## 5 Approaches of Optimal State Estimation Utilizing Filtering
### \(H_{\infty}\) Filter  
\(H_{\infty}\) is a developed filter employed to overcome the degradation that affects the Kalman Filter performances and results in unreliable state estimates. The first discovery of \(H_{\infty}\) was in the 1980s, and it is a new development compared to Kaman Filter. Therefore, there is a wider area for extra work and development in \(H_{\infty}\) filtering than Kalman filtering [30]. The authors of [125] proposed a decentralized \(H_{\infty}\) / UKF that enhances the strength of the \(H_{\infty}\) standards developed in robust control to address a non-Gaussian process and measurement noise as well as unreliable state estimates. To address the strong model non-linearities, the advent of UKF has been utilized by the proposed algorithm under uncertainties. The linear-like batch-mode regression model for statistical linearization approach equivalent to the linear Kalman filter is derived. The simulation result illustrates an RMSE comparison of the proposed algorithm performance with decentralized UKF with a measured terminal  
Figure 33: Comparing the performance of target tracking algorithms [21]. voltage phasor (DUKFV) and a decentralized UKF with a measured terminal current phasor (DUKFI) in the presence of a non-Gaussian process and measurement noise. In addition, it provided that the proposed \(H_{\infty}\)/UKF is capable of bounding the influences of numerous types of measurement and model uncertainties while achieving precise state estimates. Based on TDOA and FDOA measurements, the study focused on comparing the performance of non-linear filters for estimation of the location and velocity of a moving emitter. From Reference [125], the comparison shows that \(H_{\infty}\)/UKF is better than other conventional filters. In 2011, [PERSON] et al. proposed a novel algorithm that combines the \(H_{\infty}\) filter into the particle filter (PF). The main purpose of combining \(H_{\infty}\) with PF is a new particle sample of PF that will be taken by the \(H_{\infty}\)F algorithm [126]. Consequently, \(H_{\infty}\)F can take into account full current measurements. Moreover, the \(H_{\infty}\)F algorithm can adjust the gain inequality factor by adjusting the disturbance attenuation factor and achieve satisfying accuracy and robustness. The experimental results illustrate the estimated trajectory of the target by PF, KPF, and \(H_{\infty}\)/PF and present a comparison of an error estimated for a localization and target tracking using a PF, Kalman Particle Filter (KPF), and \(H_{\infty}\)/PF. The simulation and experimental results concluded that the proposed \(H_{\infty}\)/PF performed better than PF and the PKF in tracking maneuvering targets. In Figures 34 and 35, it is interesting to observe how estimation accuracy was improved using \(H_{\infty}\) mixed with Gauss Hermite Quadrature Kalman filters in regards to the geolocation and target tracking based on TDOA/FDOA measurements derived and implemented by the authors [21]. Figure 34: Comparing the performance of target tracking algorithms. This study focused on comparing the performance of non-linear filters for estimating the location and velocity of a moving emitter based on TDOA and FDOA measurements. The comparison shows that the \(H_{\infty}\)/GHKF is better than other conventional filters [21]. Table 4 displays a comparison between different filters employed in the optimal state estimation for an emitter source. In Table 5, geolocation and target tracking approaches, as well as algorithm specifications employed in the state-of-the-art methods, have been summarized. Consequently, we can note that the increasing number of sensors as well as combining more than one geolocation technique leads to an increase in the accuracy of the geolocation measurement. In addition, the scenarios of geolocation and emitter tracking that were verified in near-field environments were more precise compared to the scenarios in far-field environments.