How to resolve dimension error?

%% ========================== COMPUTE & PLOT IMU vs GNSS ==========================
clear; clc; close all;

disp("=== Loading Processed Data ===");
load('ECI_Data.mat');       % GNSS Data in ECI
load('IMU_Data_ECI.mat');   % IMU Data converted to ECI
load('Synthetic_GNSS_Data.mat');  % Original GNSS Data
load('Synthetic_IMU_Data.mat');   % Original IMU Data

%% -------------------- Part A: Compute Velocity & Position for IMU --------------------
disp("=== Computing IMU Velocity and Position in ECI ===");

fs_imu = 400; % IMU Sampling Frequency (Hz)
dt_imu = 1/fs_imu;  % IMU time step

% Extract IMU accelerations in ECI
a_x_eci = IMU_Data_ECI.Accel_X_ECI;
a_y_eci = IMU_Data_ECI.Accel_Y_ECI;
a_z_eci = IMU_Data_ECI.Accel_Z_ECI;

% Integrate Acceleration to Compute Velocity (Trapezoidal Rule)
v_x_eci = cumtrapz(dt_imu, a_x_eci);
v_y_eci = cumtrapz(dt_imu, a_y_eci);
v_z_eci = cumtrapz(dt_imu, a_z_eci);

% Integrate Velocity to Compute Position
p_x_eci = cumtrapz(dt_imu, v_x_eci);
p_y_eci = cumtrapz(dt_imu, v_y_eci);
p_z_eci = cumtrapz(dt_imu, v_z_eci);

% Store computed IMU ECI Data
IMU_ECI.Position_X = p_x_eci;
IMU_ECI.Position_Y = p_y_eci;
IMU_ECI.Position_Z = p_z_eci;
IMU_ECI.Velocity_X = v_x_eci;
IMU_ECI.Velocity_Y = v_y_eci;
IMU_ECI.Velocity_Z = v_z_eci;
IMU_ECI.Accel_X = a_x_eci;
IMU_ECI.Accel_Y = a_y_eci;
IMU_ECI.Accel_Z = a_z_eci;

disp("IMU Position, Velocity, and Acceleration computed in ECI Frame.");

%% -------------------- Part B: Convert ECI Data Back to ECEF --------------------
disp("=== Converting ECI Data Back to ECEF for Verification ===");

omega_e = 7.2921150e-5;  % Earth's Rotation Rate (rad/s)
t_imu = (0:length(p_x_eci)-1) * dt_imu; % Time vector for IMU

% Convert back to ECEF (rotation correction)
theta = omega_e * t_imu;

p_x_ecef = p_x_eci .* cos(theta) + p_y_eci .* sin(theta);
p_y_ecef = -p_x_eci .* sin(theta) + p_y_eci .* cos(theta);
p_z_ecef = p_z_eci; % No rotation in Z

v_x_ecef = v_x_eci .* cos(theta) + v_y_eci .* sin(theta);
v_y_ecef = -v_x_eci .* sin(theta) + v_y_eci .* cos(theta);
v_z_ecef = v_z_eci; % No rotation in Z

disp("Converted IMU ECI Data Back to ECEF Frame.");

%% -------------------- Part C: Compute GNSS Position & Velocity in ECI --------------------
disp("=== Interpolating GNSS Data for IMU Comparison ===");

fs_gnss = 10; % GNSS Sampling Frequency (Hz)
t_gnss = GNSS_Data.Posix_Time(:); % GNSS time vector

% Extract GNSS Positions in ECEF
p_x_gnss = GNSS_Data.X_ECEF_m(:);
p_y_gnss = GNSS_Data.Y_ECEF_m(:);
p_z_gnss = GNSS_Data.Z_ECEF_m(:);

% Convert GNSS ECEF Data to ECI (same method as before)
theta_gnss = omega_e * t_gnss;

p_x_eci_gnss = p_x_gnss .* cos(theta_gnss) + p_y_gnss .* sin(theta_gnss);
p_y_eci_gnss = -p_x_gnss .* sin(theta_gnss) + p_y_gnss .* cos(theta_gnss);
p_z_eci_gnss = p_z_gnss;

% Compute GNSS Velocity using Central Difference Approximation
v_x_eci_gnss = gradient(p_x_eci_gnss, t_gnss);
v_y_eci_gnss = gradient(p_y_eci_gnss, t_gnss);
v_z_eci_gnss = gradient(p_z_eci_gnss, t_gnss);

disp("GNSS Position and Velocity computed in ECI Frame.");

%% -------------------- Part D: Interpolate GNSS to IMU Rate --------------------
disp("=== Interpolating GNSS Data to IMU Sampling Rate ===");

p_x_eci_gnss_interp = interp1(t_gnss, p_x_eci_gnss, t_imu, 'linear', 'extrap');
p_y_eci_gnss_interp = interp1(t_gnss, p_y_eci_gnss, t_imu, 'linear', 'extrap');
p_z_eci_gnss_interp = interp1(t_gnss, p_z_eci_gnss, t_imu, 'linear', 'extrap');

v_x_eci_gnss_interp = interp1(t_gnss, v_x_eci_gnss, t_imu, 'linear', 'extrap');
v_y_eci_gnss_interp = interp1(t_gnss, v_y_eci_gnss, t_imu, 'linear', 'extrap');
v_z_eci_gnss_interp = interp1(t_gnss, v_z_eci_gnss, t_imu, 'linear', 'extrap');

disp("GNSS Data Interpolated to IMU Sampling Rate.");

%% -------------------- Part E: Plot Position, Velocity & Acceleration --------------------
disp("=== Plotting IMU vs GNSS Comparisons ===");

figure('Name','Position Comparison in ECI','NumberTitle','off');
subplot(3,1,1);
plot(t_imu, p_x_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, p_x_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('X (m)'); legend('GNSS','IMU');
title('X Position (ECI)'); axis tight;

subplot(3,1,2);
plot(t_imu, p_y_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, p_y_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('Y (m)'); legend('GNSS','IMU');
title('Y Position (ECI)'); axis tight;

subplot(3,1,3);
plot(t_imu, p_z_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, p_z_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('Z (m)'); legend('GNSS','IMU');
title('Z Position (ECI)'); axis tight;

figure('Name','Velocity Comparison in ECI','NumberTitle','off');
subplot(3,1,1);
plot(t_imu, v_x_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, v_x_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('X (m/s)'); legend('GNSS','IMU');
title('X Velocity (ECI)'); axis tight;

subplot(3,1,2);
plot(t_imu, v_y_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, v_y_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('Y (m/s)'); legend('GNSS','IMU');
title('Y Velocity (ECI)'); axis tight;

subplot(3,1,3);
plot(t_imu, v_z_eci_gnss_interp, 'g-','LineWidth',1.5); hold on; grid on;
plot(t_imu, v_z_eci, 'b--','LineWidth',2);
xlabel('Time (s)'); ylabel('Z (m/s)'); legend('GNSS','IMU');
title('Z Velocity (ECI)'); axis tight;

disp("=== All Plots Generated Successfully ===");

The issue with limitations of the data size so how can we resolve it ?

=== Loading Processed Data ===
=== Computing IMU Velocity and Position in ECI ===
IMU Position, Velocity, and Acceleration computed in ECI Frame.
=== Converting ECI Data Back to ECEF for Verification ===
Requested 48000x48000 (17.2GB) array exceeds maximum array size preference (15.9GB). This might
cause MATLAB to become unresponsive.

Related documentation

[Matt J]

The message says your code attempted to build a 48000x48000 matrix. Is that the intended size of the result?

Answer 1

[Harald]

Hi,

To follow up on Matt's comment: if you intended element-wise multiplication to obtain a vector with 48000 elements, the problem is that you are mixing row and column vectors. You can transpose either the row vector theta or both column vectors p_x_eci and p_y_eci to work with vectors of matching orientation.

Best wishes,

Harald