matlab segment,Segment data and estimate models for each segment

Description

segment builds models of AR, ARX, or ARMAX/ARMA

type,

A(q)y(t)=B(q)u(t−nk)+C(q)e(t)

assuming that the model parameters are piecewise constant over

time. It results in a model that has split the data record into segments

over which the model remains constant. The function models signals

and systems that might undergo abrupt changes.

The input-output data is contained in z,

which is either an iddata object or a matrix z

= [y u] where y and u are

column vectors. If the system has several inputs, u has

the corresponding number of columns.

The argument nn defines the model order.

For the ARMAX model

nn = [na nb nc nk];

where na, nb, and nc are

the orders of the corresponding polynomials. See What Are Polynomial Models?. Moreover, nk is

the delay. If the model has several inputs, nb and nk are

row vectors, giving the orders and delays for each input.

For an ARX model (nc = 0) enter

nn = [na nb nk];

For an ARMA model of a time series

z = y;

nn = [na nc];

and for an AR model

nn = na;

The output argument segm is a matrix, where

the kth row contains the parameters corresponding

to time k. This is analogous to output estimates

returned by the recursiveARX and recursiveARMAX estimators. The output

argument thm of segment contains

the corresponding model parameters that have not yet been segmented.

Each row of thm contains the parameter estimates

at the corresponding time instant. These estimates are formed by weighting

together the parameters of M (default:

5) different time-varying models, with the participating models changing

at every time step. Consider segment as

an alternative to the online estimation commands when you are not

interested in continuously tracking the changes in parameters of a

single model, but need to detect abrupt changes in the system dynamics.

The output argument V contains the sum of

the squared prediction errors of the segmented model. It is a measure

of how successful the segmentation has been.

The input argument R2 is the assumed variance

of the innovations e(t)

in the model. The default value of R2, R2

= [], is that it is estimated. Then the output argument R2e is

a vector whose kth element contains the estimate

of R2 at time k.

The argument q is the probability that the

model exhibits an abrupt change at any given time. The default value

is 0.01.

R1 is the assumed covariance matrix of the

parameter jumps when they occur. The default value is the identity

matrix with dimension equal to the number of estimated parameters.

M is the number of parallel models used in

the algorithm (see below). Its default value is 5.

th0 is the initial value of the parameters.

Its default is zero. P0 is the initial covariance

matrix of the parameters. The default is 10 times the identity matrix.

ll is the guaranteed life of each of the

models. That is, any created candidate model is not abolished until

after at least ll time steps. The default is ll

= 1. Mu is a forgetting parameter that

is used in the scheme that estimates R2. The default

is 0.97.

The most critical parameter for you to choose is R2.

It is usually more robust to have a reasonable guess of R2 than

to estimate it. Typically, you need to try different values of R2 and

evaluate the results. (See the example below.) sqrt(R2) corresponds

to a change in the value y(t)

that is normal, giving no indication that the system or the input

might have changed.