ecl_statistics Documentation

### ecl_statistics

Common statistical structures and algorithms for control systems.

# Embedded Control Library

```    This group mostly contains classes relevant to the probabilistics of mobile robot slam.

Include the following at the top of any translation unit that requires the ecl
probabilistic tools.
```

```    Include the following at the top of any translation unit which
requires this library:
```
// Statistics Classes
using ecl::CovarianceEllipsoid2f; // also 2d, 3f, 3d typedef variants

You will also need to link to -lecl_statistics.

# Usage

## Covariance Ellipsoids

mplemented by the template class `CovarianceEllipsoid` - this takes two template parameters. The first is the float type used (usually `float`/`double`) and the second, the dimension of the ellipsoid to be determined.

Specialisations are enabled for 2 and 3 dimensional types only as we haven't had a need to develop a general implementation.

== Typedefs ==

Typedefs exist for the template class in the eigen style:

{{{ #!cplusplus using ecl::CovarianceEllipsoid2f; using ecl::CovarianceEllipsoid2d; using ecl::CovarianceEllipsoid3f; using ecl::CovarianceEllipsoid3d; }}}

== Usage ==

You typically feed the covariance ellipsoid with a positive definite symmetric matrix (eigen matrix). Take care entering the positive definite symmetric matrix - the class does not yet do checking to make sure it is positive definite symmetric.

You can either input the matrix via the constructor - in which case it will automatically calculate the ellipsoid properties, or pass it in later via the `compute()` method:

Matrix2d M;
M << 3.0, 1.0, 1.0, 5.0; // must be a positive definite, symmetric matrix
// OR
ellipse.compute(M);
Matrix2d M;
M << 3.0, 1.0, 1.0, 5.0;
// ellipse minor and major axis lengths
const Vector2d& lengths = ellipse.lengths();
double eigen_value_0 = lengths*lengths;
// angle between x-axis and major axis of the ellipse
double angle = ellipse.rotation();
// values of the intercepts of the ellipse with x and y axes
const Vector2d& intercepts = ellipse.intercepts();
// the ellipse axes/covariance eigenvectors as column vectors in a matrix
const Matrix2d& axes = ellipse.axes();

The 3d version is similar, but will only calculate intercepts and axes respectively. Note that the axes are sorted (to ensure a right-handed co-ordinate system) and normalised.

Matrix3d P;
double sigmaX(0.1);
double sigmaY(0.5);
double sigmaT(0.3);
P << sigmaX*sigmaX, 0, 0, 0, sigmaY*sigmaY, 0, 0, 0, sigmaT*sigmaT;
const Vector3d& lengths = ellipse.lengths();
double eigen_value_0 = lengths*lengths;
const Matrix3d& axes = ellipse.axes();

# Unit Tests

```    - src/test/covariance_ellipsoids.cpp
```

# ChangeLog

```    - <b>Jan 10</b> : 3d ellipses via the ecl::CovarianceEllipsoid<double,3> solver.
- <b>Nov 09</b> : 2d ellipses via the ecl::CovarianceEllipsoid<double,2> solver.```

ecl_statistics
Author(s): Daniel Stonier
autogenerated on Thu Jun 6 2019 21:58:42