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Top1. Introduction
Current proliferation of Digital and ubiquitous devices with its attendant advancement in Technology have contributed immensely, to the upsurge in the study of Non-linear Kalman Filtering (NLKF) and its application in surveillance networks and Military intelligence systems for tracking of objects. This complements the advancement in the life style of social beings (Humans). NLKF is a filtering algorithm that is used in linearizing NLS for effective tracking of objects in dynamic environments which is significantly better than any strictly linear filter. Frankly speaking, Ohm’s law is only linear up to a certain threshold, however, many systems are more close to been linear since they give a satisfactory result (Akram, Liu, Tahir, Ali, & Wang, 2019; Julier & Uhlmann, 1997). More so, the most effective applications of KF has been in circumstances of non-linear dynamics or measurements, hence the objective is to linearize the system first and then apply the normal Kalman Filter (KF) to obtain the current state of the system addressed in (Musoff & Zarchan, 2005).
Furthermore, there are two types of linearization carried out with respect to NLS, namely the linearization of trajectory or solution of stochastic system (i.e. continuously with state estimates resulting from measurement) and linearization with a set of chosen sample points respectively referred to as EKF by (Gao, Zhang, & Petersen, 2017) and UKF by (Wan & Van Der Merwe, 2000) as well as the normal KF in (Faragher, 2012), where the trajectories are linearized independent of measurement data. When both models (state transition and observation model) are highly non- linear, EKF give poor performance because the covariance is propagated through linearization of the underlying nonlinear model. But in case of UKF, a deterministic sampling technique is used known as unscented transform to pick a set of sample points around the mean known as sigma points. The Sigma points are propagated through non-linear functions, from which estimate of mean and covariance are calculated. More so, EKF is used to linearize all non-linear models in order to could apply linear KF (Julier & Uhlmann, 1997). Further, there is a challenge in applying KF to realistically map signals in high dimensional space into a low space and also how to obtain an appropriate approximation model. Hence, incorporating locality-sensitive with KF seems to be the most practical way to address the issue for effective target tracking. TT, which is the prediction of the future location of a dynamic object based on its estimates and measurements.
Moving objects are monitored and detected by sensor nodes and their trajectories further predicted by sensor nodes based on their observations on movements of the target. Signals that are transmitted are usually opposed by some form of inertial and these signals need to be subjected to some form of filtering. This is done digitally through an algorithm that discriminates, defined based on the traits of signals. The filters used to achieve this purpose of NLKF are the UKF and the EKF, both of which could be implemented in addressing the issues of white noise and other signal defects in NKL. TT, the estimation of the future trajectory of a targeted object calculated on its past events or states. NLKF has been widely used as tracking filter to estimate the position, the acceleration and the velocity of a target object, whose performance in the situation of maneuver could be challenging. As a result, to alleviate the issues discussed so far, different methods have been employed over the years by past studies the resolve the challenges with NLKF approaches for TT. A robust and fast tracking algorithm was developed in (Zhan & Wan, 2007), named iterated UKF (IUKF). The IUKF algorithm could obtain more accurate state and covariance estimation. the proposed method has potential advantages in tracking accuracy, convergence speed, and robustness when compared with the conventional nonlinear methods such as EKF and UKF as established through arithmetical simulation and experiment results. (Di, Joo, & Beng, 2009) iterated the relevance of TT for wireless sensor networks and also highlighted that KF and its variants are amongst the most popular algorithms in addressing signal tracking issues.