I think this works great. It's well commented, practically self documenting but if you have any questions, ask.
% Initialization steps.
clc; % Clear the command window.
fprintf('Beginning to run %s.m ...\n', mfilename);
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
% Load data and plot it.
hFig1 = figure;
sa = load('acceleration.mat')
accel = sa.acceleration1;
st = load('time.mat')
t = st.time1;
plot(t, accel, 'b.-', 'MarkerSize', 9);
grid on;
hold on;
fontSize = 20;
xlabel('Time', 'FontSize', fontSize);
ylabel('Acceleration', 'FontSize', fontSize);
title('Original Signal', 'FontSize', fontSize);
hFig1.WindowState = 'maximized'; % Maximize the figure window.
% Draw a line at y=0
yline(0, 'LineWidth', 2);
% A moving trend is influenced by the huge outliers, so get rid of those first.
% Find outliers
outlierIndexes = isoutlier(accel);
plot(t(outlierIndexes), accel(outlierIndexes), 'ro', 'MarkerSize', 15);
% Extract the good data.
tGood = t(~outlierIndexes);
accelGood = accel(~outlierIndexes);
% plot(t(~outlierIndexes), accel(~outlierIndexes), 'mo', 'MarkerSize', 10); % Plot circles around the good data.
% Do a Savitzky-Golay filter (moving quadratic).
windowWidth = 51; % Smaller for tighter following of original data, bigger for smoother curve.
smoothedy = sgolayfilt(accelGood, 2, windowWidth);
hold on;
plot(tGood, smoothedy, 'r-', 'LineWidth', 2);
legend('Original Signal', 'X axis', 'Outliers', 'Smoothed Signal');
% Now it looks pretty reasonable since we didn't include the outliers.
% But smoothedy has fewer points so if we're to subtract it from the original
% we have to fill in the missing points.
smoothedy = interp1(tGood, smoothedy, t);
% Now subtract the smoothed signal to get the variation
signal = accel - smoothedy;
% Plot it.
hFig2 = figure;
plot(t, signal, 'b.-', 'MarkerSize', 9);
grid on;
hold on;
title('Corrected Signal', 'FontSize', fontSize);
xlabel('Time', 'FontSize', fontSize);
ylabel('Acceleration', 'FontSize', fontSize);
hFig2.Units = 'normalized';
hFig2.Position = [.2, .2, .5, .5]; % Size the figure window.
% Draw a line at y=0
yline(0, 'LineWidth', 2);
