# Reduced-Complexity Tracking Algorithms on Chip for Real-Time Location Estimation
## 1 Introduction  
Given the rapid advance in wireless communication and mobile network technologies, the development of micro-electromechanical systems, the extensive use of satellite navigation technologies, the increased demand for intelligent nursing care systems, and the maturing technologies in cloud computing and Internet of Things (IoT), the database systems can collect the big data with mobile devices, and then they analyze, compute, and extract the useful information from the disorganized data in the database [1; 2; 3; 4; 5; 6]. Afterward, they can supply useful information via location-based services (LBSs) for different purposes. Recently, people have paid more attention to rapid and friendly approaches. Namely, the expectations in terms of market opportunities are the continuously and rapidly increasing attention on mobile computing, IoT, smart agriculture, and smart city issues. In order to improve the positioning and tracking accuracy, fusion approaches between the absolute approach and relative approach can be considered an important technique for positioning and tracking systems [7; 8; 9; 10; 11; 12; 13]. Namely, to improve localization accuracy, most filters utilize Bayesian estimators such as the Kalman filter (KF), extended KF (EKF), orunscent KF (UKF) applied to linear and nonlinear systems. KF approaches are based on the state space equation of the linear system, and provide a recursive solution to the linear optimal filtering problem. The solution is on the basis of recursive, and it is suitable for stationary and non-stationary environments. In the light of KF-based approaches, each updated state is computed based on the previous estimate and new input data. Namely, KF-based approaches only need to store the previously estimated data, it does not need to store the entire past observation data [7; 8; 9; 10; 14]. KF-based approaches are suitable for dealing with the estimation of the state vector in the linear model of the dynamic system. If the nonlinear model is generated by the linearization program, the filter is on the basis of the EKF algorithm generally [7; 10; 14; 15; 16]. EKF-based algorithms are on the basis of KF algorithms with excellent accuracy. EKF-based algorithms are used as techniques to perform recursive nonlinear estimation, and these approaches are described in terms of difference equations in the case of discrete-time systems. Therefore, EKF-based approaches are one of the state estimation algorithms suitable for many embedded systems. For nonlinear systems, an EKF-based algorithm only provides an optimal approximation for performing recursive nonlinear estimation. Nevertheless, the UKF-based algorithm can perform better than the EKF-based algorithm. The differences between EKF and UKF approaches are represented for propagating through system dynamics based on Gaussian random variables (GRV) [7; 14; 17]. For EKF-based approaches, the state distribution is approximated by GRV and then propagated analytically through the first-order linearization of the nonlinear system. Namely, EKF-based approaches may introduce large errors in the true posterior mean and covariance of the transformed GRV, and it leads to reduce the performance of the systems. The UKF algorithm is based on a deterministic sampling approach. The state distribution is approximated by a GRV. For propagating through the true nonlinear system, the sample points completely capture the true mean and covariance of the GRV [14]. Namely, for the nonlinear system, UKF-based approaches capture the posterior mean and covariance to second-order series expansion. UKF-based approaches do not require an explicit Jacobian calculation, and the computational complexity of UKF algorithms is the same as that of EKF algorithms [14]. The fusion approach based on the traditional KF tracking algorithm requires inverse operations which are high computational complexity, and direct implementation of the KF algorithm may be too complex to be applied to the practical systems.