org.apache.commons.math3.filter

## Class KalmanFilter

- java.lang.Object
- - org.apache.commons.math3.filter.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
Version:
  $Id: KalmanFilter.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
  Kalman filter resources, An introduction to the Kalman filter by Greg Welch and Gary Bishop, Kalman filter example by Dan Simon, `ProcessModel`, `MeasurementModel`

### Field Summary

Fields
`private RealMatrix` `controlMatrix` The control matrix, equivalent to B.
`private RealMatrix` `errorCovariance` The error covariance matrix, equivalent to P.
`private RealMatrix` `measurementMatrix` The measurement matrix, equivalent to H.
`private RealMatrix` `measurementMatrixT` The transposed measurement matrix.
`private MeasurementModel` `measurementModel` The measurement model used by this filter instance.
`private ProcessModel` `processModel` The process model used by this filter instance.
`private RealVector` `stateEstimation` The internal state estimation vector, equivalent to x hat.
`private RealMatrix` `transitionMatrix` The transition matrix, equivalent to A.
`private RealMatrix` `transitionMatrixT` The transposed transition matrix.

### 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
`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`

### Field Detail

#### processModel

    private final ProcessModel processModel

The process model used by this filter instance.

#### measurementModel

    private final MeasurementModel measurementModel

The measurement model used by this filter instance.

#### transitionMatrix

    private RealMatrix transitionMatrix

The transition matrix, equivalent to A.

#### transitionMatrixT

    private RealMatrix transitionMatrixT

The transposed transition matrix.

#### controlMatrix

    private RealMatrix controlMatrix

The control matrix, equivalent to B.

#### measurementMatrix

    private RealMatrix measurementMatrix

The measurement matrix, equivalent to H.

#### measurementMatrixT

    private RealMatrix measurementMatrixT

The transposed measurement matrix.

#### stateEstimation

    private RealVector stateEstimation

The internal state estimation vector, equivalent to x hat.

#### errorCovariance

    private RealMatrix errorCovariance

The error covariance matrix, equivalent to P.

### 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