**Block Category:** Matrix Operation

**Inputs:**

•**X:*** *Vector of independent input values.

•**Y:*** *Vector of dependent output values.

•**Signal In:** Scalar *x* value.

**Outputs:**

•**Coeffs: **Regression coefficients (column vector with the topmost
element associated with the nth power of the **Signal In** value.

•**Signal Out: **Result of applying the regression polynomial to the
**Signal In*** *value.

**Description:** The polyFit block performs a polynomial
regression relating a vector of input value ) to a vector of output values
*y* as an nth order polynomial, where the polynomial order is a
user-configurable value ranging from 0 – 256.

The polynomial can be calculated once at simulation start or iteratively.

**Calculate coefficients once on startup:** Calculates
the polynomial fit once at start of the simulation, which is fine for static
data sets. The fit algorithm is numerically costly, so it should only be run if
needed.

**Polynomial Order:** Specifies the maximum exponent for
the polynomial fit.

**1. Input and output signal
connections**

The block diagram below shows the input and output signal connections for a polyFit block.

Here, the *xVector *variable
is a row vector of recorded values of the independent variable; the
*yVector* variable is a row vector of recorded dependent variables (with
the same number of columns as the *xVector*); and the *x* variable is
a scalar independent value that is applied to the regression polynomial
coefficients (shown as the column vector *Coeffs* = [-20.655; 305.17]) to
produce the *Signal Out* variable labeled as *yHat*.

**2. Static fit**

The block diagram below shows how
a polyFit block is used to fit a first order polynomial to a 10-element data
set. The data set consists of a 10-element row vector of independent *x*
values recorded in the *xVector* variable block and a corresponding
10-element row vector of dependent *y* values recorded in the
*yVector* variable block. The scalarToVec block is used to create the two
vectors with the following settings: “rows” = 1 and “columns” = 10. The
polyFit block is configured to fit a first order polynomial and to calculate the
coefficients once at startup.

The RegressionCoefficients are calculated as

[C1 = 3.97576; C2 = 8.50909]

The regression formula used by the
polyFit block to calculate *yHat* is:

*yHat* = C1 * *x* +
C2

The plot block compares the
*yHat* variable with the dependent variable vector *yVector* when the
*Signal In* is a sweep of the *xVector* values. A unit ramp is used to
create the *x* signal. The *yHat* value from the polyFit block is
plotted in blue; a calculation of the *yHa*t signal is plotted in red. The
green trace is the recorded dependent variable from the *yVector*.

**3. Recursive fit**

This block diagram shows how the
polyFit block is used to fit a second order polynomial to a 100-element moving
window data set. The generation of the independent input signal *x* and the
dependent output signal *y* are shown in the upper part of the block
diagram.

The buffer blocks are used to
record the 100-element moving window of *x* and *y* values at 0.2 sec
intervals. Since the simulation update time is 0.01 sec, the buffer interval
causes the moving window data sets to overlap with one another.

The polyFit block is configured to fit a second order polynomial and to calculate the coefficients at each time step of the simulation.

The polyFit output signal
*yHat* is plotted with the recorded dependent variable
*y*.