Bayesian signal processing of doppler radar data

De Villiers, Charl Felix (2016-12)

Thesis (MEng)--Stellenbosch University, 2016.

Thesis

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.

AFRIKAANSE OPSOMMING: Die doelwit van hierdie tesis is die ondersoek na 'n Bayesiese benadering tot seinprosessering van Doppler radar data. Die probleem van belang behels gemete Doppler radarseine wat gerig is op gholfspelers wat gholfstokke swaai. Veranderinge in die weerkaatste seine se frekwensies hou verband met die bewegings van fisiese voorwerpe. Verbeterings op die benaderings van die Doppler-verskuiwings kan lei tot meer akkurate skattings van die spoed van die fisiese voorwerpe. Dit kan lei tot beter beramings van die snelhede van die voorwerpe (soos die gholfstok en -bal) en kan 'n mens toelaat om hul trajekte beter te bereken, aangesien hul beginpunte wel bekend is. Hierdie inligting sal van onskatbare waarde vir gholfspelers en afrigters wees. Ons maak gebruik van Bayesiese spektrale analise (BSA) om die Dopplersein, wat in tydstappe opgebreek is, te ontleed. BSA stel ons in staat om die spektrale parameters van die Doppler radarseine met gebruik van waarskynlikheidsleer af te skat, asook om modelle te vergelyk en die mees waarskynlike model te kies. Ons vind dat die Doppler radarseine vervat gedrag wat meer kompleks is as wat ons BSA modelle kan beskryf. Die BSA resultate is egter steeds nuttig en kan verbeter word deur meer inligting in te sluit. Ons benadering is om die multi-teikenvolging van die frekwensie-komponente van die BSA modelle in die konteks van Bayesiese waarskynlikheidsleer te plaas en om dan die parameters van belang se marginale waarskynlikheidsdigtheidsfunksies te bereken met behulp van waarskynlikheidsgrafiese modelle (PGM'e). Hierdie benadering vergoed vir die inherente statistiese aard van ons BSA resultate deur die modellering van die plaaslike seingedrag, sowel as die algehele tendens van die sein deur die groepering van die seinmonsters in seinsegmente. Hierdie seinsegmente stem ooreen met die verskillende gedeeltes van die fisiese gholfswaai wat verskillende aantal voorwerpe se Doppler-verskuiwings asook verskillende seindinamika bevat. Ons modelleer die segment-oorgange as 'n links-na-regs verloop. PGM'e is goed geskik vir hierdie modul^ere benadering en bied voordele aan soos om die probleem te ontbind in plaaslike afhanklikhede. Ons was ook in staat om 'n \gemiste-teiken" model met behulp van die PGMraamwerk te implementeer. Die model lyk soos 'n multi-teiken Kalman filter gekombineer met 'n verskuilde Markov model. Ons het die PGM'e as beide 'n diskrete en 'n hibriede bundelgra ek ge mplementeer en was in staat daartoe om verbeterings te maak op die Doppler-verskuiwings van die radar sein. Ons het gevind dat die gemiste-teiken model en links-na-regs segment-oorgange verbeter op die konvensionele multi-teikenvolging en het toegelaat dat die PGM'e die korrekte seinsegmente kies, asook om frekwensie-komponente op te spoor in gebiede waar 'n frekwensie-komponent vermis was. Een van die uitdagings wat gedenti seer was in ons ondersoek, is die beraming van beide die proses- en metingsruis van die multi-teikenvolging. Aanbevelings sluit die gebruik van eksplisiete tydsduur modelle vir die sein segment oorgange in, asook die gebruik van alternatiewe diskretiseringsmetodes.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100198
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