Browsing by Author "De Villiers, Charl Felix"
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- ItemBayesian signal processing of doppler radar data(Stellenbosch : Stellenbosch University, 2016-12) De Villiers, Charl Felix; Du Preez, J. A.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.ENGLISH ABSTRACT: The aim of this thesis is to investigate a Bayesian approach to signal processing of Doppler radar data. The problem of interest involves measured Doppler radar signals measured for golf players' club swings where the frequency shifts are related to the movements of physical objects. Smoothing the frequency shifts of the Doppler signal allows for more accurate estimates of the speeds of the physical objects of interest which is a step towards estimating the velocities of the objects such as the club and ball and can allow one to calculate their trajectories, as their starting points are known. This information would be invaluable to golf players and coaches, who will be able to improve players' skills based on the knowledge of club velocity at impact, the ball spin, and other properties of interest of the golf swing. We use a Bayesian statistical method called Bayesian spectrum analysis (BSA) to analyse the Doppler signals that were divided into time intervals. BSA allows us to estimate the spectral parameters of the Doppler radar signals in a probabilistic manner, as well as compare competing models in order to select the most probable model from a list of models. We find that the Doppler radar signals contained behaviour that is more complex than our BSA models are able to describe. The BSA results are, however, still useful and can be improved upon by including more prior information. Our approach is to model the multitarget tracking of the frequency components from BSA in the context of Bayesian probability theory, and to then solve the marginal posterior distributions of the parameters of interest using probabilistic graphical models (PGMs). We compensate for uncertainty in the characteristics of our BSA results by modelling the local signal behaviour, as well as the overall trend of the signal by grouping parts of the signal into segments. These signal segments correspond to different parts of the physical golf swing that contain a different number of objects' Doppler shifts and different signal dynamics. We modelled the segment transition as a left-to-right progression. PGMs are well suited to this modular approach and provide the benefit of deconstructing the problem at hand into a set of local dependencies. We also implemented a \missed-target" model using the PGMs framework. The resulting model resembles a multitarget Kalman filter combined with a hidden Markov model. We implement the PGMs as both a fully discrete and a hybrid cluster graph and are able to successfully smooth parts of the Doppler radar frequency shifts. We find that the missed-target model and left-to-right segment transition improve upon the conventional multitarget tracking and allow the PGMs to select the correct signal segment and to smooth over regions where a frequency component was missing. One of the challenges identified in our investigation is estimating both the process noise and measurement noise of the multitarget tracking. Future recommendations include using explicit duration models for the signal signal segment transitions and using alternative discretisation methods.