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 >().setOne(), T memory=0.99, T cov_regularisation=1e-9, T gain_clamp=10)
	Creates a recursive least square object with start parameters/covariance and a memory factor.

void	input (const T &y, const Eigen::Matrix< T, NMeasurements, 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

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

void	set_cov_regularisation (const T &reg)
	Set the value for the covariant regularisation.

T	cov_regularisation () const

void	set_memory (const T &memory)
	Sets the memory factor.

const T &	memory () const
	Returns the memory factor.

void	set_gain_clamp (const T &gain_clamp)
	Limits the update gain K.

const T &	gain_clamp ()
	Returns the currect gain clamp factor.

const Eigen::Vector< T, NParams > &	gain () const
	Returns the gain K used in the parameter update.

Detailed Description

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

Calculates the recursive least square for online parameter estimation.

Uses the recursive least squares algorithm:

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

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

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

For a number of outputs greater than one (NOutputs>1) the model uses the 'Multi-Output System with shared parameter vector'. This allows to use multiple sensors observing the same system states and parameters to increase the estimation result.

There is a default regularisation therm (default: 1e-9) added to the diagonal elements of the covariance updata

There is gain clamping (default: [-10, +10]) applied to the parameter update therem K.

Constructor & Destructor Documentation

◆ ReccursiveLeastSquares()

template<class T , size_t NParams, size_t NMeasurements = 1>

controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::ReccursiveLeastSquares	(	const Eigen::Vector< T, NParams > &	param_hint = `Eigen::Vector<T, NParams>().setOne()`,
		T	memory = `0.99`,
		T	cov_regularisation = `1e-9`,
		T	gain_clamp = `10`
	)

inline

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

Implicitly sets the covariance matrix to a diagonal matrix where each diagonal element has a value of 1000. Large diagonal elements mean that the algorithm is very uncertain about the parameters.

Assertions/Assumptions:

0 < memory <= 1
cov_regularisation >= 0

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. (In literature often called the: forgetting factor) 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 0.8 and 0.98
cov_regularisation	Adds a small positive number to the diagonal of the covariance matrix P at every iteration for numerical stability: it prevents the covariance matrix from collapsing to zero reduces the risk of the matrix becoming ill conditioned improves robustness of the gain computation when excitation is weak Typical values are between `1e-12` and `1e-6` depending on numerical precision and signal scaling
gain_clamp	Limits/clamps the elements of the recursive gain vector `K = P s / (λ + sᵀ P s)` to the range `[-gain_clamp, +gain_clamp]`. Prevents sudden large scale parameter updates caused by: poor excitation nearly singulare covariance matrices Very small gain denominators Important notes: clamping the gain breaks strict optimality and introduces a bias. Typical values are between 5 and 50.

Member Function Documentation

◆ cov()

template<class T , size_t NParams, size_t NMeasurements = 1>

const Eigen::Matrix< T, NParams, NParams > & controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::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

◆ cov_regularisation()

template<class T , size_t NParams, size_t NMeasurements = 1>

T controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::cov_regularisation ( ) const

inline

◆ estimate()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

returns the current best estimate

Returns: the parameter vector

◆ gain()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

Returns the gain K used in the parameter update.

The gain K can be seen as a measure of uncertainty

Returns: The gain vector;

◆ gain_clamp()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

Returns the currect gain clamp factor.

Returns: The currect gain clamp factor

◆ input()

template<class T , size_t NParams, size_t NMeasurements = 1>

void controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::input	(	const T &	y,
		const Eigen::Matrix< T, NMeasurements, 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

◆ memory()

template<class T , size_t NParams, size_t NMeasurements = 1>

const T & controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::memory ( ) const

inline

Returns the memory factor.

The memory factor [0, 1], where:

larger values: Old parameters and inputs are remembered for longer (slower changes, more robust to noise).
smaller values: Old parameters are forgotten more quickly (faster changes)

Returns: The current memory factor

◆ set_cov()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

◆ set_cov_regularisation()

template<class T , size_t NParams, size_t NMeasurements = 1>

void controlpp::ReccursiveLeastSquares< T, NParams, NMeasurements >::set_cov_regularisation ( const T & reg )

inline

Set the value for the covariant regularisation.

Often used values: 1e-6 or 1e-9

Parameters

reg	The regularisation coefficient that will be added to the diagonal of the covariance matrix

◆ set_gain_clamp()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

Limits the update gain K.

Limits the update gain K from -gain_clamp to +gain_clamp. Prevents too fast updates and ill conditioned updates. For example from a lack of excitation variety

default is 10

Parameters

gain_clamp The new gain clamp

◆ set_memory()

template<class T , size_t NParams, size_t NMeasurements = 1>

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

inline

Sets the memory factor.

The memory factor [0, 1], where:

larger values: Old parameters and inputs are remembered for longer (slower changes, more robust to noise).
smaller values: Old parameters are forgotten more quickly (faster changes)

Parameters

memory The new memory factor

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

include/controlpp/Estimators.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ReccursiveLeastSquares()

Assertions/Assumptions:

Member Function Documentation

◆ cov()

◆ cov_regularisation()

◆ estimate()

◆ gain()

◆ gain_clamp()

◆ input()

◆ memory()

◆ set_cov()

◆ set_cov_regularisation()

◆ set_gain_clamp()

◆ set_memory()