Noise component of model
noise_model = noise2meas(sys,noise)
returns the noise component,
noise_model, of a linear identified
noise2meas to convert a
time-series model (no inputs) to an input/output model. The converted model can be used
for linear analysis, including viewing pole/zero maps, and plotting the step
specifies the noise variance normalization method.
Identified linear model.
Noise variance normalization method, specified as one of the following values:
Noise component of
G is the transfer function between the measured input, u(t), and the output, y(t). H is the noise model and describes the effect of the disturbance, e(t), on the model’s response.
An equivalent state-space representation of
v(t) is white noise with independent
channels and unit variances. The white-noise signal
e(t) represents the model’s
innovations and has variance
LLT. The noise-variance
data is stored using the
The model type of
To obtain the model coefficients of
Convert Noise Component of Linear Identified Model into Input/Output Model
Convert a time-series model to an input/output model that may be used by linear analysis tools.
Identify a time-series model.
load iddata9 z9 sys = ar(z9,4,'ls');
sys is an
idpoly model with no inputs.
sys to a measured model.
noise_model = noise2meas(sys);
noise_model is an
idpoly model with one input.
You can use
noise_model for linear analysis functions such as
Normalizing Noise Variance
Convert an identified linear model to an input/output model, and normalize its noise variance.
Identify a linear model using data.
load twotankdata; z = iddata(y,u,0.2); sys = ssest(z,4);
sys is an
idss model, with a noise variance of 6.6211e-06. The value of is
sqrt(sys.NoiseVariance), which is 0.0026.
View the disturbance matrix.
ans = 4×1 0.2719 -1.6570 -0.6318 -0.2877
Obtain a model that absorbs the noise variance of
noise_model_normalize = noise2meas(sys,'normalize');
noise_model_normalize is an
View the matrix for
ans = 4×1 0.0007 -0.0043 -0.0016 -0.0007
noise_model_normalize.B is equal to
Compare the bode response with a model that ignores the noise variance of
noise_model_innovation = noise2meas(sys,'innovations'); bodemag(noise_model_normalize,noise_model_innovation); legend('Normalized noise variance','Ignored noise variance');
The difference between the bode magnitudes of the
noise_model_normalized is approximately 51 dB. As expected, the magnitude difference is approximately equal to
Introduced in R2012a