# Satellite-Based Localization of IoT Devices Using Joint Doppler and Angle-of-Arrival Estimation
## 2 Related Works
[25] applies it to the maximum likelihood (ML) cost function up to the second order. To further improve satellite-based localization performance, multiple types of measurements could be fused to compensate for the shortcomings of each measurement type. However, combining different types of measurements poses some degree of difficulty. For example, the work in [16] uses a maximum likelihood estimator (MLE), which is based on importance sampling to estimate the Doppler and AoA measurements. MLE is chosen to achieve higher accuracy compared to the other methods, such as using two sequential one dimension (1D) optimization problems [27] or the use of a combination of two 1D frequency-multiple signal classification/estimation of signal parameters via rotational invariance techniques (MUSIC/ESPRIT) and one 1D space-MUSIC/ESPRIT to form a tree-structured frequency-space-frequency (FSF) MUSIC/ESPRIT algorithm [28]. For the first method, the 1D sequential optimization is run one-at-a-time, while the other parameters are fixed. Then, the process is repeated to optimize the previously fixed parameters and set the other parameters as fixed variables. However, this method is an iterative process and only converges to a local maximum [27]. Furthermore, the latter approach [28] can estimate the Doppler and angle of two sources. If the Doppler or angle of the two sources is very similar, the estimation is only possible assuming they are using the same radio resources (in this case, the same frequency band) and that the other parameters are well separated from the closed one. Furthermore, it is essential to know or estimate a priori the number of sources with the same angle or Doppler. In [16], a maximum joint likelihood of Doppler and AoA is proposed. Formulating a closed-form solution of the joint likelihood function does not seem to be possible [16]. Therefore, the work in [16] suggests using a global maximization method for the nonlinear likelihood optimization. In this work, [16], the Doppler and AoA are estimated from the received complex signal. Other than that, WIVE can also be used to eliminate the correlation between the measurement matrix and the pseudolinear noise vector by exploiting the instrumental variables. In [19], an improved version of the weighted instrumental variable estimator (I-WIVE) is proposed to cater to large measurement noise as the WIVE algorithm is only asymptotically unbiased when small measurement noise is present. I-WIVE is developed by estimating the bias of WIVE and subtracting it from the WIVE estimate. It is proven from the simulation results that the I-WIVE has better performance than the WIVE. Most of the work presented in the literature for the joint Doppler and AoA measurements revolves around the estimation of the measurements [16; 27; 28] instead of localizing the source directly. The satellite-based localization literature [5; 6; 10] typically reports the usage of either the Doppler shift frequency or AoA measurements. Therefore, to address the gap, we present a satellite-based ground IoT device localization framework using both the Doppler and AoA measurements by expressing a likelihood function that characterizes the joint measurements given the proposed ground IoT device's location.