new developments in track and vertex reconstruction

New developments New developments in track and vertex in track and vertex

reconstructionreconstruction

Talk given at DESY/UniversitTalk given at DESY/Universität Hamburg, 24.01.05ät Hamburg, 24.01.05Are Strandlie, Are Strandlie,

Gjøvik University College, NorwayGjøvik University College, Norway

A. Strandlie, DESY, 24.01.2005

OutlineOutline

IntroductionIntroduction Review of traditional track Review of traditional track

reconstruction algorithmsreconstruction algorithms New developmentsNew developments

Gaussian-sum filter for electron Gaussian-sum filter for electron reconstructionreconstruction

Gaussian-sum filter for vertex reconstructionGaussian-sum filter for vertex reconstruction Deterministic Annealing Filter for combined Deterministic Annealing Filter for combined

track finding and fitting (very preliminary – track finding and fitting (very preliminary – work in progress)work in progress)

Summary and conclusionsSummary and conclusions


IntroductionIntroduction

Rudi FrRudi Frühwirthühwirth

gave a similargave a similar

presentation here presentation here

two years agotwo years ago


IntroductionIntroduction

I will – after a brief review – mainly focus I will – after a brief review – mainly focus on what has happened after Rudi’s talkon what has happened after Rudi’s talk

The amount of topics will therefore be The amount of topics will therefore be limitedlimited

Hopefully at least some of the topics can Hopefully at least some of the topics can be covered in enough detail to be be covered in enough detail to be understandableunderstandable

The main focus will be on track The main focus will be on track reconstruction, except one example of a reconstruction, except one example of a vertex reconstruction algorithmvertex reconstruction algorithm


ReviewReview

Track reconstruction is traditionally divided Track reconstruction is traditionally divided into two separate parts:into two separate parts: track findingtrack finding or or pattern recognition pattern recognition (division of (division of

full set of hits in a detector into several sub-sets – full set of hits in a detector into several sub-sets – each subset containing hits believed to come from each subset containing hits believed to come from one particle)one particle)

track fittingtrack fitting ( (estimationestimation of track parameters of track parameters from the track candidates or sub-sets of hits from the track candidates or sub-sets of hits produced by the track finder)produced by the track finder)

Methods used for these tasks as well as the Methods used for these tasks as well as the boundaries between them have continuously boundaries between them have continuously changed over the yearschanged over the years


ReviewReview Track finding in Track finding in early bubble chamber early bubble chamber

experimentsexperiments was done in a was done in a purely manual waypurely manual way:: events were events were inspected on a scanning tableinspected on a scanning table machinesmachines measuring bubble positions on the event measuring bubble positions on the event

image image were guided by an operatorwere guided by an operator One of the popular, early methods for automatic One of the popular, early methods for automatic

track finding was the so-called track finding was the so-called Hough transformHough transform finding straight lines by transforming each finding straight lines by transforming each

measurement to a line in a parameter spacemeasurement to a line in a parameter space measurements lying along straight lines in original measurements lying along straight lines in original

picture create lines crossing at one point in parameter picture create lines crossing at one point in parameter spacespace

Tracks were fitted by a Tracks were fitted by a global least-squares global least-squares estimatorestimator


ReviewReview

CERN CERN

2m bubble2m bubble

chamberchamber


ReviewReview

The famousThe famous

””scanning ladies”scanning ladies”


ReviewReview

bubble bubble

chamberchamber

picture andpicture and

subdivision subdivision

into segmentsinto segments


ReviewReview

one segmentone segment

projection ofprojection of

transformtransform


ReviewReview New challenges had to be faced by least-New challenges had to be faced by least-

squares fitting algorithms when electronic squares fitting algorithms when electronic experiments came on stage in early 70’sexperiments came on stage in early 70’s

Prime example: Prime example: Split Field Magnet (SFM)Split Field Magnet (SFM) detector at the detector at the CERN Intersecting Storage CERN Intersecting Storage Rings (ISR)Rings (ISR) precise treatment of material effectsprecise treatment of material effects in wire in wire

chambers was neededchambers was needed also important effects from also important effects from crossing beam pipe crossing beam pipe

at shallow anglesat shallow angles correct approach pioneered by correct approach pioneered by M. ReglerM. Regler (CERN (CERN

73-2 1973)73-2 1973) Track finding was still mainly considered as a Track finding was still mainly considered as a

separate procedure preceding the track fitseparate procedure preceding the track fit


ReviewReview

SFM detector at CERN ISRSFM detector at CERN ISR


ReviewReview

excerpt from paperexcerpt from paper

by Nagy et al.by Nagy et al.

(Nucl. Phys. B 1979)(Nucl. Phys. B 1979)

correct weightingcorrect weighting

enabled very preciseenabled very precise

cross-section measurementscross-section measurements


ReviewReview

In In WA13 experimentWA13 experiment at CERN, a at CERN, a new new formulation formulation of theof the least-squares least-squares method was developed method was developed

This method – the so-called This method – the so-called progressive progressive methodmethod due to P. Billoir – due to P. Billoir – included included measurements recursivelymeasurements recursively into the fit into the fit (NIM 1984)(NIM 1984)

Estimates of track parameters were Estimates of track parameters were updated each time information from new updated each time information from new measurement was includedmeasurement was included


ReviewReview

layout oflayout of

WA13 WA13

experimentexperiment


ReviewReview During development of reconstruction During development of reconstruction

software for DELPHI experiment at LEP software for DELPHI experiment at LEP collider at CERN, it was realized by R. collider at CERN, it was realized by R. FrFrühwirth that ühwirth that progressive method was progressive method was equivalent to Kalman filterequivalent to Kalman filter (NIM A 1987) (NIM A 1987)

Immediate implications:Immediate implications: existence of existence of Kalman smootherKalman smoother easy to obtain easy to obtain optimal estimates anywhere optimal estimates anywhere

along the trackalong the track enables enables efficient outlier rejectionefficient outlier rejection, as track , as track

parameter predictions are calculated from all parameter predictions are calculated from all other measurements in a trackother measurements in a track


ReviewReview Due to the recursive nature of the Kalman filter, Due to the recursive nature of the Kalman filter,

it was soon realized that it could be used for it was soon realized that it could be used for track finding and fitting concurrentlytrack finding and fitting concurrently

given an estimate of the track parameters of a given an estimate of the track parameters of a segment of the track, hits inside a search window segment of the track, hits inside a search window compatible with the prediction into the next layer are compatible with the prediction into the next layer are considered for being included in the track candidateconsidered for being included in the track candidate

no more strict separation between these proceduresno more strict separation between these procedures Application of Kalman filter as track finder was Application of Kalman filter as track finder was

pioneered by P. Billoir in DELPHI pioneered by P. Billoir in DELPHI experimentexperiment at LEP at LEP (Billoir, Comp. Phys. Comm. (CPC) (Billoir, Comp. Phys. Comm. (CPC) 1989)1989)


ReviewReview

It was tried out on It was tried out on real datareal data for the for the first time in first time in ZEUS experiment at ZEUS experiment at DESYDESY (Billoir and Qian, NIM A 1990)(Billoir and Qian, NIM A 1990)

The method was generalized by R. The method was generalized by R. Mankel to possibly Mankel to possibly propagate several propagate several track candidatestrack candidates concurrentlyconcurrently in in HERA-B experiment at DESYHERA-B experiment at DESY (Mankel, (Mankel, NIM A 1997)NIM A 1997)

Is today by far the Is today by far the most widely used most widely used methodmethod for track finding and fitting for track finding and fitting


ReviewReview

principle ofprinciple of

methodmethod

result from eventresult from event

in DELPHI TPCin DELPHI TPC


ReviewReview

reconstructedreconstructed

event fromevent from

ZEUSZEUS


ReviewReview

Main Tracker inMain Tracker in

HERA-BHERA-B

principle of concurrentprinciple of concurrent

track evolutiontrack evolution


ReviewReview

Track finding and track fitting was Track finding and track fitting was traditionally considered as separate taskstraditionally considered as separate tasks

In bubble chamber and early electronic In bubble chamber and early electronic experiments many types of track finding experiments many types of track finding algorithms were usedalgorithms were used

Tracks were in all (or at least most) cases Tracks were in all (or at least most) cases fitted by a global least-squares methodfitted by a global least-squares method

Since the invention of the Kalman filter, Since the invention of the Kalman filter, strict boundaries between track finding strict boundaries between track finding and fitting do no longer exist and fitting do no longer exist


ReviewReview Kalman filter has been the dominating Kalman filter has been the dominating

method in track reconstruction for many method in track reconstruction for many yearsyears

Most important developments after the Kalman Most important developments after the Kalman filter:filter: adaptive methods (Deterministic Annealing Filter adaptive methods (Deterministic Annealing Filter

(DAF), Multi-track Filter (MTF))(DAF), Multi-track Filter (MTF)) Gaussian-sum filters (GSF)Gaussian-sum filters (GSF)

Both of these classes of methods can be regarded Both of these classes of methods can be regarded as generalizations of the Kalman filteras generalizations of the Kalman filter DAF is an iteratively reweighted Kalman filterDAF is an iteratively reweighted Kalman filter GSF takes the form of several Kalman filters running in GSF takes the form of several Kalman filters running in

parallelparallel


ReviewReview

GSF works by GSF works by modelling non-modelling non-Gaussian effects of various kinds Gaussian effects of various kinds as Gaussian mixturesas Gaussian mixtures measurement errorsmeasurement errors bremsstrahlung energy lossbremsstrahlung energy loss multiple scatteringmultiple scattering non-Gaussian tails in track parameter non-Gaussian tails in track parameter

distributions used for vertex fitting distributions used for vertex fitting


ReviewReview Adaptive methods work by Adaptive methods work by

downweighting non-Gaussian effectsdownweighting non-Gaussian effects measurement errorsmeasurement errors resolution of left-right ambiguitiesresolution of left-right ambiguities distorted hitsdistorted hits wrongly associated tracks in a vertex fitwrongly associated tracks in a vertex fit immature convergence of alignment parameters immature convergence of alignment parameters

in sequential procedure (with tracks)in sequential procedure (with tracks) I will in the following concentrate on a few, I will in the following concentrate on a few,

recent applications of Gaussian-sum filters recent applications of Gaussian-sum filters and adaptive methodsand adaptive methods


New developmentsNew developments

GSF forGSF for

electron electron reconstructionreconstruction



An important effect needing treatment An important effect needing treatment during track reconstruction is during track reconstruction is energy energy lossloss

Ionization loss is often regarded as Ionization loss is often regarded as deterministic correction to track deterministic correction to track modelmodel

Electrons need special treatment:Electrons need special treatment: suffer from suffer from bremsstrahlungbremsstrahlung energy loss energy loss dominant componentdominant component of energy loss above of energy loss above

~100 MeV/c~100 MeV/c



distribution ofdistribution of

relative energyrelative energy

lossloss

strongly peakedstrongly peaked

with long tailwith long tail


New developmentsNew developments Kalman filter implicitely assumes that Kalman filter implicitely assumes that

bremsstrahlung distribution is Gaussianbremsstrahlung distribution is Gaussian since it is known to be optimal only when errors are since it is known to be optimal only when errors are

GaussianGaussian such an approximation is quite crude for the such an approximation is quite crude for the

bremsstrahlung distributionbremsstrahlung distribution Plausible that approach which better takes the Plausible that approach which better takes the

actual shape of the distribution into account can do actual shape of the distribution into account can do betterbetter

GSF algorithm for electron reconstruction uses an GSF algorithm for electron reconstruction uses an approximation of the bremsstrahlung approximation of the bremsstrahlung distribution by Gaussian mixturesdistribution by Gaussian mixtures instead of a instead of a single Gaussiansingle Gaussian


New developmentsNew developments In the GSF, track states are described by In the GSF, track states are described by

Gaussian mixtures instead of single GaussiansGaussian mixtures instead of single Gaussians As with the Kalman filter, the GSF proceeds As with the Kalman filter, the GSF proceeds

by alternating propagation and update stepsby alternating propagation and update steps Adding material effects in a detector layer Adding material effects in a detector layer

amounts to a convolution of the density of the amounts to a convolution of the density of the predicted state with the density describing the predicted state with the density describing the disturbance of the track in the materialdisturbance of the track in the material

This leads to a potential combinatorial This leads to a potential combinatorial explosion in the number of components in the explosion in the number of components in the state mixturestate mixture number of components has to be limited to a number of components has to be limited to a

tolerable valuetolerable value


New developmentsNew developments Gaussian-mixture approximations of Gaussian-mixture approximations of

the Bethe-Heitler distributionthe Bethe-Heitler distribution (well- (well-know, analytical approximation of the know, analytical approximation of the bremsstrahlung distribution) have been bremsstrahlung distribution) have been calculated recentlycalculated recently

Expressions exist in the published Expressions exist in the published literature literature (Fr(Frühwirth, CPC 2003)ühwirth, CPC 2003)

These have been used in aThese have been used in a GSF GSF implementation implementation in the CMS tracker at in the CMS tracker at CERN CERN (W.Adam, R. Frühwirth, A. Strandlie, T. (W.Adam, R. Frühwirth, A. Strandlie, T. Todorov, Proc. CHEP’03, 2003)Todorov, Proc. CHEP’03, 2003)



Rz-projectionRz-projection

of one quadrantof one quadrant

of CMS trackerof CMS tracker



The mixture parameters (weights, mean The mixture parameters (weights, mean values and variances) have been obtained values and variances) have been obtained by minimizing the following distances by minimizing the following distances with respect to the mixture parameters:with respect to the mixture parameters:


New developmentsNew developments In order to avoid a combinatorial explosion of In order to avoid a combinatorial explosion of

components, several strategies were tried out for components, several strategies were tried out for limiting the number:limiting the number: pair with smallest distance (Kullback-Leibler) pair with smallest distance (Kullback-Leibler)

repeatedly combined into single componentrepeatedly combined into single component component with largest weight combined with the component with largest weight combined with the

closest one. Repeated with remaining componentsclosest one. Repeated with remaining components components with smallest weights droppedcomponents with smallest weights dropped

First approach turned out to be superior, slightly First approach turned out to be superior, slightly better than the second better than the second

The third is fast but not precise and does not The third is fast but not precise and does not preserve the first two moments of the mixture, preserve the first two moments of the mixture, leading to a biased estimateleading to a biased estimate



estimated distributionestimated distribution

of charged,of charged,

inverse momentuminverse momentum

for single trackfor single track

GSF estimateGSF estimate

clearly non-Gaussian!clearly non-Gaussian!



residuals of estimatedresiduals of estimated

with respect to truewith respect to true

parameters in aparameters in a

simplified simulationsimplified simulation

of the CMS trackerof the CMS tracker



pull quantitiespull quantities

--

not Gaussian either!not Gaussian either!



half-widths of intervalshalf-widths of intervals

covering 68 %covering 68 %

of normalised of normalised

momentum residuals momentum residuals

as function of maximumas function of maximum

number of componentsnumber of components

kept during reconstructionkept during reconstruction



same quantities assame quantities as

previous slideprevious slide

as a functionas a function

of momentumof momentum



probability transformprobability transform

(generalization of(generalization of

chisquare probability)chisquare probability)

of charged, inverseof charged, inverse

momentummomentum



intervals coveringintervals covering

68 % and 95 %68 % and 95 %

of residual momentumof residual momentum

distributions as a distributions as a

function of momentumfunction of momentum

FULLFULL

SIMULATIONSIMULATION



same quantitiessame quantities

as previous slideas previous slide

but withbut with

Gaussian smearedGaussian smeared

measurementsmeasurements



probability transformprobability transform

for charged, inversefor charged, inverse

momentum momentum


New developmentsNew developmentsresolution improvesresolution improves

by 20 % for KFby 20 % for KF

and 35 % for GSFand 35 % for GSF



GSF forGSF for

vertexvertex

reconstructionreconstruction



Kalman filter for vertex reconstruction:Kalman filter for vertex reconstruction: all tracks believed to come from the same all tracks believed to come from the same

vertex are fitted together in a least-squares vertex are fitted together in a least-squares fashion in order to yield the vertex positionfashion in order to yield the vertex position

the parameter vector for a track is considered the parameter vector for a track is considered as a measurementas a measurement

information from these are introduced information from these are introduced recursively, each time yielding an improved recursively, each time yielding an improved vertex positionvertex position

as for the Kalman filter for track reconstruction, as for the Kalman filter for track reconstruction, the procedure is mathematically equivalent to a the procedure is mathematically equivalent to a global least-squares fitglobal least-squares fit



presentationpresentation

by T. Speerby T. Speer

and and

R. FrR. Frühwirthühwirth

at CHEP’04at CHEP’04

implementedimplemented

in CMSin CMS

experimentexperiment

at LHCat LHC



DAF forDAF for

vertex fittingvertex fitting



DAF forDAF for

combined track combined track

finding and finding and fittingfitting



Deterministic Annealing Filter (DAF) was Deterministic Annealing Filter (DAF) was originally invented for resolving left-right originally invented for resolving left-right ambiguities in the ATLAS TRT (ambiguities in the ATLAS TRT (FrFrühwirth and ühwirth and

Strandlie, CPC 1999Strandlie, CPC 1999)) turned out to be very precise and robust for turned out to be very precise and robust for

this purposethis purpose later successfully applied to vertex fitting in later successfully applied to vertex fitting in

CMSCMS implemented for alignment with tracks in CMSimplemented for alignment with tracks in CMS reconstruction of tracks in narrow jets in CMSreconstruction of tracks in narrow jets in CMS



DAF has been implemented in DAF has been implemented in standard standard reconstruction program in CMS trackerreconstruction program in CMS tracker (Winkler, PhD Thesis 2003)(Winkler, PhD Thesis 2003)

Systematic comparisonsSystematic comparisons to standard, to standard, combinatorial Kalman filter (CKF) have been combinatorial Kalman filter (CKF) have been mademade track finding performed by CKF in both cases, track finding performed by CKF in both cases,

fitting procedure differentfitting procedure different Clear improvementsClear improvements in resolution of track in resolution of track

parameters seen in ”difficult” situations, such parameters seen in ”difficult” situations, such as reconstruction of high-energy narrow jetsas reconstruction of high-energy narrow jets



impact parameter impact parameter

resolutionresolution

probabilityprobability

distributionsdistributions



b-taggingb-tagging

efficienciesefficiencies

forfor

DAF almostDAF almost

independentindependent

of jet energyof jet energy


New developmentsNew developments Very recent idea: evaluate the viability of Very recent idea: evaluate the viability of

the DAF as a the DAF as a combined track finder and combined track finder and fitter fitter in scenarios with in scenarios with potentially very potentially very large amounts of hit distortions and large amounts of hit distortions and additional noiseadditional noise as with the Kalman filter, form a track seed as as with the Kalman filter, form a track seed as

the starting point of the track findingthe starting point of the track finding Kalman filter builds up a combinatorial Kalman filter builds up a combinatorial

tree of track candidates starting from the tree of track candidates starting from the seedseed nowadays therefore often called a nowadays therefore often called a

combinatorial Kalman filter (CKF)combinatorial Kalman filter (CKF)



Basic idea of this application of the Basic idea of this application of the DAF:DAF: collect hits around the extrapolation of collect hits around the extrapolation of

the track candidate from the seedthe track candidate from the seed run the DAF on this set of hitsrun the DAF on this set of hits monitor the chisquare of the track in monitor the chisquare of the track in

order to decide whether the track order to decide whether the track candidate is a good track or notcandidate is a good track or not



Potential advantages with respect to Potential advantages with respect to Kalman filter:Kalman filter: no combinatorial explosion in a dense no combinatorial explosion in a dense

track environment or with presence of track environment or with presence of large amounts of noiselarge amounts of noise

DAF known to be very robust when DAF known to be very robust when fitting tracks with distorted hits and fitting tracks with distorted hits and additional noiseadditional noise



Potential disadvantages with respect Potential disadvantages with respect to Kalman filter:to Kalman filter: naive hit collection performed by blind naive hit collection performed by blind

extrapolation from seed can yield track extrapolation from seed can yield track candidate with many hits due to limited candidate with many hits due to limited precision of seed and potentially long precision of seed and potentially long extrapolation distancesextrapolation distances

not obvious how fast the DAF will not obvious how fast the DAF will converge and what it will converge toconverge and what it will converge to



Current study (R. FrCurrent study (R. Frühwirth, A. Strandlie):ühwirth, A. Strandlie): simulation experiment of tracker setup similar simulation experiment of tracker setup similar

to barrel part of CMS and ATLAS inner trackersto barrel part of CMS and ATLAS inner trackers three innermost layers have resolution typical three innermost layers have resolution typical

to that of a pixel detectorto that of a pixel detector ten outermost layers resemble a silicon strip ten outermost layers resemble a silicon strip

detectordetector tracks propagated inwards-out and hits tracks propagated inwards-out and hits

simulated with knowledge of the measurement simulated with knowledge of the measurement resolution and the amount of material in the resolution and the amount of material in the detectordetector



additional, nearby noise hits generatedadditional, nearby noise hits generated fraction of good hits distortedfraction of good hits distorted seeds formed by three 3D hits in layers seeds formed by three 3D hits in layers

closest to the beamclosest to the beam track candidates followed outwards track candidates followed outwards

from seedfrom seed DAF and combinatorial Kalman filter DAF and combinatorial Kalman filter

(CKF) implemented and compared (CKF) implemented and compared



First scenario: assuming that collection First scenario: assuming that collection of hits in a band around the tracks has of hits in a band around the tracks has been performed by separate procedurebeen performed by separate procedure therefore simulating additional noise hits therefore simulating additional noise hits

inside this bandinside this band also distorting a fraction of the true track also distorting a fraction of the true track

hitshits running CKF in the standard way outwards running CKF in the standard way outwards

from the seedfrom the seed for the DAF, using direct propagation from for the DAF, using direct propagation from

seed towards end of tracker as initial trackseed towards end of tracker as initial track



average number of track candidates for CKFaverage number of track candidates for CKF



CKFCKF

1/p_T1/p_T


DAFDAF

1/p_T1/p_T



New developmentsNew developments With no distorted hits (but with additional noise):With no distorted hits (but with additional noise):

CKF about as accurate as DAFCKF about as accurate as DAF fraction of track candidates with contamination about 2 fraction of track candidates with contamination about 2

% for both% for both With 25 % distorted hits:With 25 % distorted hits:

contamination fraction 22 % for CKF and 14 % for DAFcontamination fraction 22 % for CKF and 14 % for DAF With 50 % distorted hitsWith 50 % distorted hits

contamination fraction 42 % for CKF and 35 % for DAFcontamination fraction 42 % for CKF and 35 % for DAF DAF significantly more precise than CKFDAF significantly more precise than CKF

CKF about 15 times slower than DAF (keeping up CKF about 15 times slower than DAF (keeping up to 64 candidates per seed), but CKF does not to 64 candidates per seed), but CKF does not perform much worse with a significantly smaller perform much worse with a significantly smaller amount of candidatesamount of candidates


New developmentsNew developments Second (more realistic) scenario: noise hits Second (more realistic) scenario: noise hits

simulated in entire tracker and hit collection simulated in entire tracker and hit collection performed as part of the track findingperformed as part of the track finding density of noise hits decreasing with second or density of noise hits decreasing with second or

third power of radiusthird power of radius largest occupancy in the innermost layerslargest occupancy in the innermost layers CKF proceeds ”standard” way by building up CKF proceeds ”standard” way by building up

combinatorial tree of track candidates from each combinatorial tree of track candidates from each seedseed

DAF uses two-stage procedureDAF uses two-stage procedure extrapolate three layers after seed, pick up hits in extrapolate three layers after seed, pick up hits in

search window and run to convergencesearch window and run to convergence extrapolate towards end of tracker in more narrow extrapolate towards end of tracker in more narrow

search window, pick up hits and run to convergencesearch window, pick up hits and run to convergence



densitydensity

of noiseof noise

hitshits


New developmentsNew developmentsaverage number of track candidates for CKFaverage number of track candidates for CKF


New developmentsNew developmentsaverage number of hits in search window for DAFaverage number of hits in search window for DAF


New developmentsNew developmentsnumber of DAF iterationsnumber of DAF iterations



CKF and DAFCKF and DAF

resolutions resolutions

without distortedwithout distorted

hitshits



CKF and DAFCKF and DAF

resolutions resolutions

with 10 %with 10 %

distorted hitsdistorted hits


New developmentsNew developments DAF performs very well when efficient hit collection DAF performs very well when efficient hit collection

procedure can be assumedprocedure can be assumed superior to CKF in particular for significant fraction of superior to CKF in particular for significant fraction of

distorted track hitsdistorted track hits Some outliers (fraction increasing with noise Some outliers (fraction increasing with noise

density) when using the DAF also for the hit density) when using the DAF also for the hit collectioncollection due to convergence to wrong set of hits in first pass (i.e. due to convergence to wrong set of hits in first pass (i.e.

first three layers after the seed)first three layers after the seed) for the remaining (non-outlier) set of tracks, the DAF is for the remaining (non-outlier) set of tracks, the DAF is

more precisemore precise main challenge will be to overcome the difficult first phase main challenge will be to overcome the difficult first phase

of track finding when noise level is highof track finding when noise level is high could form seeds at the outside where noise level is smallercould form seeds at the outside where noise level is smaller work still very much in progress…..work still very much in progress…..


Summary and Summary and conclusionsconclusions

A brief review of traditional A brief review of traditional algorithms has been givenalgorithms has been given

Some recent developments have Some recent developments have been presented in some detail:been presented in some detail: GSF for electron reconstructionGSF for electron reconstruction GSF for vertex reconstructionGSF for vertex reconstruction DAF for combined track finding and DAF for combined track finding and

fittingfitting



The Kalman filter is still very The Kalman filter is still very much alive and is the default much alive and is the default choice for many applicationschoice for many applications

New developments such as New developments such as Gaussian-sum filters and Gaussian-sum filters and adaptive methods have been adaptive methods have been shown to be superior for some shown to be superior for some applications and are still gaining applications and are still gaining popularitypopularity



Main drawbacks with advanced Main drawbacks with advanced methods:methods: in general more time consuming in general more time consuming

than Kalman filterthan Kalman filter in my opinion approaching the limit in my opinion approaching the limit

of complexity:of complexity: have to be used with some intelligencehave to be used with some intelligence requires substantial degree of expertise requires substantial degree of expertise

by the implementerby the implementer


Thanks toThanks to

Rainer MankelRainer Mankel

for inviting mefor inviting me

to this seminar!to this seminar!

new developments in track and vertex reconstruction

Documents

combined track

track candidates

track fita

track findermethods

automatic track finding

reviewtrack reconstruction

squares method

regler cern