kalman (Control Design and Simulation Module, MathScript Function)
Member of the ssdesign class.
Syntax
[SysKal, L, P, M, Z] = kalman(SysInSS, Q, R, N)
Description
Calculates the optimal steady-state Kalman gain L that minimizes the covariance of the state estimation error. You can use this function to calculate L for continuous and discrete system models.
Inputs
| Name | Description |
| SysInSS | Specifies a linear time-invariant (LTI) model in state-space form. |
| Q | Specifies the auto-covariance matrix of the process noise, if the SysInSS model is discrete. If the model is continuous, Q specifies the auto-intensity matrix of the process noise. Q is a real matrix that is symmetric and positive semi-definite. |
| R | Specifies the auto-covariance matrix of the measurement noise, if the SysInSS model is discrete. If the model is continuous, R specifies the auto-intensity matrix of the process noise. R is a real matrix that is symmetric and positive definite. |
| N | Specifies the cross-covariance matrix between the process noise and the measurement noise, if the SysInSS model is discrete. If the model is continuous, N specifies the cross-intensity matrix between the process noise and the measurement noise. The default is an appropriately sized matrix of zeros, which specifies the process noise and measurement noise are uncorrelated. N must be valid such that (Q-N*inv(R)*N') is positive semi-definite. N is a real matrix. |
Outputs
| Name | Description |
| SysKal | Returns the definition of the Kalman filter with the gain matrix L applied. SysKal is an LTI model in state-space form. |
| L | Returns the gain matrix that minimizes the covariance of the state estimation error. L is a real matrix. |
| P | Returns the steady-state covariance of the estimation error. P is a real matrix. |
| M | Returns the steady-state innovation gain matrix. This gain matrix weights the difference between the observed and estimated outputs in the updated state estimates for discrete estimators. M is a real matrix. |
| Z | Returns the steady-state error covariance of the error between the actual states and the updated state estimates in the discrete estimation process. Z is a real matrix. |
Examples
SysInSS = ss(-1, 1, 1, 0)[SysKal, L, P] = kalman(SysInSS, 1, 2)