Linear estimators have been extensively utilized for wireless location estimation for their simplicity and closed form property. In the paper, the class of linear estimator by introducing an additional variable, e.g., the well-adopted linear least squares (LLS) estimator, is discussed. There exists information loss from the linearization of location estimator to the nonlinear location estimation, which prevents the linear estimator from approaching the Cramér-Rao lower bound (CRLB). The linearized location estimation problem-based CRLB (L-CRLB) is derived in this paper to provide a portrayal that can fully characterize the behavior for this type of linearized location estimator. The relationships between the proposed L-CRLB and the conventional CRLB are obtained and theoretically proven in this paper. As suggested by the L-CRLB, higher estimation accuracy can be achieved if the mobile station (MS) is located inside the convex hull of the base stations (BSs) compared to the case that the MS is situated outside of the geometric layout. This result motivates the proposal of geometry-assisted localization (GAL) algorithm in order to consider the geometric effect associated with the linearization loss. Based on the initial estimation, the GAL algorithm fictitiously moves the BSs based on the L-CRLB criteria. Two different implementations, including the GAL with two-step least squares estimator (GAL-TSLS) and the GAL with Kalman filter (GAL-KF), are proposed to consider the situations with and without the adoption of MS's historical estimation. Simulation results show that the GAL-KF scheme can compensate the linearization loss and improve the performance of conventional location estimators.
- Cramér-Rao lower bound (CRLB)
- Kalman filter
- Linear least squares (LLS) estimator
- location estimation
- two-step least squares estimator