Introduction to Kalman Filtering Science Assignment Help

Assignment Task

Task    

In this project, you will learn about Bayesian filtering for object tracking, using methodological tools covered in the lecture materials of B39AX. We will introduce the main principles of Kalman Filter in scenarios where the object is assumed to have an almost constant velocity. The object is assumed to have a single spatial coordinate but the model can be generalised to higher dimensions, e.g. 2D coordinates and beyond.Section 1 provides a short introduction and motivation for the Kalman filter. In Section 2 you will use the concepts seen during the online videoand live sessions to develop the equations of one Kalman filter. 
1 Introduction
The filtering or tracking framework investigated in this project originates from the work of R. E. Kalman [1] (1960) describing a recursive solution to the discrete-data linear filtering problem. Since then, this method has been extensively used and modified in a variety of tracking applications, assisted navigation and multiple target tracking. In this project, we will use single target tracking as exemplar application. The estimation of the trajectory of an object is of prime importance in navigation as the sensors used to estimate positions often provide noisy incorrect measurements. For instance, GPS readings can be prone to errors due to multi-path, in particular in dense urban areas. If the signal is lost, it is also very useful to be able to predict how the vehicle moves to interpolate the trajectory until new measurements are recorded.Trajectory estimation can be performed either in an offline or an online fashion. Offline methods usually consider the complete time period during which we want to estimate the trajectory and use all the measurements simultaneously. Thus, for any time instant during that period, such methods can use the previous measurements but also the future measurements to estimate the current object position. Conversely, online methods generally only consider past measurements to estimate current states (positions, velocities). While offline methods are generally more precise, they cannot be applied in real-time and they can suffer from large memory requirements (as the whole data sequence needs to stored) and high computational complexity. Online methods can be significantly faster and less computationally intensity as they only process each observation only once. Hence, they can often is applied in real-time scenarios
 

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