Fitting two curves with shared parameters to two datasets

I want to fit the two functions

to a dataset of the form . Here are a dimensionless distance and two angles (degrees) respectively.

I am trying to follow the procedure describe here.

I generate the dataset using the above functions with some Gaussian noise on top. The data generation seems to work fine.

Yet, the call "lsqcurvefit(fun, x0, alpha_data_tab, beta_data_tab);" gives me an error which indicates that there are some dimension mismatch. However, I do not see it. Can anyone help me with this issue?

clc
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clear all
set(0,'defaulttextinterpreter','latex')
set(0,'defaultAxesTickLabelInterpreter','latex');
set(0,'defaultLegendInterpreter','latex');
set(0, 'DefaultLineLineWidth', 2);
set(0,'defaultAxesFontSize',15)

%True parameters
Af0_true = -0.017767; %Fast initial amplitude
As0_true = 0.017767; %Slow initial amplitude
lambda_f_true = -4.0571e-04; %Fast damping parameter; 1/cm
lambda_s_true = 6.4718e-05; %Slow damping parameter; 1/cm
angular_vel_f_true = 0.0228; %Angular velocity; rad/cm
angular_vel_s_true = 0.0050; %Angular velocity; rad/cm

dx = 0.01; %cm
s_true = 0:dx:1000; %cm
std = 0.1; %deg

spacing = 4;
s_data1 = 275:spacing:300;
s_data2 = 350:spacing:375;
s_data3 = 425:spacing:450;
s_data4 = 500:spacing:525;

s_data = [s_data1, s_data2, s_data3, s_data4];

[s, alpha, beta, s_data, alpha_data, beta_data] = dataMaker(Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true, s_true, s_data, std);

alpha_data_tab = [s_data(:), alpha_data(:)]; % Concatenate Vectors
beta_data_tab = [s_data(:), beta_data(:)]; % Concatenate Vectors

fun1 = @(v,s_data)v(1)*exp(v(3)*s_data).*cos(v(5)*s_data) + v(2)*exp(v(4)*s_data).*cos(v(6)*s_data);
fun2 = @(v,s_data)v(1)*exp(v(3)*s_data).*sin(v(5)*s_data) + v(2)*exp(v(4)*s_data).*sin(v(6)*s_data);
fun = @(v,s_data)[fun1(v,s_data)', fun2(v,s_data)']; % Composite Function

%initial guess
percent = 0.2; %Percent deviation
x0 = [Af0_true-percent*Af0_true, As0_true-percent*As0_true, lambda_f_true-percent*lambda_f_true, lambda_s_true-percent*lambda_s_true,...
    angular_vel_f_true-percent*angular_vel_f_true, angular_vel_s_true-percent*angular_vel_s_true];

fun(x0, s_data)

ans = 28×2

0.0027 0.0253 0.0016 0.0250 0.0005 0.0247 -0.0005 0.0244 -0.0015 0.0240 -0.0025 0.0235 -0.0034 0.0229 -0.0102 0.0130 -0.0102 0.0121 -0.0103 0.0112

X = lsqcurvefit(fun, x0, alpha_data_tab, beta_data_tab);

Error using lsqcurvefit
Function value and YDATA sizes are not equal.

function [s_total, alpha_total, beta_total, s_data, alpha_data, beta_data] = dataMaker(Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true, s_total, s_data, std_deg)
s_total = s_total;
std_rad = std_deg*(pi/180); %rad

%True parameter vector
v0 = [Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true];
alpha_total = v0(1)*exp(v0(3)*s_total).*cos(v0(5)*s_total) + v0(2)*exp(v0(4)*s_total).*cos(v0(6)*s_total);
beta_total = v0(1)*exp(v0(3)*s_total).*sin(v0(5)*s_total) + v0(2)*exp(v0(4)*s_total).*sin(v0(6)*s_total);

s_data = s_data;
alpha_data = v0(1)*exp(v0(3)*s_data).*cos(v0(5)*s_data) + v0(2)*exp(v0(4)*s_data).*cos(v0(6)*s_data);
beta_data = v0(1)*exp(v0(3)*s_data).*sin(v0(5)*s_data) + v0(2)*exp(v0(4)*s_data).*sin(v0(6)*s_data);

alpha_noise = std_rad*randn(1,length(s_data));
beta_noise = std_rad*randn(1,length(s_data));
alpha_data = alpha_data + alpha_noise;
beta_data = beta_data + beta_noise;
end

Answer 1

[Torsten]

clc
close all
clear all
set(0,'defaulttextinterpreter','latex')
set(0,'defaultAxesTickLabelInterpreter','latex');
set(0,'defaultLegendInterpreter','latex');
set(0, 'DefaultLineLineWidth', 2);
set(0,'defaultAxesFontSize',15)

%True parameters
Af0_true = -0.017767; %Fast initial amplitude
As0_true = 0.017767; %Slow initial amplitude
lambda_f_true = -4.0571e-04; %Fast damping parameter; 1/cm
lambda_s_true = 6.4718e-05; %Slow damping parameter; 1/cm
angular_vel_f_true = 0.0228; %Angular velocity; rad/cm
angular_vel_s_true = 0.0050; %Angular velocity; rad/cm

dx = 0.01; %cm
s_true = 0:dx:1000; %cm
std = 0.1; %deg

spacing = 4;
s_data1 = 275:spacing:300;
s_data2 = 350:spacing:375;
s_data3 = 425:spacing:450;
s_data4 = 500:spacing:525;

s_data = [s_data1, s_data2, s_data3, s_data4];

[s, alpha, beta, s_data, alpha_data, beta_data] = dataMaker(Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true, s_true, s_data, std);

%alpha_data_tab = [s_data(:), alpha_data(:)]; % Concatenate Vectors
%beta_data_tab = [s_data(:), beta_data(:)]; % Concatenate Vectors
xdata = s_data;
ydata = [alpha_data(:),beta_data(:)];

fun1 = @(v,s_data)v(1)*exp(v(3)*s_data).*cos(v(5)*s_data) + v(2)*exp(v(4)*s_data).*cos(v(6)*s_data);
fun2 = @(v,s_data)v(1)*exp(v(3)*s_data).*sin(v(5)*s_data) + v(2)*exp(v(4)*s_data).*sin(v(6)*s_data);
fun = @(v,s_data)[fun1(v,s_data)', fun2(v,s_data)']; % Composite Function

%initial guess
percent = 0.2; %Percent deviation
x0 = [Af0_true-percent*Af0_true, As0_true-percent*As0_true, lambda_f_true-percent*lambda_f_true, lambda_s_true-percent*lambda_s_true,...
    angular_vel_f_true-percent*angular_vel_f_true, angular_vel_s_true-percent*angular_vel_s_true];

%X = lsqcurvefit(fun, x0, alpha_data_tab, beta_data_tab);
X = lsqcurvefit(fun, x0, xdata, ydata);

function [s_total, alpha_total, beta_total, s_data, alpha_data, beta_data] = dataMaker(Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true, s_total, s_data, std_deg)
s_total = s_total;
std_rad = std_deg*(pi/180); %rad

%True parameter vector
v0 = [Af0_true, As0_true, lambda_f_true, lambda_s_true, angular_vel_f_true, angular_vel_s_true];
alpha_total = v0(1)*exp(v0(3)*s_total).*cos(v0(5)*s_total) + v0(2)*exp(v0(4)*s_total).*cos(v0(6)*s_total);
beta_total = v0(1)*exp(v0(3)*s_total).*sin(v0(5)*s_total) + v0(2)*exp(v0(4)*s_total).*sin(v0(6)*s_total);

s_data = s_data;
alpha_data = v0(1)*exp(v0(3)*s_data).*cos(v0(5)*s_data) + v0(2)*exp(v0(4)*s_data).*cos(v0(6)*s_data);
beta_data = v0(1)*exp(v0(3)*s_data).*sin(v0(5)*s_data) + v0(2)*exp(v0(4)*s_data).*sin(v0(6)*s_data);

alpha_noise = std_rad*randn(1,length(s_data));
beta_noise = std_rad*randn(1,length(s_data));
alpha_data = alpha_data + alpha_noise;
beta_data = beta_data + beta_noise;
end