org.apache.commons.math3.filter

## Class KalmanFilter

• public class KalmanFilter
extends Object
Implementation of a Kalman filter to estimate the state xk of a discrete-time controlled process that is governed by the linear stochastic difference equation:
 xk = Axk-1 + Buk-1 + wk-1

with a measurement xk that is
 zk = Hxk + vk.


The random variables wk and vk represent the process and measurement noise and are assumed to be independent of each other and distributed with normal probability (white noise).

The Kalman filter cycle involves the following steps:

1. predict: project the current state estimate ahead in time
2. correct: adjust the projected estimate by an actual measurement

The Kalman filter is initialized with a ProcessModel and a MeasurementModel, which contain the corresponding transformation and noise covariance matrices. The parameter names used in the respective models correspond to the following names commonly used in the mathematical literature:

• A - state transition matrix
• B - control input matrix
• H - measurement matrix
• Q - process noise covariance matrix
• R - measurement noise covariance matrix
• P - error covariance matrix
Since:
3.0
Kalman filter resources, An introduction to the Kalman filter by Greg Welch and Gary Bishop, Kalman filter example by Dan Simon, ProcessModel, MeasurementModel
• ### Constructor Summary

Constructors
Constructor and Description
KalmanFilter(ProcessModel process, MeasurementModel measurement)
Creates a new Kalman filter with the given process and measurement models.
• ### Method Summary

Methods
Modifier and Type Method and Description
void correct(double[] z)
Correct the current state estimate with an actual measurement.
void correct(RealVector z)
Correct the current state estimate with an actual measurement.
double[][] getErrorCovariance()
Returns the current error covariance matrix.
RealMatrix getErrorCovarianceMatrix()
Returns a copy of the current error covariance matrix.
int getMeasurementDimension()
Returns the dimension of the measurement vector.
int getStateDimension()
Returns the dimension of the state estimation vector.
double[] getStateEstimation()
Returns the current state estimation vector.
RealVector getStateEstimationVector()
Returns a copy of the current state estimation vector.
void predict()
Predict the internal state estimation one time step ahead.
void predict(double[] u)
Predict the internal state estimation one time step ahead.
void predict(RealVector u)
Predict the internal state estimation one time step ahead.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### KalmanFilter

public KalmanFilter(ProcessModel process,
MeasurementModel measurement)
throws NullArgumentException,
NonSquareMatrixException,
DimensionMismatchException,
MatrixDimensionMismatchException
Creates a new Kalman filter with the given process and measurement models.
Parameters:
process - the model defining the underlying process dynamics
measurement - the model defining the given measurement characteristics
Throws:
NullArgumentException - if any of the given inputs is null (except for the control matrix)
NonSquareMatrixException - if the transition matrix is non square
DimensionMismatchException - if the column dimension of the transition matrix does not match the dimension of the initial state estimation vector
MatrixDimensionMismatchException - if the matrix dimensions do not fit together
• ### Method Detail

• #### getStateDimension

public int getStateDimension()
Returns the dimension of the state estimation vector.
Returns:
the state dimension
• #### getMeasurementDimension

public int getMeasurementDimension()
Returns the dimension of the measurement vector.
Returns:
the measurement vector dimension
• #### getStateEstimation

public double[] getStateEstimation()
Returns the current state estimation vector.
Returns:
the state estimation vector
• #### getStateEstimationVector

public RealVector getStateEstimationVector()
Returns a copy of the current state estimation vector.
Returns:
the state estimation vector
• #### getErrorCovariance

public double[][] getErrorCovariance()
Returns the current error covariance matrix.
Returns:
the error covariance matrix
• #### getErrorCovarianceMatrix

public RealMatrix getErrorCovarianceMatrix()
Returns a copy of the current error covariance matrix.
Returns:
the error covariance matrix
• #### predict

public void predict()
Predict the internal state estimation one time step ahead.
• #### predict

public void predict(double[] u)
throws DimensionMismatchException
Predict the internal state estimation one time step ahead.
Parameters:
u - the control vector
Throws:
DimensionMismatchException - if the dimension of the control vector does not fit
• #### predict

public void predict(RealVector u)
throws DimensionMismatchException
Predict the internal state estimation one time step ahead.
Parameters:
u - the control vector
Throws:
DimensionMismatchException - if the dimension of the control vector does not match
• #### correct

public void correct(double[] z)
throws NullArgumentException,
DimensionMismatchException,
SingularMatrixException
Correct the current state estimate with an actual measurement.
Parameters:
z - the measurement vector
Throws:
NullArgumentException - if the measurement vector is null
DimensionMismatchException - if the dimension of the measurement vector does not fit
SingularMatrixException - if the covariance matrix could not be inverted
• #### correct

public void correct(RealVector z)
throws NullArgumentException,
DimensionMismatchException,
SingularMatrixException
Correct the current state estimate with an actual measurement.
Parameters:
z - the measurement vector
Throws:
NullArgumentException - if the measurement vector is null
DimensionMismatchException - if the dimension of the measurement vector does not fit
SingularMatrixException - if the covariance matrix could not be inverted