fitPiecewiseLinear(​t, z, tGuess)

Computes a best-fit linear spline with arbitrary grid spacing

% [tGrid, zGrid] = fitThreeLines(t, z, tMidGuess)
%
% This function fits a piecewise linear function to a data set. The number
% of knot points is fixed, but the optimization computes the optimal grid
% spacing and the value at each knot point.
%
% INPUTS:
% t = [1,n] = time stamp
% z = [1,n] = data value
% tGuess = [1,k] = guess at the knot times. Mapped to [t(1), t(end)]
%
% OUTPUTS:
% tGrud = [1, k] = knot times for best-fit linear spline
% zGriz = [1, k] = data values for best-fit linear spline
% objVal = scalar = fitting error for the best-fit solution
% exitFlag = FMINCON exit flag for data fitting
%