CD Continuous Recursive Kalman Filter Function
Owning Palette: Continuous Linear Systems Functions
Installed With: Control Design and Simulation Module
Implements a Kalman filter for a continuous linear time-invariant (LTI) or linear time-variant (LTV) stochastic state-space model. This function calculates the Kalman filtered state estimates and outputs at time t.
Dialog Box Options |
Block Diagram Inputs |
Block Diagram Outputs |
Place on the block diagram | Find on the Functions palette |
Dialog Box Options
Parameter | Description | ||
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Parameters | Lists all the parameters associated with this function. Select a parameter from this list to configure the parameter. When you select a parameter, the parameter and its associated Parameter source control appear in the Parameter Information section of the configuration dialog box. | ||
Preview | Displays a graphical preview, if available, of the function output or configuration. | ||
Parameter Information | Contains the parameters you can configure for this function. You must select a parameter from the Parameters list to make that parameter and its associated Parameter source control visible in the Parameter Information section of the configuration dialog box. | ||
Parameter source | Specifies whether you configure this parameter using the Configuration Dialog Box or a Terminal on the simulation diagram. The default value is Configuration Dialog Box. If you select Terminal, LabVIEW displays an input for that parameter on the simulation diagram, and you can wire values to that input to configure this function programmatically. If you select Configuration Dialog Box, LabVIEW removes that input from the simulation diagram. You then must set the value for this parameter inside the configuration dialog box. | ||
Stochastic State-Space Model | Specifies a mathematical representation of a stochastic system. You can construct a stochastic state-space model using the CD Construct Stochastic Model VI.
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Second-Order Statistics Noise Model | Specifies a mathematical representation of the noise model of a stochastic state-space model. You can create a noise model using the CD Construct Noise Model VI.
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Initial State Estimate xhat(t0) | Specifies the initial states from which this function begins estimating the model states. If you do not specify a value for this parameter, Initial State Estimate xhat(t0) is a vector of zeros. | ||
Input u(t) | Specifies the control action this function applies to the model. If you specify a vector of zeros for Input u(t), this function does not apply any control action. | ||
Output y(t) | Specifies the measurement made on the stochastic state-space model. | ||
Initial Estimation Error Covariance P(t0) | Specifies the initial covariance matrix of the estimation error. If you do not specify a value for this parameter, Initial Estimation Error Covariance P(t0) is a matrix of zeros. |
Block Diagram Inputs
Parameter | Description | ||
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Stochastic State-Space Model | Specifies a mathematical representation of a stochastic system. You can construct a stochastic state-space model using the CD Construct Stochastic Model VI.
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Second-Order Statistics Noise Model | Specifies a mathematical representation of the noise model of a stochastic state-space model. You can create a noise model using the CD Construct Noise Model VI.
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Initial State Estimate xhat(t0) | Specifies the initial states from which this function begins estimating the model states. If you do not specify a value for this parameter, Initial State Estimate xhat(t0) is a vector of zeros. | ||
Input u(t) | Specifies the control action this function applies to the model. If you specify a vector of zeros for Input u(t), this function does not apply any control action. | ||
Output y(t) | Specifies the measurement made on the stochastic state-space model. | ||
Initial Estimation Error Covariance P(t0) | Specifies the initial covariance matrix of the estimation error. If you do not specify a value for this parameter, Initial Estimation Error Covariance P(t0) is a matrix of zeros. |
Block Diagram Outputs
Parameter | Description |
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Estimated Output yhat(t) | Returns the estimated values of the model outputs at time t. |
Estimated State xhat(t) | Returns the estimated model states at time t. |
Estimation Error Covariance P(t) | Returns the covariance matrix of the estimation error associated with the estimated model states xhat(t). |
Kalman Filter Gain L(t) | Returns the estimator gain matrix this function uses to estimate the model states xhat(t) at time t. |
CD Continuous Recursive Kalman Filter Details
The following equations define the outputs this function calculates:
Estimated Output yhat(t) = C(t)xhat(t) + D(t)u(t)
Kalman Filter Gain L(t) = [P(t)CT(t) + G(t)Q(t)HT(t) + G(t)N(t)] . [H(t)Q(t)HT(t) + H(t)N(t) + NT(t)H(t)T+R(t)]–1
Estimation Error Covariance P(t) = A(t)P(t) + P(t)AT(t) + G(t)Q(t)GT(t) – P(t)C(t)T[H(t)Q(t)H(t)T + H(t)N(t) + NT(t)HT(t) + R]–1C(t)P(t) – [G(t)Q(t)HT(t) + G(t)N(t)][H(t)Q(t)HT(t) + H(t)N(t) + NT(t)HT(t) + R]–1 . [G(t)Q(t)HT(t) + G(t)N(t)]T
Estimated State xhat(t) = A(t)xhat(t) + B(t)u(t) + L(t)[y(t) – yhat(t)]