Estimate track parameters from seed

Detailed Description

The implemented method is based on the conformal map transformation.

It estimates the full free track parameters, i.e. (x, y, z, t, dx, dy, dz, q/p) at the bottom space point. The magnetic field (which can be along any direction) is also necessary for the momentum estimation.

It resembles the method used in ATLAS for the track parameters estimated from seed, i.e. the function InDet::SiTrackMaker_xk::getAtaPlane here: https://acode-browser.usatlas.bnl.gov/lxr/source/athena/InnerGeometry/InDetRecTools/SiTrackMakerTool_xk/src/SiTrackMaker_xk.cxx

Classes
struct	Acts::EstimateTrackParamCovarianceConfig
	Configuration for the estimation of the covariance matrix of the track parameters with estimateTrackParamCovariance. More...

Functions
BoundMatrix	Acts::estimateTrackParamCovariance (const EstimateTrackParamCovarianceConfig &config, const BoundVector &params, bool hasTime)
	Estimate the covariance matrix of the given track parameters based on the provided configuration.
Result< BoundVector >	Acts::estimateTrackParamsFromSeed (const GeometryContext &gctx, const Surface &surface, const Vector3 &sp0, double t0, const Vector3 &sp1, const Vector3 &sp2, const Vector3 &bField)
	Estimate bound track parameters from three space points.
FreeVector	Acts::estimateTrackParamsFromSeed (const Vector3 &sp0, double t0, const Vector3 &sp1, const Vector3 &sp2, const Vector3 &bField, Vector3 *tangent0=nullptr, Vector3 *tangent1=nullptr, Vector3 *tangent2=nullptr)
	Estimate free track parameters from three space points.
Result< FreeVector >	Acts::estimateTrackParamsFromSpacePoints (std::span< const Vector3 > spacePoints, const Vector3 &bField, double t0=0, std::size_t geometricRefineIterations=0, std::span< const double > weights={}, std::size_t referenceIndex=0)
	Estimate free track parameters from an ordered set of N >= 3 space points.

Function Documentation

estimateTrackParamCovariance()

BoundMatrix Acts::estimateTrackParamCovariance	(	const EstimateTrackParamCovarianceConfig &	config,
		const BoundVector &	params,
		bool	hasTime )

Estimate the covariance matrix of the given track parameters based on the provided configuration.

The assumption is that we can model the uncertainty of the track parameters as a diagonal matrix with the provided initial sigmas. The inflation factors are used to inflate the initial variances based on the provided configuration. The uncertainty of q/p is estimated based on the relative uncertainty of the q/pt and the theta uncertainty.

Parameters

config	is the configuration for the estimation
params	is the track parameters
hasTime	is true if the track parameters have time

Returns

the covariance matrix of the track parameters

estimateTrackParamsFromSeed() [1/2]

Result< BoundVector > Acts::estimateTrackParamsFromSeed	(	const GeometryContext &	gctx,
		const Surface &	surface,
		const Vector3 &	sp0,
		double	t0,
		const Vector3 &	sp1,
		const Vector3 &	sp2,
		const Vector3 &	bField )

Estimate bound track parameters from three space points.

Parameters

gctx	is the geometry context
surface	is the surface of the bottom space point. The estimated bound track parameters will be represented at this surface.
sp0	is the bottom space point
t0	is the time of the bottom space point
sp1	is the middle space point
sp2	is the top space point
bField	is the magnetic field vector

Returns

bound parameters

estimateTrackParamsFromSeed() [2/2]

FreeVector Acts::estimateTrackParamsFromSeed	(	const Vector3 &	sp0,
		double	t0,
		const Vector3 &	sp1,
		const Vector3 &	sp2,
		const Vector3 &	bField,
		Vector3 *	tangent0 = nullptr,
		Vector3 *	tangent1 = nullptr,
		Vector3 *	tangent2 = nullptr )

Estimate free track parameters from three space points.

Optionally estimates the tangents at the three space points from helix fit. This can be used as an input for the strip space point calibration, which requires the track tangents at each space point as input.

Parameters

sp0	is the bottom space point
t0	is the time of the bottom space point
sp1	is the middle space point
sp2	is the top space point
bField	is the magnetic field vector
tangent0	is the output tangent at the bottom space point
tangent1	is the output tangent at the middle space point
tangent2	is the output tangent at the top space point

Returns

the free parameters

estimateTrackParamsFromSpacePoints()

Result< FreeVector > Acts::estimateTrackParamsFromSpacePoints	(	std::span< const Vector3 >	spacePoints,
		const Vector3 &	bField,
		double	t0 = 0,
		std::size_t	geometricRefineIterations = 0,
		std::span< const double >	weights = {},
		std::size_t	referenceIndex = 0 )

Estimate free track parameters from an ordered set of N >= 3 space points.

Least-squares generalization of estimateTrackParamsFromSeed. A Taubin circle fit transverse to the field, optionally refined geometrically, and a linear fit of the field coordinate against the transverse arc length. Points are taken in track order and are not sorted.

The parameters are expressed at spacePoints[referenceIndex], by default the first one. The fit itself does not depend on that choice: every point contributes to the same helix, and the reference only selects where it is evaluated. Reporting at a point deeper in the detector lets a downstream track finder start where the hit density, and with it the combinatorics, is lower, at the cost of a longer extrapolation back to the beam line.

A vanishing curvature degenerates to a line and only the direction is estimated. Without a field q/p stays zero.

Weights are relative (e.g. inverse-variance) factors on every fit stage. An empty span means uniform, a non-empty one must match spacePoints in size.

Parameters

spacePoints	the ordered global space point positions
bField	the homogeneous magnetic field vector
t0	the time assigned to the reference point (eFreeTime)
geometricRefineIterations	number of Gauss-Newton refinement iterations on top of the algebraic circle fit (0 disables it)
weights	optional per-point weights for all fit stages (empty span = uniform)
referenceIndex	index of the space point the parameters are expressed at; must be a valid index into spacePoints

Returns

the free parameters at the reference point, or an error