Create State-Space Model with Unknown Parameters
Explicitly Create State-Space Model Containing Unknown Parameters
This example shows how to create a time-invariant, state-space model containing unknown parameter values usingssm
.
Define a state-space model containing two dependent MA(1) states, and an additive-error observation model. Symbolically, the equation is
Note that the states and are the two dependent MA(1) processes. The states and help construct the lag-one, MA effects. For example, picks up the first disturbance ( ), and picks up . In all, , which is an MA(1) with as an input.
Specify the state-transition coefficient matrix. UseNaN
values to indicate unknown parameters.
A = [0 NaN NaN 0; 0 0 0 0; 0 0 0 NaN; 0 0 0 0];
Specify the state-disturbance-loading coefficient matrix.
B = [NaN 0; 1 0; 0 NaN; 0 1];
Specify the measurement-sensitivity coefficient matrix.
C = [1 0 0 0; 0 0 1 0];
Specify the observation-innovation coefficient matrix.
D = [NaN 0; 0 NaN];
Usessm
to define the state-space model.
Mdl = ssm(A,B,C,D)
Mdl = State-space model type: ssm State vector length: 4 Observation vector length: 2 State disturbance vector length: 2 Observation innovation vector length: 2 Sample size supported by model: Unlimited Unknown parameters for estimation: 7 State variables: x1, x2,... State disturbances: u1, u2,... Observation series: y1, y2,... Observation innovations: e1, e2,... Unknown parameters: c1, c2,... State equations: x1(t) = (c1)x2(t-1) + (c2)x3(t-1) + (c4)u1(t) x2(t) = u1(t) x3(t) = (c3)x4(t-1) + (c5)u2(t) x4(t) = u2(t) Observation equations: y1(t) = x1(t) + (c6)e1(t) y2(t) = x3(t) + (c7)e2(t) Initial state distribution: Initial state means are not specified. Initial state covariance matrix is not specified. State types are not specified.
Mdl
is anssm
model containing unknown parameters. A detailed summary ofMdl
prints to the Command Window. It is good practice to verify that the state and observations equations are correct.
PassMdl
and data toestimate
to estimate the unknown parameters.
隐式地创建定常State-Space Model
This example shows how to create a time-invariant state-space model by passing a parameter-mapping function describing the model tossm
(that is,implicitlycreate a state-space model). The state model is AR(1) model. The states are observed with bias, but without random error. Set the initial state mean and variance, and specify that the state is stationary.
Write a function that specifies how the parameters inparams
map to the state-space model matrices, the initial state values, and the type of state.
% Copyright 2015 The MathWorks, Inc.function[A,B,C,D,Mean0,Cov0,StateType] = timeInvariantParamMap(params)% Time-invariant state-space model parameter mapping function example. This% function maps the vector params to the state-space matrices (A, B, C, and% D), the initial state value and the initial state variance (Mean0 and% Cov0), and the type of state (StateType). The state model is AR(1)% without observation error.varu1 = exp(params(2));% Positive variance constraintA = params(1); B = sqrt(varu1); C = params(3); D = []; Mean0 = 0.5; Cov0 = 100; StateType = 0;end
Save this code as a file namedtimeInvariantParamMap
to a folder on your MATLAB® path.
Create the state-space model by passing the functiontimeInvariantParamMap
as a function handle tossm
.
Mdl = ssm(@timeInvariantParamMap);
The software implicitly defines the state-space model. Usually, you cannot verify state-space models that you implicitly define.
Mdl
is anssm
含有未知参数的模型对象。你这n estimate the unknown parameters by passingMdl
and response data toestimate
.
See Also
Related Examples
- Explicitly Create State-Space Model Containing Known Parameter Values
- Create State-Space Model Containing ARMA State
- Implicitly Create Time-Varying State-Space Model
- Create State-Space Model with Random State Coefficient