Unscented Kalman Filter

Estimate states of discrete-time nonlinear system using unscented Kalman filter

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Library:
Control System Toolbox / State Estimation
System Identification Toolbox / Estimators

Description

TheUnscented Kalman Filterblock estimates the states of a discrete-time nonlinear system using the discrete-time unscented Kalman filter algorithm.

Consider a plant with statesx, inputu, outputy, process noisew, and measurement noisev. Assume that you can represent the plant as a nonlinear system.

Using the state transition and measurement functions of the system and the unscented Kalman filter algorithm, the block produces state estimates $\hat{x}$ for the current time step. For information about the algorithm, seeExtended and Unscented Kalman Filter Algorithms for Online State Estimation.

You create the nonlinear state transition function and measurement functions for the system and specify these functions in the block. The block supports state estimation of a system with multiple sensors that are operating at different sampling rates. You can specify up to five measurement functions, each corresponding to a sensor in the system. For more information, seeState Transition and Measurement Functions.

Ports

Input

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`y1,y2,y3,y4,y5`— Measured system outputs
vector

Measured system outputs corresponding to each measurement function that you specify in the block. The number of ports equals the number of measurement functions in your system. You can specify up to five measurement functions. For example, if your system has two sensors, you specify two measurement functions in the block. The first porty1is available by default. When you clickApply, the software generates porty2corresponding to the second measurement function.

Specify the ports asN-dimensional vectors, whereNis the number of quantities measured by the corresponding sensor. For example, if your system has one sensor that measures the position and velocity of an object, then there is only one porty1. The port is specified as a 2-dimensional vector with values corresponding to position and velocity.

Dependencies

The first porty1is available by default. Portsy2toy5are generated when you clickAdd Measurement, and clickApply.

Data Types:single|double

`StateTransitionFcnInputs`— Additional optional input argument to state transition function
scalar | vector | matrix

Additional optional input argument to the state transition functionfother than the statexand process noisew. For information about state transition functions see,State Transition and Measurement Functions.

Suppose that your system has nonadditive process noise, and the state transition functionfhas the following form:

x(k+1) = f(x(k),w(k),StateTransitionFcnInputs).

Herekis the time step, andStateTransitionFcnInputsis an additional input argument other thanxandw.

If you createfusing a MATLAB^®function (.mfile), the software generates the portStateTransitionFcnInputs当你点击Apply. You can specify the inputs to this port as a scalar, vector, or matrix.

If your state transition function has more than one additional input, use a金宝app仿真软件的功能(Simulink)block to specify the function. When you use a金宝app仿真软件的功能block, you provide the additional inputs directly to the金宝app仿真软件的功能block usingInport(Simulink)blocks. No input ports are generated for the additional inputs in theUnscented Kalman Filterblock.

Dependencies

This port is generated only if both of the following conditions are satisfied:

You specifyfinFunctionusing a MATLAB function, andfis on the MATLAB path.
f只需要一个额外的input argument apart fromxandw.

Data Types:single|double

`MeasurementFcn1Inputs,MeasurementFcn2Inputs,MeasurementFcn3Inputs,MeasurementFcn4Inputs,MeasurementFcn5Inputs`— Additional optional input argument to each measurement function
scalar | vector | matrix

Additional optional inputs to the measurement functions other than the statexand measurement noisev. For information about measurement functions see,State Transition and Measurement Functions.

MeasurementFcn1Inputscorresponds to the first measurement function that you specify, and so on. For example, suppose that your system has three sensors and nonadditive measurement noise, and the three measurement functionsh1,h2, andh3have the following form:

y1[k] = h1(x[k],v[k],MeasurementFcn1Inputs)

y2[k] = h2(x[k],v[k],MeasurementFcn2Inputs)

y3[k] = h3(x[k],v[k])

Herekis the time step, andMeasurementFcn1InputsandMeasurementFcn2Inputsare the additional input arguments toh1andh2.

If you specifyh1,h2, andh3using MATLAB functions (.mfiles) inFunction, the software generates portsMeasurementFcn1InputsandMeasurementFcn2Inputs当你点击Apply. You can specify the inputs to these ports as scalars, vectors, or matrices.

If your measurement functions have more than one additional input, use金宝app仿真软件的功能(Simulink)blocks to specify the functions. When you use a金宝app仿真软件的功能block, you provide the additional inputs directly to the金宝app仿真软件的功能block usingInport(Simulink)blocks. No input ports are generated for the additional inputs in theUnscented Kalman Filterblock.

Dependencies

一个港口corresponding to a measurement functionh只有以下两个生成conditi吗ons are satisfied:

You specifyhinFunctionusing a MATLAB function, andhis on the MATLAB path.
h只需要一个额外的input argument apart fromxandv.

Data Types:single|double

`Q`— Time-varying process noise covariance
scalar | vector | matrix

Time-varying process noise covariance, specified as a scalar, vector, or matrix depending on the value of theProcess noiseparameter:

Process noiseisAdditive— Specify the covariance as a scalar, anNs-element vector, or anNs-by-Ns米atrix, whereNsis the number of states of the system. Specify a scalar if there is no cross-correlation between process noise terms, and all the terms have the same variance. Specify a vector of lengthNs, if there is no cross-correlation between process noise terms, but all the terms have different variances.
Process noiseisNonadditive— Specify the covariance as aW-by-W米atrix, whereWis the number of process noise terms in the state transition function.

Dependencies

This port is generated if you specify the process noise covariance asTime-Varying. The port appears when you clickApply.

Data Types:single|double

`R1,R2,R3,R4,R5`— Time-varying measurement noise covariance
米atrix

Time-varying measurement noise covariances for up to five measurement functions of the system, specified as matrices. The sizes of the matrices depend on the value of theMeasurement noiseparameter for the corresponding measurement function:

Measurement noiseisAdditive— Specify the covariance as anN-by-N米atrix, whereNis the number of measurements of the system.
Measurement noiseisNonadditive— Specify the covariance as aV-by-V米atrix, whereVis the number of measurement noise terms in the corresponding measurement function.

Dependencies

一个港口is generated if you specify the measurement noise covariance asTime-Varyingfor the corresponding measurement function. The port appears when you clickApply.

Data Types:single|double

`Enable1、Enable2 Enable3、Enable4 Enable5`— Enable correction of estimated states when measured data is available
scalar

Suppose that measured output data is not available at all time points at the porty1that corresponds to the first measurement function. Use a signal value other than0at theEnable1port to enable the correction of estimated states when measured data is available. Specify the port value as0when measured data is not available. Similarly, if measured output data is not available at all time points at the portyifor thei^th米easurement function, specify the corresponding portEnableias a value other than0.

Dependencies

一个港口corresponding to a measurement function is generated if you selectAdd Enable portfor that measurement function. The port appears when you clickApply.

Data Types:single|double|Boolean

Output

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`xhat`— Estimated states
vector

Estimated states, returned as a vector of sizeNs, whereNsis the number of states of the system. To access the individual states, use theSelector(Simulink)block.

When theUse the current measurements to improve state estimatesparameter is selected, the block outputs the corrected state estimate $\hat{x} [k | k]$ at time stepk, estimated using measured outputs until timek. If you clear this parameter, the block returns the predicted state estimate $\hat{x} [k | k - 1]$ for timek, estimated using measured output until a previous timek-1. Clear this parameter if your filter is in a feedback loop and there is an algebraic loop in your Simulink^®米odel.

Data Types:single|double

`P`— State estimation error covariance
米atrix

State estimation error covariance, returned as anNs-by-Ns米atrix, whereNsis the number of states of the system. To access the individual covariances, use theSelector(Simulink)block.

Dependencies

This port is generated if you selectOutput state estimation error covariancein theSystem Modeltab, and clickApply.

Data Types:single|double

Parameters

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System Model Tab

State Transition

`Function`— State transition function name
`米yStateTransitionFcn`(default) | function name

The state transition function calculates theNs-element state vector of the system at time stepk+1, given the state vector at time stepk.Nsis the number of states of the nonlinear system. You create the state transition function and specify the function name inFunction. For example, ifvdpStateFcn.mis the state transition function that you created and saved, specifyFunctionasvdpStateFcn.

The inputs to the function you create depend on whether you specify the process noise as additive or nonadditive inProcess noise.

Process noiseisAdditive— The state transition functionfspecifies how the states evolve as a function of state values at previous time step:
x(k+1) = f(x(k),Us1(k),...,Usn(k)),
wherex(k)is the estimated state at timek, andUs1,...,Usnare any additional input arguments required by your state transition function, such as system inputs or the sample time. To see an example of a state transition function with additive process noise, typeedit vdpStateFcnat the command line.
Process noiseisNonadditive— The state transition function also specifies how the states evolve as a function of the process noisew:
x(k+1) = f(x(k),w(k),Us1(k),...,Usn(k)).

For more information, seeState Transition and Measurement Functions.

You can createfusing a金宝app仿真软件的功能(Simulink)block or as a MATLAB function (.mfile).

You can use a MATLAB function only iffhas one additional input argumentUs1other thanxandw.
x(k+1) = f(x(k),w(k),Us1(k))
The software generates an additional input portStateTransitionFcnInputsto specify this argument.
If you are using a金宝app仿真软件的功能block, specifyxandwusingArgument Inport(Simulink)blocks and the additional inputsUs1,...,UsnusingInport(Simulink)blocks in the金宝app仿真软件的功能block. You do not provideUs1,...,Usnto theUnscented Kalman Filterblock.

Programmatic Use

Block Parameter:StateTransitionFcn

Type:character vector, string

Default:'myStateTransitionFcn'

`Process noise`— Process noise characteristics
`Additive`(default) |`Nonadditive`

Process noise characteristics, specified as one of the following values:

Additive— Process noisewis additive, and the state transition functionfthat you specify inFunctionhas the following form:
x(k+1) = f(x(k),Us1(k),...,Usn(k)),
wherex(k)is the estimated state at timek, andUs1,...,Usnare any additional input arguments required by your state transition function.
Nonadditive— Process noise is nonadditive, and the state transition function specifies how the states evolve as a function of the stateandprocess noise at the previous time step:
x(k+1) = f(x(k),w(k),Us1(k),...,Usn(k)).

Programmatic Use

Block Parameter:HasAdditiveProcessNoise

Type:character vector

Values:'Additive','Nonadditive'

Default:'Additive'

`Covariance`— Time-invariant process noise covariance
`1`(default) | scalar | vector | matrix

Time-invariant process noise covariance, specified as a scalar, vector, or matrix depending on the value of theProcess noiseparameter:

Process noiseisAdditive— Specify the covariance as a scalar, anNs-element vector, or anNs-by-Ns米atrix, whereNsis the number of states of the system. Specify a scalar if there is no cross-correlation between process noise terms and all the terms have the same variance. Specify a vector of lengthNs, if there is no cross-correlation between process noise terms but all the terms have different variances.
Process noiseisNonadditive— Specify the covariance as aW-by-W米atrix, whereWis the number of process noise terms.

If the process noise covariance is time-varying, selectTime-varying. The block generates input portQto specify the time-varying covariance.

Dependencies

This parameter is enabled if you do not specify the process noise asTime-Varying.

Programmatic Use

Block Parameter:ProcessNoise

Type:character vector, string

Default:'1'

`Time-varying`— Time-varying process noise covariance
`'off'`(default) |`“上”`

如果你select this parameter, the block includes an additional input portQto specify the time-varying process noise covariance.

Programmatic Use

Block Parameter:HasTimeVaryingProcessNoise

Type:character vector

Values:'off',“上”

Default:'off'

Initialization

`Initial state`— Initial state estimate
`0`(default) | vector

Initial state estimate value, specified as anNs-element vector, whereNsis the number of states in the system. Specify the initial state values based on your knowledge of the system.

Programmatic Use

Block Parameter:InitialState

Type:character vector, string

Default:'0'

`Initial covariance`— State estimation error covariance
`1`(default) | scalar | vector | matrix

State estimation error covariance, specified as a scalar, anNs-element vector, or anNs-by-Ns米atrix, whereNsis the number of states of the system. If you specify a scalar or vector, the software creates anNs-by-Nsdiagonal matrix with the scalar or vector elements on the diagonal.

指定一个高价值的协方差时do not have confidence in the initial state values that you specify inInitial state.

Programmatic Use

Block Parameter:InitialStateCovariance

Type:character vector, string

Default:'1'

Unscented Transformation Parameters

`Alpha`— Spread of sigma points
`1e-3`(default) | scalar value between 0 and 1

The unscented Kalman filter algorithm treats the state of the system as a random variable with a mean state value and variance. To compute the state and its statistical properties at the next time step, the algorithm first generates a set of state values distributed around the mean value by using the unscented transformation. These generated state values are called sigma points. The algorithm uses each of the sigma points as an input to the state transition and measurement functions to get a new set of transformed state points and measurements. The transformed points are used to compute the state and state estimation error covariance value at the next time step.

The spread of the sigma points around the mean state value is controlled by two parametersAlphaandKappa. A third parameter,Beta, impacts the weights of the transformed points during state and measurement covariance calculations:

Alpha— Determines the spread of the sigma points around the mean state value. Specify as a scalar value between 0 and 1 (0<Alpha<=1). It is usually a small positive value. The spread of sigma points is proportional toAlpha. Smaller values correspond to sigma points closer to the mean state.
Kappa— A second scaling parameter that is typically set to 0. Smaller values correspond to sigma points closer to the mean state. The spread is proportional to the square-root ofKappa.
Beta— Incorporates prior knowledge of the distribution of the state. For Gaussian distributions,Beta= 2 is optimal.

If you know the distribution of state and state covariance, you can adjust these parameters to capture the transformation of higher-order moments of the distribution. The algorithm can track only a single peak in the probability distribution of the state. If there are multiple peaks in the state distribution of your system, you can adjust these parameters so that the sigma points stay around a single peak. For example, choose a smallAlphato generate sigma points close to the mean state value.

For more information, seeUnscented Kalman Filter Algorithm.

Programmatic Use

Block Parameter:Alpha

Type:character vector, string

Default:'1e-3'

`Beta`— Characterization of state distribution
`2`(default) | scalar value greater than or equal to 0

Characterization of the state distribution that is used to adjust weights of transformed sigma points, specified as a scalar value greater than or equal to 0. For Gaussian distributions,Beta= 2 is the optimal choice.

For more information, see the description forAlpha.

Programmatic Use

Block Parameter:Beta

Type:character vector, string

Default:'2'

`Kappa`— Spread of sigma points
`0`(default) | scalar value between 0 and 3

Spread of sigma points around mean state value, specified as a scalar value between 0 and 3 (0<=Kappa<=3).Kappais typically specified as0. Smaller values correspond to sigma points closer to the mean state. The spread is proportional to the square root ofKappa. For more information, see the description forAlpha.

Programmatic Use

Block Parameter:Kappa

Type:character vector, string

Default:'0'

Measurement

`Function`— Measurement function name
`米yMeasurementFcn`(default) | function name

The measurement function calculates theN-element output measurement vector of the nonlinear system at time stepk, given the state vector at time stepk. You create the measurement function and specify the function name inFunction. For example, ifvdpMeasurementFcn.mis the measurement function that you created and saved, specifyFunctionasvdpMeasurementFcn.

The inputs to the function you create depend on whether you specify the measurement noise as additive or nonadditive inMeasurement noise.

Measurement noiseisAdditive— The measurement functionhspecifies how the measurements evolve as a function of state Values:
y(k) = h(x(k),Um1(k),...,Umn(k)),
wherey(k)andx(k)are the estimated output and estimated state at timek, andUm1,...,Umnare any optional input arguments required by your measurement function. For example, if you are using a sensor for tracking an object, an additional input could be the sensor position.
To see an example of a measurement function with additive process noise, typeedit vdpMeasurementFcnat the command line.
Measurement noiseisNonadditive— The measurement function also specifies how the output measurement evolves as a function of the measurement noisev:
y(k) = h(x(k),v(k),Um1(k),...,Umn(k)).
To see an example of a measurement function with nonadditive process noise, typeedit vdpMeasurementNonAdditiveNoiseFcn.

For more information, seeState Transition and Measurement Functions.

You can createhusing a金宝app仿真软件的功能(Simulink)block or as a MATLAB function (.mfile).

You can use a MATLAB function only ifhhas one additional input argumentUm1other thanxandv.
y[k] = h(x[k],v[k],Um1(k))
The software generates an additional input portMeasurementFcnInputto specify this argument.
If you are using a金宝app仿真软件的功能block, specifyxandvusingArgument Inport(Simulink)blocks and the additional inputsUm1,...,UmnusingInport(Simulink)blocks in the金宝app仿真软件的功能block. You do not provideUm1,...,Umnto theUnscented Kalman Filterblock.

If you have multiple sensors in your system, you can specify multiple measurement functions. You can specify up to five measurement functions using theAdd Measurementbutton. To remove measurement functions, useRemove Measurement.

Programmatic Use

Block Parameter:MeasurementFcn1,MeasurementFcn2,MeasurementFcn3,MeasurementFcn4,MeasurementFcn5

Type:character vector, string

Default:'myMeasurementFcn'

`Measurement noise`— Measurement noise characteristics
`Additive`(default) |`Nonadditive`

Measurement noise characteristics, specified as one of the following values:

Additive— Measurement noisevis additive, and the measurement functionhthat you specify inFunctionhas the following form:
y(k) = h(x(k),Um1(k),...,Umn(k)),
wherey(k)andx(k)are the estimated output and estimated state at timek, andUm1,...,Umnare any optional input arguments required by your measurement function.
Nonadditive— Measurement noise is nonadditive, and the measurement function specifies how the output measurement evolves as a function of the stateand米easurement noise:
y(k) = h(x(k),v(k),Um1(k),...,Umn(k)).

Programmatic Use

Block Parameter:HasAdditiveMeasurementNoise1,HasAdditiveMeasurementNoise2,HasAdditiveMeasurementNoise3,HasAdditiveMeasurementNoise4,HasAdditiveMeasurementNoise5

Type:character vector

Values:'Additive','Nonadditive'

Default:'Additive'

`Covariance`— Time-invariant measurement noise covariance
`1`(default) | matrix

Time-invariant measurement noise covariance, specified as a matrix. The size of the matrix depends on the value of theMeasurement noiseparameter:

Measurement noiseisAdditive— Specify the covariance as anN-by-N米atrix, whereNis the number of measurements of the system.
Measurement noiseisNonadditive— Specify the covariance as aV-by-V米atrix, whereVis the number of measurement noise terms.

If the measurement noise covariance is time-varying, selectTime-varying. The block generates input portRito specify the time-varying covariance for thei^th米easurement function.

Dependencies

This parameter is enabled if you do not specify the process noise asTime-Varying.

Programmatic Use

Block Parameter:MeasurementNoise1,MeasurementNoise2,MeasurementNoise3,MeasurementNoise4,MeasurementNoise5

Type:character vector, string

Default:'1'

`Time-varying`— Time-varying measurement noise covariance
`off`(default) |`on`

如果你select this parameter for the measurement noise covariance of the first measurement function, the block includes an additional input portR1. You specify the time-varying measurement noise covariance inR1. Similarly, if you selectTime-varyingfor thei^th米easurement function, the block includes an additional input portRito specify the time-varying measurement noise covariance for that function.

Programmatic Use

Block Parameter:HasTimeVaryingMeasurementNoise1,HasTimeVaryingMeasurementNoise2,HasTimeVaryingMeasurementNoise3,HasTimeVaryingMeasurementNoise4,HasTimeVaryingMeasurementNoise5

Type:character vector

Values:'off',“上”

Default:'off'

`添加启用端口`— Enable correction of estimated states only when measured data is available
`off`(default) |`on`

Suppose that measured output data is not available at all time points at the porty1that corresponds to the first measurement function. SelectAdd Enable portto generate an input portEnable1. Use a signal at this port to enable the correction of estimated states only when measured data is available. Similarly, if measured output data is not available at all time points at the portyifor thei^th米easurement function, select the correspondingAdd Enable port.

Programmatic Use

Block Parameter:HasMeasurementEnablePort1,HasMeasurementEnablePort2,HasMeasurementEnablePort3,HasMeasurementEnablePort4,HasMeasurementEnablePort5

Type:character vector

Values:'off',“上”

Default:'off'

Settings

`Use the current measurements to improve state estimates`— Choose between corrected or predicted state estimate
`on`(default) |`off`

When this parameter is selected, the block outputs the corrected state estimate $\hat{x} [k | k]$ at time stepk, estimated using measured outputs until timek. If you clear this parameter, the block returns the predicted state estimate $\hat{x} [k | k - 1]$ for timek, estimated using measured output until a previous timek-1. Clear this parameter if your filter is in a feedback loop and there is an algebraic loop in your Simulink model.

Programmatic Use

Block Parameter:UseCurrentEstimator

Type:character vector

Values:'off',“上”

Default:“上”

`Output state estimation error covariance`— Output state estimation error covariance
`off`(default) |`on`

如果你select this parameter, a state estimation error covariance output portPis generated in the block.

Programmatic Use

Block Parameter:OutputStateCovariance

Type:character vector

Values:'off',“上”

Default:'off'

`Data type`— Data type for block parameters
`double`(default) |`single`

Use this parameter to specify the data type for all block parameters.

Programmatic Use

Block Parameter:DataType

Type:character vector

Values:'single','double'

Default:'double'

`Sample time`— Block sample time
`1`(default) | positive scalar

Block sample time, specified as a positive scalar. If the sample times of your state transition and measurement functions are different, selectEnable multirate operationin theMultiratetab, and specify the sample times in theMultiratetab instead.

Dependencies

This parameter is available if in theMultiratetab, theEnable multirate operationparameter isoff.

Programmatic Use

Block Parameter:SampleTime

Type:character vector, string

Default:'1'

Multirate Tab

`Enable multirate operation`— Enable specification of different sample times for state transition and measurement functions
`off`(default) |`on`

Select this parameter if the sample times of the state transition and measurement functions are different. You specify the sample times in theMultiratetab, inSample time.

Programmatic Use

Block Parameter:EnableMultirate

Type:character vector

Values:'off',“上”

Default:'off'

`Sample times`— State transition and measurement function sample times
positive scalar

If the sample times for state transition and measurement functions are different, specifySample time. Specify the sample times for the measurement functions as positive integer multiples of the state transition sample time. The sample times you specify correspond to the following input ports:

Ports corresponding to state transition function — Additional input to state transition functionStateTransitionFcnInputsand time-varying process noise covarianceQ. The sample times of these ports must always equal the state transition function sample time, but can differ from the sample time of the measurement functions.
Ports corresponding toi^th米easurement function — Measured outputyi, additional input to measurement functionMeasurementFcniInputs, enable signal at portEnablei, and time-varying measurement noise covarianceRi. The sample times of these ports for the same measurement function must always be the same, but can differ from the sample time for the state transition function and other measurement functions.

Dependencies

This parameter is available if in theMultiratetab, theEnable multirate operationparameter ison.

Programmatic Use

Block Parameter:StateTransitionFcnSampleTime,MeasurementFcn1SampleTime1,MeasurementFcn1SampleTime2,MeasurementFcn1SampleTime3,MeasurementFcn1SampleTime4,MeasurementFcn1SampleTime5

Type:character vector, string

Default:'1'

Model Examples

Estimate States of Nonlinear System with Multiple, Multirate Sensors

Use anExtended Kalman Filterblock to estimate the states of a system with multiple sensors that are operating at different sampling rates.

Compute Residuals and State Estimation Errors

Estimate the states of a discrete-time Van der Pol oscillator and compute state estimation errors and residuals for validating the estimation. The residuals are the output estimation errors, that is, they are the difference between the measured and estimated outputs.

Nonlinear State Estimation of a Degrading Battery System

Estimate the states of a nonlinear system using an Unscented Kalman Filter in Simulink™. The example also illustrates how to develop an event-based Kalman Filter to update system parameters for more accurate state estimation. This example also requires Simscape™ and Stateflow®.

More About

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State Transition and Measurement Functions

The algorithm computes the state estimates $\hat{x}$ of the nonlinear system using state transition and measurement functions specified by you. You can specify up to five measurement functions, each corresponding to a sensor in the system. The software lets you specify the noise in these functions as additive or nonadditive.

Additive Noise Terms— The state transition and measurements equations have the following form:

$\begin{array}{l} x [k + 1] = f (x [k], u_{s} [k]) + w [k] \\ y [k] = h (x [k], u_{米} [k]) + v [k] \end{array}$

Herefis a nonlinear state transition function that describes the evolution of statesxfrom one time step to the next. The nonlinear measurement functionhrelatesxto the measurementsyat time stepk.wandvare the zero-mean, uncorrelated process and measurement noises, respectively. These functions can also have additional optional input arguments that are denoted byu_sandu_米in the equations. For example, the additional arguments could be time stepkor the inputsuto the nonlinear system. There can be multiple such arguments.
Note that the noise terms in both equations are additive. That is,x(k+1)is linearly related to the process noisew(k), andy(k)is linearly related to the measurement noisev(k). For additive noise terms, you do not need to specify the noise terms in the state transition and measurement functions. The software adds the terms to the output of the functions.
Nonadditive Noise Terms— The software also supports more complex state transition and measurement functions where the statex[k] and measurementy[k] are nonlinear functions of the process noise and measurement noise, respectively. When the noise terms are nonadditive, the state transition and measurements equation have the following form:

$\begin{array}{l} x [k + 1] = f (x [k], w [k], u_{s} [k]) \\ y [k] = h (x [k], v [k], u_{米} [k]) \end{array}$

Compatibility Considerations

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Numerical Changes

Behavior changed in R2020b

Starting in R2020b, numerical improvements in theUnscented Kalman Filteralgorithm might produce results that are different from the results you obtained in previous versions.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

The state transition and measurement functions that you specify must use only the MATLAB commands and Simulink blocks that support code generation. For a list of blocks that support code generation, seeSimulink Built-In Blocks That Support Code Generation(Simulink Coder). For a list of commands that support code generation, seeFunctions and Objects Supported for C/C++ Code Generation(MATLAB Coder).

Generated code uses an algorithm that is different from the algorithm that theUnscented Kalman Filterblock itself uses. You might see some numerical differences in the results obtained using the two methods.

Unscented Kalman Filter

Description

Ports

Input

y1,y2,y3,y4,y5— Measured system outputsvector

Dependencies

StateTransitionFcnInputs— Additional optional input argument to state transition functionscalar | vector | matrix

Dependencies

MeasurementFcn1Inputs,MeasurementFcn2Inputs,MeasurementFcn3Inputs,MeasurementFcn4Inputs,MeasurementFcn5Inputs— Additional optional input argument to each measurement functionscalar | vector | matrix

Dependencies

Q— Time-varying process noise covariancescalar | vector | matrix

Dependencies

R1,R2,R3,R4,R5— Time-varying measurement noise covariance米atrix

Dependencies

Enable1、Enable2 Enable3、Enable4 Enable5— Enable correction of estimated states when measured data is availablescalar

Dependencies

Output

xhat— Estimated statesvector

P— State estimation error covariance米atrix

Dependencies

Parameters

System Model Tab

Function— State transition function name米yStateTransitionFcn(default) | function name

Programmatic Use

Process noise— Process noise characteristicsAdditive(default) |Nonadditive

Programmatic Use

Covariance— Time-invariant process noise covariance1(default) | scalar | vector | matrix

Dependencies

Programmatic Use

Time-varying— Time-varying process noise covariance'off'(default) |“上”

Programmatic Use

Initial state— Initial state estimate0(default) | vector

Programmatic Use

Initial covariance— State estimation error covariance1(default) | scalar | vector | matrix

Programmatic Use

Alpha— Spread of sigma points1e-3(default) | scalar value between 0 and 1

Programmatic Use

Beta— Characterization of state distribution2(default) | scalar value greater than or equal to 0

Programmatic Use

Kappa— Spread of sigma points0(default) | scalar value between 0 and 3

Programmatic Use

Function— Measurement function name米yMeasurementFcn(default) | function name

Programmatic Use

Measurement noise— Measurement noise characteristicsAdditive(default) |Nonadditive

Programmatic Use

Covariance— Time-invariant measurement noise covariance1(default) | matrix

Dependencies

Programmatic Use

Time-varying— Time-varying measurement noise covarianceoff(default) |on

Programmatic Use

添加启用端口— Enable correction of estimated states only when measured data is availableoff(default) |on

Programmatic Use

Use the current measurements to improve state estimates— Choose between corrected or predicted state estimateon(default) |off

Programmatic Use

Output state estimation error covariance— Output state estimation error covarianceoff(default) |on

Programmatic Use

Data type— Data type for block parametersdouble(default) |single

Programmatic Use

Sample time— Block sample time1(default) | positive scalar

Dependencies

Programmatic Use

Multirate Tab

Enable multirate operation— Enable specification of different sample times for state transition and measurement functionsoff(default) |on

Programmatic Use

Sample times— State transition and measurement function sample timespositive scalar

Dependencies

Programmatic Use

Model Examples

Estimate States of Nonlinear System with Multiple, Multirate Sensors

Compute Residuals and State Estimation Errors

Nonlinear State Estimation of a Degrading Battery System

More About

State Transition and Measurement Functions

Compatibility Considerations

Numerical Changes

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™.

See Also

Blocks

Functions

`y1,y2,y3,y4,y5`— Measured system outputs
vector

`StateTransitionFcnInputs`— Additional optional input argument to state transition function
scalar | vector | matrix

`MeasurementFcn1Inputs,MeasurementFcn2Inputs,MeasurementFcn3Inputs,MeasurementFcn4Inputs,MeasurementFcn5Inputs`— Additional optional input argument to each measurement function
scalar | vector | matrix

`Q`— Time-varying process noise covariance
scalar | vector | matrix

`R1,R2,R3,R4,R5`— Time-varying measurement noise covariance
米atrix

`Enable1、Enable2 Enable3、Enable4 Enable5`— Enable correction of estimated states when measured data is available
scalar

`xhat`— Estimated states
vector

`P`— State estimation error covariance
米atrix

`Function`— State transition function name
`米yStateTransitionFcn`(default) | function name

`Process noise`— Process noise characteristics
`Additive`(default) |`Nonadditive`

`Covariance`— Time-invariant process noise covariance
`1`(default) | scalar | vector | matrix

`Time-varying`— Time-varying process noise covariance
`'off'`(default) |`“上”`

`Initial state`— Initial state estimate
`0`(default) | vector

`Initial covariance`— State estimation error covariance
`1`(default) | scalar | vector | matrix

`Alpha`— Spread of sigma points
`1e-3`(default) | scalar value between 0 and 1

`Beta`— Characterization of state distribution
`2`(default) | scalar value greater than or equal to 0

`Kappa`— Spread of sigma points
`0`(default) | scalar value between 0 and 3

`Function`— Measurement function name
`米yMeasurementFcn`(default) | function name

`Measurement noise`— Measurement noise characteristics
`Additive`(default) |`Nonadditive`

`Covariance`— Time-invariant measurement noise covariance
`1`(default) | matrix

`Time-varying`— Time-varying measurement noise covariance
`off`(default) |`on`

`添加启用端口`— Enable correction of estimated states only when measured data is available
`off`(default) |`on`

`Use the current measurements to improve state estimates`— Choose between corrected or predicted state estimate
`on`(default) |`off`

`Output state estimation error covariance`— Output state estimation error covariance
`off`(default) |`on`

`Data type`— Data type for block parameters
`double`(default) |`single`

`Sample time`— Block sample time
`1`(default) | positive scalar

`Enable multirate operation`— Enable specification of different sample times for state transition and measurement functions
`off`(default) |`on`

`Sample times`— State transition and measurement function sample times
positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.