Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN

These data are already preprocessed so they are already syncronized and they are of the same size. However, when I tried running, MATLAB says: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN. What seems to be the problem with this and how can this be fixed?

% load data
clear;
clc;
ld1 = load('CALT23A.mat'); 
ld2 = load('CALT23D.mat');
ld3 = load('CALT23M.mat');
ld4 = load('CALT23S.mat');
ld5 = load('CALT23K.mat');
%% 
% Accelerometer
accx = mean([ld1.Acceleration.X ld2.Acceleration.X ld3.Acceleration.X ld4.Acceleration.X],2,'omitnan');
accy = mean([ld1.Acceleration.Y ld2.Acceleration.Y ld3.Acceleration.Y ld4.Acceleration.Y],2,'omitnan');
accz = mean([ld1.Acceleration.Z ld2.Acceleration.Z ld3.Acceleration.Z ld4.Acceleration.Z],2,'omitnan');
accelerometerReadings = [accx accy accz];
% Gyroscope
angx = mean([ld1.AngularVelocity.X ld2.AngularVelocity.X ld3.AngularVelocity.X ld5.AngularVelocity.X],2,'omitnan');
angy = mean([ld1.AngularVelocity.Y ld2.AngularVelocity.Y ld3.AngularVelocity.Y ld5.AngularVelocity.Y],2,'omitnan');
angz = mean([ld1.AngularVelocity.Z ld2.AngularVelocity.Z ld3.AngularVelocity.Z ld5.AngularVelocity.Z],2,'omitnan');
gyroscopeReadings = [angx angy angz];
% Magnetometer 
magx = mean([ld1.MagneticField.X ld2.MagneticField.X ld3.MagneticField.X ld4.MagneticField.X],2,'omitnan');
magy = mean([ld1.MagneticField.Y ld2.MagneticField.Y ld3.MagneticField.Y ld4.MagneticField.Y],2,'omitnan');
magz = mean([ld1.MagneticField.Z ld2.MagneticField.Z ld3.MagneticField.Z ld4.MagneticField.Z],2,'omitnan');
magnetometerReadings = [magx magy magz];
%GPS 
lat = mean([ld1.Position.latitude ld2.Position.latitude ld3.Position.latitude ld4.Position.latitude],2,'omitnan');
long = mean([ld1.Position.longitude ld2.Position.longitude ld3.Position.longitude ld4.Position.longitude],2,'omitnan');
speed = mean([ld1.Position.speed ld2.Position.speed ld3.Position.speed ld4.Position.speed],2,'omitnan');
gps_speed_combined = speed;
%% IMU Filter (indirect Kalman Filter)
fuse = imufilter('SampleRate',100, 'DecimationFactor',1,'AccelerometerNoise',0.5,'GyroscopeNoise',0.01); 
q1 = fuse(accelerometerReadings, gyroscopeReadings);
orient1 = eulerd(q1, 'ZYX','frame');
f = figure;
f.Position(1:4) = [100 20 1100 600];
plot(orient1(:,3)); hold off 
grid on
axis tight
xlabel('Time (sec)');
ylabel('Angle (deg)');
title('Orientation Estimate using IMU Filter')
saveas(gcf, 'imufilter.png')

[Walter Roberson]

Which line is producing the error?

It would help debugging if we had the .mat files.

[Mark John Castro]

The line where I started running the IMU filter is producing the error whis is this:

q1 = fuse(accelerometerReadings, gyroscopeReadings);

Unfortunately, I can't upload the .mat files because of their sizes.

[dpb]

One (or both) of the arrays is/are nearly singular -- that is, two (or more) columns are nearly scalar multiples of each other. In other words, one of the traces is almost perfectly the same as another except for a scale factor in the x, y, z directions.

Plot the three components and see which two are the culprits or divide X by Y and Z, respectively, and compute the average ratios and std. The variance of one or both ratios will be very near zero for those that are coincident.

Maybe you confused two channels and what you think is Y or Z is actually another copy of X or similar? Or, a perfectly 45 linear motion or constant circular would produce the same x,y accelerations resulting in a real case where both the x- and y-channels should be the same.

Anyways, that's the basic problem; you have multiple readings that match each other in one or the other or both...

[dpb]

ADDENDUM:

In a first try on here I couldn't duplicate the error with test randomized data, even if passed identical columns so I dunno what's going on. I don't have whatever TB fuse you're using is from and debugging on this platform is nigh upon impossible so can't really tell from just where the issue may have arisen.

But see <Cleve's Condition Number> for all you could ever want to know about what it is and represents...

Mayhaps our resident math whiz @John D&#39;Errico will stumble over this and have more insight as to what is going on internally.

I'd suggest the above heuristics to just examine the traces, though, to see what they look like and, of course you can always run rcond on them yourself to see if can isolate which is the culprit.

[dpb]

ADDENDUM SECOND:

Oh! Head slap! The other other possibility is as simple as

x=rand(5);
x(2,2)=nan;
rcond(x)

ans = NaN

If there's a NaN in one of the time traces, that'll do it if the input checking doesn't catch it out before passing the input on to the guts of the routine...

Need to do a

any(isnan(accelerometerReadings))
any(isnan(gyroscopeReadings))

If either returns true, you've found the culprit...