'z' — Zero initial conditions.

'e' — Estimate initial conditions such that the prediction error for observed output is minimized.

For nonlinear grey-box models, only those initial states i that are designated as free in the model (sys.InitialStates(i).Fixed = false) are estimated. To estimate all the states of the model, first specify all the Nx states of the idnlgrey model sys as free.

for i = 1:Nx
sys.InitialStates(i).Fixed = false;
end 

Similarly, to fix all the initial states to values specified in sys.InitialStates, first specify all the states as fixed in the sys.InitialStates property of the nonlinear grey-box model.

'd' — Similar to 'e', but absorbs nonzero delays into the model coefficients. The delays are first converted to explicit model states, and the initial values of those states are also estimated and returned.

Use this option for linear models only.

Vector or Matrix — Initial guess for state values, specified as a numerical column vector of length equal to the number of states. For multi-experiment data, specify a matrix with Ne columns, where Ne is the number of experiments. Otherwise, use a column vector to specify the same initial conditions for all experiments. Use this option for state-space (idss and idgrey) and nonlinear models (idnlarx, idnlhw, and idnlgrey) only.

initialCondition object — initialCondition object that represents a model of the free response of the system to initial conditions. For multiexperiment data, specify a 1-by-N_e array of objects, where N_e is the number of experiments.

Use this option for linear models only.

Structure with the following fields, which contain the historical input and output values for a time interval immediately before the start time of the data used in the prediction:

For an example, see Use Historical Data to Specify Initial Conditions for Model Prediction.

For multi-experiment data, configure the initial conditions separately for each experiment by specifying InitialCondition as a structure array with Ne elements. To specify the same initial conditions for all experiments, use a single structure.

The software uses data2state to map the historical data to states. If your model is not idss, idgrey, idnlgrey, or idnlarx, the software first converts the model to its state-space representation and then maps the data to states. If conversion of your model to idss is not possible, the estimated states are returned empty.

x0obj — Specification object created using idpar. Use this object for discrete-time state-space (idss and idgrey) and nonlinear grey-box (idnlgrey) models only. Use x0obj to impose constraints on the initial states by fixing their value or specifying minimum or maximum bounds.

[] — No input offsets.

A column vector of length Nu, where Nu is the number of inputs. The software subtracts the offset value InputOffset(i) from the ith input signal before using the input to predict the model response.

Nu-by-Ne matrix — For multi-experiment data, specify InputOffset as an Nu-by-Ne matrix, where Ne is the number of experiments. The software subtracts the offset value InputOffset(i,j) from the ith input signal of the jth experiment before prediction.

If you specify a column vector of length Nu, then the offset value InputOffset(i) is subtracted from the ith input signal of all the experiments.

[] — No output offsets.

A column vector of length Ny, where Ny is the number of outputs. The software subtracts the offset value OutputOffset(i) from the ith output signal before using the output to predict the model response. After prediction, the software adds the offsets to the predicted response to give the final predicted response.

Ny-by-Ne matrix — For multi-experiment data, specify OutputOffset as an Ny-by-Ne matrix, where Ne is the number of experiments. The software subtracts the offset value OutputOffset(i,j) from the ith output signal of the jth experiment before prediction.

If you specify a column vector of length Ny, then the offset value OutputOffset(i) is subtracted from the ith output signal of all the experiments.

After prediction, the software adds the removed offsets to the predicted response to give the final predicted response.

[] — No weighting is used by the software for initial condition estimation. This option is the same as using eye(Ny) for the output weight, where Ny is the number of outputs.

'noise' — The software uses the inverse of the NoiseVariance property of the model as the weight.

A positive, semidefinite matrix of dimension Ny-by-Ny, where Ny is the number of outputs.