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Top1. Introduction
Kalman filter (KF) or a linear quadratic estimation has received a lot of attention in the area of object tracking in recent years, since it forms the basis upon which all tracking methodologies are built, including non – linear state estimates and is an algorithm that uses series of observable measurements over a certain period. It may contain statistical noise and many other inaccuracies, and produces estimates of unknown variables that may turn to be more accurate compared to those centered on single measurement alone. KF in recent years has become a hot research topic with regards to object filtering and object tracking. KF has many application areas including guidance and navigation and control of vehicles, particularly aircraft and spacecraft (Musoff & Zarchan, 2005); time series analysis in the areas signal processing and econometrics; planning and control in robotics; trajectory optimization and biology in modelling the movement of the central nervous system. The KF is conceptualized as having two distinct phases known as predict and update phases. The predict phase uses the state estimate from the previous time-step to produce an estimate of the state at the current time-step (the priori state estimate) but however, it does not include observation information from the current time-step (Wolpert & Ghahramani, 2000). In the update state however, current priori prediction is combined with current observation information to refine the state estimate and thus improve the estimate and is termed posteriori state estimate. The generalization and the extension of KF has led to the development of the Extended Kalman Filter (EKF) and the Unscented KF (UKF) which works best with non-linear systems and it is one of the motivational factors driving this research.
KF is implemented for systems whose dynamics are not linear, to locate the problems by using the two popular extensions of KF. In case of the EKF, it is not necessary that both models (state transition and observation model) be linear functions of the state, but, may instead be non-linear functions (Julier & Uhlmann, 1997a). 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, So that, we could apply linear Kalman filter (Julier & Uhlmann, 1997a). The other issue is the application of KF to realistically map signals in high dimensional space into a low space and how to obtain a feasible or an appropriate approximation model. The use of a locality sensitive with KF currently seems to be the most practical way to address the issue.
Target Tracking (TT) on other hand is the prediction of the future location of a dynamic object or system 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. Topical areas of TT that are of research interest are filtering and prediction, modelling of target dynamics, probabilistic systems, data fusion and associations and sensor assessments. Signals that are transmitted are usually opposed by some form of inertial and these signals need to be subjected to some form of filtering which is done digitally through an algorithm that discriminates defined based on the traits of signals. The filters used to achieve this purpose of Non-Linear KF (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 nonlinear systems.