RLS Filter
Recursive least squares (RLS) algorithm to compute the output, errors and weighting factors.
Description
Block RLS Filter recursively calculates an estimate of the FIR filter weights required to minimise the error between the output signal and the expected signal .
For more information, see Sect. Extras.
Ports
Input
#
Input
—
input signal
scalar | vector-column
Details
An input signal specified as a scalar or column vector.
| Data types |
|
| Complex numbers support |
Yes |
#
Desired
—
desired signal
scalar | vector-column
Details
The desired signal specified as a scalar or vector-column.
The desired signal must have the same data type, complexity and dimensions as the signal on the Input port.
| Data types |
|
| Complex numbers support |
Yes |
Output
#
Output
—
desired signal estimation
scalar | vector-column
Details
An estimate of the desired signal returned as a scalar or vector-column. It has the same size and complexity as the input signal.
The output signal has the same data type as the desired signal.
| Data types |
|
| Complex numbers support |
Yes |
#
Error
—
Error between output and desired signals
scalar | vector-column
Details
The error between the output and desired signals, returned as a scalar or column vector.
The error signal has the same data type as the desired signal.
The goal of the RLS filter is to minimise this error. The block adapts its coefficients, aiming for their optimal values that give an output signal that closely matches the desired signal.
| Data types |
|
| Complex numbers support |
Yes |
#
Wts
—
filter weights
scalar | vector-column
Details
Filter weights returned as scalar or vector-columns.
The output signal has the same length as specified in the Filter length parameters.
At each step the block outputs the current updated filter weights.
| Data types |
|
| Complex numbers support |
Yes |
Parameters
Main
#
Filter length —
length of the vector of FIR filter coefficients
Int64 integer
Details
FIR filter coefficient vector length as a positive integer.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Specify forgetting factor via —
method of setting the forgetting rate
Dialog
Details
Forgetting rate. Defined as:
-
Dialog- the forgetting factor is specified via the Forgetting factor (0 to 1) parameter.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Forgetting factor (0 to 1) —
forgetting factor of the RLS algorithm
Real number
Details
RLS algorithm forgetting factor , specified as a scalar in the range .
This parameters determines how quickly the filter forgets information about the previous count.
Setting means infinite memory, with the filter adapting the weighting coefficients. Typically, , where is the length of the filter.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Initial value of filter weights —
initial value of filter weights
Scalar / array of real and/or complex numbers
Details
Initial values of FIR filter weight coefficients , given as a scalar or vector with length equal to the filter length.
If the value is a scalar, the block uses the scalar value to create a vector of filter weight coefficients. This vector has a length equal to the filter length and all its values are equal to the scalar value.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Initial input variance estimate —
initial estimate of input data covariance
Real number
Details
Initial values of the input covariance estimate, 1/P(n) in the form:
-
Scalar - P(n) is a diagonal matrix with diagonal elements equal to the scalar value.
-
Square matrix - each dimension of the matrix is equal to the value in the Filter length parameters.
Initial value P(n)= , where the value is specified in the Initial input variance estimate parameters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Reset port —
reset port
None
Details
Enables the Reset reset port. Defined as:
-
None.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
Extras
*Algorithms.
Matrix expression of the RLS filter:
where is the inverse of the exponential weighting factor.
The value of the variables is presented in the table:
Variable |
Description |
|
Index of the current time |
|
Vector of buffered input samples at step |
|
Inverse covariance matrix at step |
|
Vector of gain at a step |
|
Vector of filter coefficient estimates at a step |
|
Filtered signal at a step |
|
Error estimate at step |
|
Expected signal at step |
|
Forgetting coefficient |
The implementation of the algorithm in block is optimised by usage of the symmetry of the inverse covariance matrix P(n). This reduces the total number of computations by half.
Literature
-
Hayes, M.H.. "Statistical Digital Signal Processing and Modeling." New York: John Wiley & Sons, 1996.