unscentedKalmanFilter
Create unscented Kalman filter object for online state estimation
Syntax
Description
creates an unscented Kalman filter object for online state estimation of a
discretetime nonlinear system. obj
= unscentedKalmanFilter(StateTransitionFcn
,MeasurementFcn
,InitialState
)StateTransitionFcn
is a
function that calculates the state of the system at time k,
given the state vector at time k1.
MeasurementFcn
is a function that calculates the output
measurement of the system at time k, given the state at time
k. InitialState
specifies the
initial value of the state estimates.
After creating the object, use the correct
and predict
commands to update state
estimates and state estimation error covariance values using a discretetime
unscented Kalman filter algorithm and realtime data.
specifies additional attributes of the unscented Kalman filter object using one
or more obj
= unscentedKalmanFilter(StateTransitionFcn
,MeasurementFcn
,InitialState
,Name,Value
)Name,Value
pair arguments.
creates an unscented Kalman filter object using the specified state transition
and measurement functions. Before using the obj
= unscentedKalmanFilter(StateTransitionFcn
,MeasurementFcn
)predict
and
correct
commands, specify the initial state values
using dot notation. For example, for a twostate system with initial state
values [1;0]
, specify obj.State =
[1;0]
.
specifies additional attributes of the unscented Kalman filter object using one
or more obj
= unscentedKalmanFilter(StateTransitionFcn
,MeasurementFcn
,Name,Value
)Name,Value
pair arguments. Before using the
predict
and correct
commands,
specify the initial state values using Name,Value
pair
arguments or dot notation.
creates an unscented Kalman filter object with properties specified using one or
more obj
= unscentedKalmanFilter(Name,Value
)Name,Value
pair arguments. Before using the
predict
and correct
commands,
specify the state transition function, measurement function, and initial state
values using Name,Value
pair arguments or dot
notation.
Object Description
unscentedKalmanFilter
creates an object for online state
estimation of a discretetime nonlinear system using the discretetime unscented Kalman
filter algorithm.
Consider a plant with states x, input u, output y, process noise w, and measurement noise v. Assume that you can represent the plant as a nonlinear system.
The algorithm computes the state estimates $$\widehat{x}$$ of the nonlinear system using state transition and measurement functions specified by you. 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:
$$\begin{array}{l}x[k]=f(x[k1],{u}_{s}[k1])+w[k1]\\ y[k]=h(x[k],{u}_{m}[k])+v[k]\end{array}$$
Here f is a nonlinear state transition function that describes the evolution of states
x
from one time step to the next. The nonlinear measurement function h relatesx
to the measurementsy
at time stepk
.w
andv
are the zeromean, uncorrelated process and measurement noises, respectively. These functions can also have additional input arguments that are denoted byu_{s}
andu_{m}
in the equations. For example, the additional arguments could be time stepk
or the inputsu
to the nonlinear system. There can be multiple such arguments.Note that the noise terms in both equations are additive. That is,
x(k)
is linearly related to the process noisew(k1)
, andy(k)
is linearly related to the measurement noisev(k)
.Nonadditive Noise Terms — The software also supports more complex state transition and measurement functions where the state x[k] and measurement y[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:
$$\begin{array}{l}x[k]=f(x[k1],w[k1],{u}_{s}[k1])\\ y[k]=h(x[k],v[k],{u}_{m}[k])\end{array}$$
When you perform online state estimation, you first create the nonlinear state
transition function f and measurement function h.
You then construct the unscentedKalmanFilter
object using these
nonlinear functions, and specify whether the noise terms are additive or nonadditive.
After you create the object, you use the predict
command to predict state estimates at the next time step, and
correct
to correct state estimates using the unscented Kalman filter
algorithm and realtime data. For information about the algorithm, see Extended and Unscented Kalman Filter Algorithms for Online State Estimation.
You can use the following commands with unscentedKalmanFilter
objects:
Command  Description 

correct  Correct the state and state estimation error covariance at time step k using measured data at time step k. 
predict  Predict the state and state estimation error covariance at time the next time step. 
residual  Return the difference between the actual and predicted measurements. 
clone  Create another object with the same object property values. Do not create additional objects using syntax

For unscentedKalmanFilter
object properties, see Properties.