LTPDA Toolbox™

Method matrix/crb

  CRB computes the inverse of the Fisher Matrix
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  DESCRIPTION: CRB computes the inverse of the Fisher Matrix
 
  CALL:        bs = crb(in,pl)
 
  INPUTS:      in      - matrix objects with input signals to the system
               model   - symbolic models containing the transfer function model
 
               pl      - parameter list
 
  OUTPUTS:     bs   - covariance matrix AO
 
  Parameters Description
 
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Method Details
Access	public
Defining Class	matrix
Sealed	0
Static	0

Parameter Description

Sets for this method …
Default

Default
no description
Key	Default Value	Options	Description
crb
INNAMES	1	none	Input names. Used for ssm models.
OUTNAMES	1	none	Output names. Used for ssm models.
FITPARAMS, PARAMETER NAMES, PARAM NAMES	''	none	The names of the parameters. Used for printing and for the case of the SSM.
PARAMSVALUES, X0, P0	[]	none	The numerical values of the parameters.
MODEL	''	none	An array of matrix models
INPUT	''	none	The input signal to the system. It should be a matrix of AOs, the rows denoting the channels, and the columns the number of experiments. An array of matrix objects is also accepted.
PINV	0	0 1	Use the Penrose-Moore pseudoinverse
TOL	[]	none	Tolerance for the Penrose-Moore pseudoinverse
DIFFSTEP	[]	none	Numerical differentiation step for ssm models
NGRID	[]	none	Number of points in the grid to compute the optimal differentiation step for ssm models
STEPRANGES	[]	none	An array with upper and lower values for the parameters ranges. To be used to compute the optimal differentiation step for ssm models.
LOG PARAMETERS	[]	none	An array with upper and lower values for the parameters ranges. To be used to compute the optimal differentiation step for ssm models.
FREQUENCIES	[]	none	The frequencies to perform the analysis.
FSOUT	[]	none	Resampling.
F1	[]	none	Initial frequency for the analysis.
F2	[]	none	Final frequency for the analysis.
NOISE SCALE	'PSD'	'PSD' 'LPSD'	Select the way to handle the noise/weight data. Can use the PSD/CPSD or the LPSD/CLPSD functions.
YUNITS	'm s^-2'	none	The Y units of the noise time series, in case the MFH object is a 'core' type.
TRIM	[100 -100]	none	A 2x1 vector that denotes the samples to split from the star and end of the time-series (split in offsets).
REGULARIZE	0	0 1	If the resulting fisher matrix is not positive definite, try a numerical trick to continue sampling.
NEARESTSPD	0	0 1	Try to find the nearest symmetric and positive definite covariance matrix, with the 'nearestSPD' method from MATLAB file exchange.
VERSION	'core'	'core' 'ao'	Choose between 'AO' and 'CORE' types. Applies to MFH models.
NFFT	-1	none	The number of samples in each fft [default: length of input data]. A string value containing the variable 'fs' can also be used, e.g., `plist('Nfft', '2*fs')`
WIN	'BH92'	'Rectangular' 'Welch' 'Bartlett' 'Hanning' 'Hamming' 'Nuttall3' 'Nuttall4' 'Nuttall3a' 'Nuttall3b' 'Nuttall4a' 'Nuttall4b' 'Nuttall4c' 'BH92' 'SFT3F' 'SFT3M' 'FTNI' 'SFT4F' 'SFT5F' 'SFT4M' 'FTHP' 'HFT70' 'FTSRS' 'SFT5M' 'HFT90D' 'HFT95' 'HFT116D' 'HFT144D' 'HFT169D' 'HFT196D' 'HFT223D' 'HFT248D' 'Kaiser' 'levelledHanning'	The window to be applied to the data to remove the discontinuities at edges of segments. [default: taken from user prefs] Only the design parameters of the window object are used. Enter a string value containing the window name e.g. `plist('Win', 'Kaiser', 'psll', 200)` `plist('Win', 'BH92')`
PSLL	200	none	The peak sidelobe level for Kaiser windows. Note: it is ignored for all other windows
OLAP	-1	none	The segment percent overlap [-1 == take from window function]
ORDER, N	0	-1 0 1 2 3 4 5 6 7 8 9	The order of segment detrending: -1 - no detrending 0 - subtract mean 1 - subtract linear fit N - subtract fit of polynomial, order N
NAVS	-1	none	Force number of averages. If set, and if Nfft was set to 0 or -1, the number of points for each window will be calculated to match the request.
DROP WINDOW SAMPLES	1	1 0	Drop the recommended (by the window) number of samples of the final computed spectral series.
TIMES, SPLIT	[]	none	The time range to analyze. If not empty, sets the time interval to operate on. As in ao/split, the interval can be specified by: a vector of doubles a timespan object a cell array of time strings a vector of time objects
computeICSMatrix
NOUT	''	none	The number of outputs.
INVERSE	1	1 0	Set to false to return the spectrum matrix, but not inverted.
ISDIAG	0	0 1	For the case of systems where the cross-spectrum matrix is diagonal it can be set to true to skip estimating the non-diagonal elements. Useful for multiple inputs/outputs.
FS	1	none	The sampling frequency of the data.
INTERPOLATION METHOD, INTERP METHOD	'LINEAR'	'LINEAR' 'SPLINE' 'PCHIP' 'CUBIC'	The interpolation method.
FREQS	[]	none	Array of frequencies where the analysis is performed.
BIN DATA	0	0 1	Set to true to re-bin the measured noise data.
FIT NOISE MODEL	0	0 1	Set to true to attempt a fit on the noise spectra using the 'polyfitSpectrum' function.
POLYNOMIAL ORDER	[-4 -3 -2 -1 0 1 2 3 4]	none	The order of the polynomial to be used in the 'polyfitSpectrum' function.
PLOT FITS	0	0 1	Set to true to produce plots of the fits in case of 'fit noise model' is set to true.
lpsd
KDES	100	none	The desired number of averages.
JDES	1000	none	The desired number of spectral frequencies to compute.
LMIN	0	none	The minimum segment length.
SCALE	'PSD'	'PSD' 'ASD' 'PS' 'AS'	The scaling of output. Choose from: PSD - Power Spectral Density ASD - Amplitude (linear) Spectral Density PS - Power Spectrum AS - Amplitude (linear) Spectrum

Example
plist('INNAMES', [1], 'OUTNAMES', [1], 'FITPARAMS', '', 'PARAMSVALUES', [[]], 'MODEL', '', 'INPUT', '', 'PINV', [false], 'TOL', [[]], 'DIFFSTEP', [[]], 'NGRID', [[]], 'STEPRANGES', [[]], 'LOG PARAMETERS', [[]], 'FREQUENCIES', [[]], 'FSOUT', [[]], 'F1', [[]], 'F2', [[]], 'NOISE SCALE', 'PSD', 'YUNITS', 'm s^-2', 'TRIM', [[100 -100]], 'REGULARIZE', [false], 'NEARESTSPD', [false], 'VERSION', 'core', 'NFFT', [-1], 'WIN', 'BH92', 'PSLL', [200], 'OLAP', [-1], 'ORDER', [0], 'NAVS', [-1], 'DROP WINDOW SAMPLES', [true], 'TIMES', [[]], 'NOUT', '', 'INVERSE', [true], 'ISDIAG', [false], 'FS', [1], 'INTERPOLATION METHOD', 'LINEAR', 'FREQS', [[]], 'BIN DATA', [false], 'FIT NOISE MODEL', [false], 'POLYNOMIAL ORDER', [[-4 -3 -2 -1 0 1 2 3 4]], 'PLOT FITS', [false], 'KDES', [100], 'JDES', [1000], 'LMIN', [0], 'SCALE', 'PSD')

Example

plist('INNAMES', [1], 'OUTNAMES', [1], 'FITPARAMS', '', 'PARAMSVALUES', [[]], 'MODEL', '', 'INPUT', '', 'PINV', [false], 'TOL', [[]], 'DIFFSTEP', [[]], 'NGRID', [[]], 'STEPRANGES', [[]], 'LOG PARAMETERS', [[]], 'FREQUENCIES', [[]], 'FSOUT', [[]], 'F1', [[]], 'F2', [[]], 'NOISE SCALE', 'PSD', 'YUNITS', 'm s^-2', 'TRIM', [[100 -100]], 'REGULARIZE', [false], 'NEARESTSPD', [false], 'VERSION', 'core', 'NFFT', [-1], 'WIN', 'BH92', 'PSLL', [200], 'OLAP', [-1], 'ORDER', [0], 'NAVS', [-1], 'DROP WINDOW SAMPLES', [true], 'TIMES', [[]], 'NOUT', '', 'INVERSE', [true], 'ISDIAG', [false], 'FS', [1], 'INTERPOLATION METHOD', 'LINEAR', 'FREQS', [[]], 'BIN DATA', [false], 'FIT NOISE MODEL', [false], 'POLYNOMIAL ORDER', [[-4 -3 -2 -1 0 1 2 3 4]], 'PLOT FITS', [false], 'KDES', [100], 'JDES', [1000], 'LMIN', [0], 'SCALE', 'PSD')

Some information of the method matrix/crb are listed below:
Class name	matrix
Method name	crb
Category	Signal Processing
Package name	ltpda
VCS Version	967b0eec0dece803a81af8ef54ad2f8c784b20b2
Min input args	1
Max input args	-1
Min output args	1
Max output args	-1
Can be used as modifier	1
Supported numeric types	{'double'}

Method: matrix/cpsd

Method: matrix/delay

Method matrix/crb

Parameter Description

Default

Example