Create extended Kalman filter object for online state estimation
creates an extended Kalman filter object for online state estimation of a
discretetime nonlinear system. obj
= extendedKalmanFilter(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 firstorder
discretetime extended Kalman filter algorithm and realtime data.
specifies additional attributes of the extended Kalman filter object using one
or more obj
= extendedKalmanFilter(StateTransitionFcn
,MeasurementFcn
,InitialState
,Name,Value
)Name,Value
pair arguments.
creates an extended Kalman filter object using the specified state transition
and measurement functions. Before using the obj
= extendedKalmanFilter(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 extended Kalman filter object using one
or more obj
= extendedKalmanFilter(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 extended Kalman filter object with properties specified using one or
more obj
= extendedKalmanFilter(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.
extendedKalmanFilter
creates an object for online state
estimation of a discretetime nonlinear system using the firstorder discretetime
extended 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 relates x
to
the measurements y
at time step k
. w
and v
are
the zeromean, uncorrelated process and measurement noises, respectively.
These functions can also have additional input arguments that are
denoted by u_{s}
and u_{m}
in
the equations. For example, the additional arguments could be time
step k
or the inputs u
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 noise w(k1)
,
and y(k)
is linearly related to the measurement
noise v(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 extendedKalmanFilter
object using these
nonlinear functions, and specify whether the noise terms are additive or nonadditive.
You can also specify the Jacobians of the state transition and measurement functions. If
you do not specify them, the software numerically computes the Jacobians.
After you create the object, you use the predict
command to predict state estimate at the next time step, and
correct
to correct state estimates using the 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 extendedKalmanFilter
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 extendedKalmanFilter
object properties, see Properties.