Data Structures
struct	kalman_t

Functions
real	sde_fit (dmat *pcoeff, const dmat psdin, real tmax_fit, int vibid)

real	sde_fit_auto (dmat **pcoeff, const_anyarray psdin, real tfit)
	Fit PSD to SHO by maximum the damping ratio while keeping it less than. More...

void	sde_psd (dmat *psd, const dmat f, const real *coeff, int ncoeff, int nmod)

dmat *	sde_psd2 (const dmat ff, const dmat coeff)

real	reccati (dmat Kinf, dmat Pout, const dmat A, const dmat Qn, const dmat C, const dmat Rn)
	Compute the reccati equation. When noise (Rn) is too large, the iteration will fail to converge. More...

kalman_t *	sde_kalman (const dmat coeff, const real dthi, const lmat dtrat_wfs, const lmat mdirect, const dcell Gwfs, const dcell Cnn, const dmat Proj)
	Kalman filter based on SDE model. More...

void	kalman_free (kalman_t *kalman)

dmat *	kalman_test (kalman_t kalman, const dcell goff, const dmat *input, int flag)

dmat *	kalman_test2 (const dmat coeff, const real dthi, const lmat dtrat, const lmat mdirect, const dcell Gwfs, const dcell Cnn, const dmat Proj, const dcell goff, const dmat input, int flag)

dmat *	kalman_test3 (const dmat input, int flag, const char fn)

void	kalman_init (kalman_t *kalman)

void	kalman_update (kalman_t kalman, dcell meas, int idtrat)

void	kalman_output (kalman_t kalman, dmat *out, real alpha, real beta, int idtrat)

void	kalman_write (kalman_t kalman, const char format,...)

kalman_t *	kalman_read (const char *format,...)

Data Structure Documentation

◆ kalman_t

struct kalman_t

Collaboration diagram for kalman_t:

Data Fields
dmat *	AdM	discrete state propagation at dthi
dmat *	BM	From discrete state to averaged mode for dthi
lmat *	dtrat_wfs	WFS sampling period over dthi
lmat *	dtrats	uniq dtrats
lmat *	mdirect	Modes that are directly controlled by the slow loop
dcell *	Ad	discrete state propagation at dT
dcell *	Cd	From discrete state to WFS measurement
dcell *	Gwfs	WFS measurement from modes. Can be identity.
dcell *	Cnn	WFS measurement noise covariance due to photon and RoN.
dcell *	Rn	Total WFS measurement error due to signal evolution and Rwfs.
dcell *	M	M is innovation gain.
dcell *	P	Sigma_infty: Error covariance matrix
dccell *	Rlsq	least squares reconstructor
real	dthi	Sampling period of control loop
dcell *	xhat	stores x_k+1\|k
dcell *	xhat2	stores x_k+(1+j)/M\|k
dmat *	xhat3	temporary
dcell *	xout	output
dcell *	psol	current correction for psol

Function Documentation

◆ sde_fit()

real sde_fit	(	dmat **	pcoeff,
		const dmat *	psdin,
		real	tmax_fit,
		int	vibid
	)

Estiamte the total PSD power for vibration peaks using FWHM*peak If coeff0 is not null, use it immediately, otherwise, do vibration identification

◆ sde_fit_auto()

real sde_fit_auto	(	dmat **	pcoeff,
		const_anyarray	psdin_,
		real	tfit
	)

Fit PSD to SHO by maximum the damping ratio while keeping it less than.

Does not support vibration identification which have different damping characteristics.
Parameters

[in,out] pcoeff Return the SHO coefficients

psdin_ The input PSD

tfit For covariance fitting, time span.

Returns
real Fitting quality

◆ sde_psd()

void sde_psd	(	dmat **	psd,
		const dmat *	f,
		const real *	coeff,
		int	ncoeff,
		int	nmod
	)

Computes PSD of SDE with coefficients (coeff) and frequency (f)

◆ sde_psd2()

dmat* sde_psd2	(	const dmat *	ff,
		const dmat *	coeff
	)

A convenient wrapper for sde_psd()

◆ reccati()

real reccati	(	dmat **	Kinf,
		dmat **	Pout,
		const dmat *	A,
		const dmat *	Qn,
		const dmat *	C,
		const dmat *	Rn
	)

Compute the reccati equation. When noise (Rn) is too large, the iteration will fail to converge.

Parameters

Kinf	[Out] Asymptotic Kalman gain \(K_\infty\)
Pout	[Out] The Sigma_infty: Estimation error covariance matrix
A	Block diagonal stage evolution matrix
Qn	Discrete state noise covariance
C	Measurement interaction matrix
Rn	Measurement error covariance matrix

Returns: diff Converegence indicator

◆ sde_kalman()

kalman_t* sde_kalman	(	const dmat *	coeff,
		const real	dthi,
		const lmat *	dtrat_wfs,
		const lmat *	mdirect,
		const dcell *	Gwfs,
		const dcell *	Cnn,
		const dmat *	Proj
	)

Kalman filter based on SDE model.

Parameters

coeff	SDE coefficients
dthi	High order loop frequency
dtrat_wfs	WFS dtrat over high order loop. Each wfs may have a different rate. Only 1 or 2 rates are supported
mdirect	Mode indices that are directly controlled by the slower loop.
Gwfs	WFS measurement from modes. Can be identity if reconstructor is already applied.
Cnn	WFS measurement noise covariance in radian^2. nwfs*ndtrat.
Proj	Project modes in statespace to DM/correction space. Can be identity or NULL.

Returns: kalman_t*

◆ kalman_free()

void kalman_free ( kalman_t * kalman )

free the struct

◆ kalman_test()

dmat* kalman_test	(	kalman_t *	kalman,
		const dcell *	goff,
		const dmat *	input,
		int	flag
	)

Test the performance of kalman filter (LQG controller). Derived from servo_test() Gwfs2 is a different gradient interaction matrix to model the aliasing in system flag controlls the servo type: 0: both LQG 1: both integrator 2: LQG (fast) + integrator (slow)

◆ kalman_test2()

dmat* kalman_test2	(	const dmat *	coeff,
		const real	dthi,
		const lmat *	dtrat,
		const lmat *	mdirect,
		const dcell *	Gwfs,
		const dcell *	Cnn,
		const dmat *	Proj,
		const dcell *	goff,
		const dmat *	input,
		int	flag
	)

Parameters

coeff	SDE coefficients
dthi	Loop frequency
dtrat	WFS frequency as a fraction of loop
mdirect	mask for modes directly controlled by slower loop
Gwfs	WFS measurement from modes. Can be identity
Cnn	WFS measurement noise covariance in radian^2
Proj	Kalman Projection matrix
goff	Gradient measurement offset (fast loop)
input	Time series
flag	flag controlls the servo type: 0: both LQG 1: both integrator 2: LQG (fast) + integrator (slow)

◆ kalman_init()

void kalman_init ( kalman_t * kalman )

Initialize kalman filter state

◆ kalman_update()

void kalman_update	(	kalman_t *	kalman,
		dcell *	meas,
		int	idtrat
	)

Update state vector when there is a measurement. It modifies meas.

xhat3=xhat+M*(meas-Cd*xhat) //xhat is x_k|k-1. xhat3 is x_k|k xhat =Ad*xhat3; //xhat is now x_k+1|k xhat2=AdM*xhat3; //xhat2 is x_k+1/M|k

◆ kalman_output()

void kalman_output	(	kalman_t *	kalman,
		dmat **	out,
		real	alpha,
		real	beta,
		int	idtrat
	)

Output correction xhat2=AdM*xhat2 //evolve correction forward out=out*alpha+(BM*xhat2-psol)*beta

◆ kalman_write()

void kalman_write	(	kalman_t *	kalman,
		const char *	format,
			...
	)

Save kalman_t to file

[in,out]	pcoeff	Return the SHO coefficients
	psdin_	The input PSD
	tfit	For covariance fitting, time span.

Data Structures

Functions

Data Structure Documentation

◆ kalman_t

Function Documentation

◆ sde_fit()

◆ sde_fit_auto()

◆ sde_psd()

◆ sde_psd2()

◆ reccati()

◆ sde_kalman()

◆ kalman_free()

◆ kalman_test()

◆ kalman_test2()

◆ kalman_init()

◆ kalman_update()

◆ kalman_output()

◆ kalman_write()