hello
see my suggestion below (based on dummy data as you don't supply any file)
notice that to compute the velocity and acceleration you can use the function gradient instead of diff , which has the advantage to keep all data length equal . Also do not forget to use the dx spacing with diff or gradient otherwise your derivatives are wrong;
% function phi = curvefit3(x,y)
clear all;
close all;
clc;
% [data, ~] = xlsread('filename.xlsx');
% x_imp = data(:,1); %%reading rows and first column
% y_imp = data(:,2); %%reading rows and second column
%% dummy data
x_imp = (0:0.1:10)';
y_imp = 0.5 +1.2*x_imp + 0.54*x_imp.^2 + 0.02*randn(size(x_imp));
data = [x_imp y_imp];
[rows, ~] = size(data);
dx = mean(diff(x_imp));
points_curve_fit = 5:2:9;
ci = 0;
for nwindow = points_curve_fit
ci = ci+1;
for k = 1: 1 : rows -nwindow %%loop to read i+1 to i+5 rows
x = x_imp(k:k+nwindow-1,1);
y = y_imp(k:k+nwindow-1,1);
x0 = x(1);
var1 = x - x0;
var2 = var1.*var1;
%% construction of the least-squares quadratic fit to the data
%% we use the equation y =a0 + a1t + a2t^2 %%t = (x-x0)
%% numbers a0,a1 and a2 are the unknowns
x_mat = [ones(nwindow,1) var1 var2];
amat = x_mat'*x_mat;
bmat = x_mat'*y;
phi = inv(amat)*bmat;
a0 = phi(1);
a1 = phi(2);
a2 = phi(3);
error = y-(x_mat*phi);
marker = floor(nwindow/2) + 1;
if (k == 1)
err(1:marker,1) =error(1:marker,1);
else
err(k+marker-1) =error(marker);
end
pos_n = (a0+a1*var1+a2*var2);
markar = floor(nwindow/2) + 1;
if (k == 1)
pos(1:markar,1) = pos_n(1:markar,1);
else
pos(k+markar-1) = pos_n(markar);
% plot(pos,'-ob');
end %if (i == 1)
velo = gradient(pos,dx);
acc_n = gradient(velo,dx);
end
% store iteration results into 2D array (1 iteration = 1 column)
err_all(:,ci) = err; % to plot all outputs
pos_all(:,ci) = pos; % to plot all outputs
velo_all(:,ci) = velo; % to plot all outputs
acc_n_all(:,ci) = acc_n; % to plot all outputs
str_pos{ci} = ['Pos Curve Fit' num2str(points_curve_fit(ci)) ' points'];
str_velo{ci} = ['Velo Curve Fit' num2str(points_curve_fit(ci)) ' points'];
str_acc{ci} = ['Accel Curve Fit' num2str(points_curve_fit(ci)) ' points'];
str_err{ci} = ['error ' num2str(points_curve_fit(ci)) ' points'];
end
n= length(pos);
tim_pos = x_imp(1:n);
y_raw = y_imp(1:n);
fig1 = figure('name', sprintf('%d points curve fit ', points_curve_fit),'NumberTitle','off');
plot(tim_pos,y_raw,'or',tim_pos,pos_all,'-',tim_pos,velo_all,'--',tim_pos,acc_n_all,'*'); grid on;
legend([{' raw data'} str_pos str_velo str_acc]);
xlabel(' Time(sec) ');
ylabel(' Function ');
fig2 = figure('name', sprintf('%d points error ', points_curve_fit),'NumberTitle','off');
plot(tim_pos,err_all,'--');grid on;
legend(str_err);
