## 4 Approaches of Optimizing Geolocation Measurements
### Weighted Least Square (WLS)  
The weighted least squares (WLS) is defined as an ordinary least squares and linear slope in that the error covariance matrix is allowed to be different from a status matrix. This approach has been commonly used in numerous geolocations and target tracking scenarios recently. For example, in [89], the WLS algorithm was proposed for estimating the position target employing the hybrid RSS/AOA measurements of the signals received at several sensors. In an explicit manner, in the proposed algorithms, the source location coordinates with known relation between the intermediate variable and the source location coordinates are an advantage. By using 2 nd order Taylor approximation assuming perfect knowledge of the actual target location, the author derived an approximate error covariance matrix under Gaussian measurement noise. The least-squares solution is considered for computing the relative error of the covariance matrix without knowledge of the target location under measurement noise over the sensor nodes instead of the true target position. The superiority of the proposed algorithm when compared to the LS algorithm confirms the minimum estimation bias and Root Mean Square Error (RMSE) for estimating the position of the emitter source. Figure 15 illustrates the geometry of the proposed scenario.  
Figure 14: Distribution of the sensors and emitter for the proposed scenario [87].  
[PERSON] et al. proposed a practical iterative constrained weighted least squares (ICWLS) algorithm to estimate multiple targets by multiple mobile sensors and multiple calibrations, as shown in Figure 16, which used TDOA/FDOA localization measurements. The proposed method consisted of two stages. In the first stage, the location of the sensors is enhanced based on the calibration measurements as well as the previous knowledge of the sensors position. In the second stage, the estimate of the multiple target geolocation is obtained by joining the measurements of emitted signals and the estimated values obtained in the first stage [90]. The simulation results demonstrated that the proposed algorithm could produce the optimal solution to the formulated constrained WLS problem. Additionally, its estimation RMSE can achieve CRLB with calibration emitters at common noise; from that, the analytical validation results verified that the proposed algorithm is better than some existing localization algorithms [90].  
In [91], a simple algorithm is designed for movable target estimation using three or more stationary sensors. The performance of the proposed algorithm was verified by CRLB and compared with the LLS, quadratic least squares (QLS) and two-step WLS algorithms.  
Figure 16: Multi-sensors, multi-emitter calibration, and multi-agent geometry [90].  
Figure 15: Geometry of the sensor and target location in 3D [89].  
In this study, the corresponding mean relative position errors (MRPEs) and the mean square position errors (MSPEs) versus range error variance, ignoring multi-path and NLOS errors, were computed and simulated, as shown in Figure 17.  
In [75], an algebraic method for the estimation of the location and velocity of a moving source using TDOA, FDOA, and differential Doppler rate measurements of a signal received at several sensors with sensor location errors were proposed. The method depends on the two-step weighted least square estimator and the pseudo-linear set of equations. In the algorithm, the tri-combination of the geolocation measurement was proposed. The estimated precision of the emitter position and velocity is displayed to achieve the Cramer-Rao lower bound (CRLB) for Gaussian TDOA, FDOA, and differential Doppler rate noise at a measured noise level before the thresholding effect occurs.