DSP Blockset 
Compute filter estimates for an input using the Kalman adaptive filter algorithm.
Library
Filtering / Adaptive Filters
Description
The Kalman Adaptive Filter block computes the optimal linear minimum meansquare estimate (MMSE) of the FIR filter coefficients using a onestep predictor algorithm. This Kalman filter algorithm is based on the following physical realization of a dynamical system.
The Kalman filter assumes that there are no deterministic changes to the filter taps over time (i.e., the transition matrix is identity), and that the only observable output from the system is the filter output with additive noise. The corresponding Kalman filter is expressed in matrix form as
The correlation matrices, QM and QP, are specified in the parameter dialog box by scalar variance terms to be placed along the matrix diagonals, thus ensuring that these matrices are symmetric. The filter algorithm based on this constraint is also known as the randomwalk Kalman filter.
The implementation of the algorithm in the block is optimized by exploiting the symmetry of the input covariance matrix K(n). This decreases the total number of computations by a factor of two.
The block icon has port labels corresponding to the inputs and outputs of the Kalman algorithm. Note that inputs to the In
and Err
ports must be samplebased scalars. The signal at the Out
port is a scalar, while the signal at the Taps
port is a samplebased vector.
Block Ports 
Corresponding Variables 
In 
u, the scalar input, which is internally buffered into the vector u(n) 
Out 

Err 

Taps 
An optional Adapt
input port is added when the Adapt input check box is selected in the dialog box. When this port is enabled, the block continuously adapts the filter coefficients while the Adapt
input is nonzero. A zerovalued input to the Adapt
port causes the block to stop adapting, and to hold the filter coefficients at their current values until the next nonzero Adapt
input.
The FIR filter length parameter specifies the length of the filter that the Kalman algorithm estimates. The Measurement noise variance and the Process noise variance parameters specify the correlation matrices of the measurement and process noise, respectively. The Measurement noise variance must be a scalar, while the Process noise variance can be a vector of values to be placed along the diagonal, or a scalar to be repeated for the diagonal elements.
The Initial value of filter taps specifies the initial value as a vector, or as a scalar to be repeated for all vector elements. The Initial error correlation matrix specifies the initial value K(0), and can be a diagonal matrix, a vector of values to be placed along the diagonal, or a scalar to be repeated for the diagonal elements.
Dialog Box
Adapt
port.References
Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.
See Also
LMS Adaptive Filter 
DSP Blockset 
RLS Adaptive Filter 
DSP Blockset 
See Adaptive Filters for related information.
Integer Delay  LDL Factorization 