness accordingly. In this paper, we present an optimization-based method that enables to adaptively build quasi-linear observations as combinations of raw measurements. The main idea is to choose the coefficients of the linear combinations that minimize the Mean Square Error (MSE) of location estimators, while taking into account both bias errors due to linearization and measurement noise effects.