controlpp::ReccursiveLeastSquares< T, NParams, 1 > Class Template Reference

Calculates the recursive least square for online parameter estimation. More...

#include <controlpp/Estimators.hpp>

Public Member Functions
	ReccursiveLeastSquares (const Eigen::Vector< T, NParams > &param_hint=Eigen::Vector< T, NParams >().setOnes(), const Eigen::Matrix< T, NParams, NParams > &cov_hint=(Eigen::Matrix< T, NParams, NParams >::Identity() *T(1000)), T memory=0.99, T cov_regularisation=1e-9)
	Creates a recursive least square object with start parameters/covariance and a memory factor.
void	set_cov (const Eigen::Matrix< T, NParams, NParams > &cov)
void	set_param (const Eigen::Vector< T, NParams > &param)
void	set_memory (const T &memory)
void	set_gain_clamp (const T &gain_clamp)
const T &	gain_clamp () const
void	input (const T &y, const Eigen::Vector< T, NParams > &s)
	Adds a new input output pair that updates the estimate.
const Eigen::Vector< T, NParams > &	estimate () const
	returns the current best estimate
const Eigen::Matrix< T, NParams, NParams > &	cov () const
	returns the current covariance
const Eigen::Vector< T, NParams > &	gain () const
	Returns the gain used for the updata.

Detailed Description

template<class T, size_t NParams>
class controlpp::ReccursiveLeastSquares< T, NParams, 1 >

Calculates the recursive least square for online parameter estimation.

Solves the following system for \(\vec{p}\) online one interation after another

\[ y_k = \vec{s}_k^T \vec{p}_k \]

With the

• measurement \(y\),
• the data vector \(\vec{s}\) and
• the parameter vector \(\vec{p}\)

---

Uses the recursive least squares algorithm:

\[ k_j = \frac{P_{j-1} s_j}{q + s_{j}^{T} P_{j-1} s_j} \]

\[ P_j = \left( P_{j-1} - k_{j} s_{j}^{T} P_{j-1}\right) \frac{1}{q} \]

\[ p_j = p_{j-1} + k_{j} \left( y_j - s_{j}^{T} p_{j-1}\right) \]

Constructor & Destructor Documentation

ReccursiveLeastSquares()

template<class T , size_t NParams>

controlpp::ReccursiveLeastSquares< T, NParams, 1 >::ReccursiveLeastSquares ( const Eigen::Vector< T, NParams > &  param_hint = Eigen::Vector<T, NParams>().setOnes(), const Eigen::Matrix< T, NParams, NParams > &  cov_hint = (Eigen::Matrix<T, NParams, NParams>::Identity() * T(1000)), T  memory = 0.99, T  cov_regularisation = 1e-9  )

inline

Creates a recursive least square object with start parameters/covariance and a memory factor.

Parameters

param_hint	The start value of the parameter vector. If there is no prior knowledge of the values, 0 is often a good choice.
cov_hint	The start value of the covariance matrix. The covariance matrix is a measure of the uncertainty of the parameter vector. As a starting point use the square of the standard deviation of the noise if known. If there is no prior knowledge of the uncertainties setting it to a diagonal matrix with elements much greater than 1 is often a good choice
memory	The value memory that determines how much the past determines the new estimate. It has to be within the open-closed range: \((0, 1]\). Remembers more of the past with higher memory and forgets more with lower memory memory = 1: no forgetting, converges to standard least squares memory < 1: forgetting older values with an exponential decay Often used values are between 0.9and 0.995.
cov_regularisation	A value that will be added to the diagonal of the covariance matrix before each update to prevent the covariance to be become too small, ill formed and unregular. This is mainly to increase numerical stability.

Member Function Documentation

cov()

template<class T , size_t NParams>

const Eigen::Matrix< T, NParams, NParams > & controlpp::ReccursiveLeastSquares< T, NParams, 1 >::cov ( ) const

inline

returns the current covariance

acts as a measure of the uncertainty of the estimate (higher values signal higher uncertainty)

Returns

the current covariance matrix

estimate()

template<class T , size_t NParams>

const Eigen::Vector< T, NParams > & controlpp::ReccursiveLeastSquares< T, NParams, 1 >::estimate ( ) const

inline

returns the current best estimate

Returns

the parameter vector

gain()

template<class T , size_t NParams>

const Eigen::Vector< T, NParams > & controlpp::ReccursiveLeastSquares< T, NParams, 1 >::gain ( ) const

inline

Returns the gain used for the updata.

The gain can be seen as a measurement of uncertainty

Returns

The gain used in the parameter update

gain_clamp()

template<class T , size_t NParams>

const T & controlpp::ReccursiveLeastSquares< T, NParams, 1 >::gain_clamp ( ) const

inline

input()

template<class T , size_t NParams>

void controlpp::ReccursiveLeastSquares< T, NParams, 1 >::input ( const T &  y, const Eigen::Vector< T, NParams > &  s  )

inline

Adds a new input output pair that updates the estimate.

Parameters

y	The new system measurements/outputs
s	The known system inputs

Returns

The new parameter state estimate

set_cov()

template<class T , size_t NParams>

void controlpp::ReccursiveLeastSquares< T, NParams, 1 >::set_cov ( const Eigen::Matrix< T, NParams, NParams > &  cov )

inline

set_gain_clamp()

template<class T , size_t NParams>

void controlpp::ReccursiveLeastSquares< T, NParams, 1 >::set_gain_clamp ( const T &  gain_clamp )

inline

set_memory()

template<class T , size_t NParams>

void controlpp::ReccursiveLeastSquares< T, NParams, 1 >::set_memory ( const T &  memory )

inline

set_param()

template<class T , size_t NParams>

void controlpp::ReccursiveLeastSquares< T, NParams, 1 >::set_param ( const Eigen::Vector< T, NParams > &  param )

inline

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The documentation for this class was generated from the following file:

• include/controlpp/Estimators.hpp