Accelerometer Low Pass Filtering

Still on the BigNerdRanch iOS Development book.

In the Accelerometer chapter, they first implement accelerometer tracking but it's fairly jumpy. They then suggest to apply a low pass filter to it by changing the original code:

- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration
{
    HypnosisView *hv = (HypnosisView *)[self view];

    [hv setXShift:10.0 * [acceleration x]];
    [hv setYShift:10.0 * [acceleration y]];

    [hv setNeedsDisplay];
}

to this:

- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration
{
    HypnosisView *hv = (HypnosisView *)[self view];

    float xShift = [hv xShift] * 0.8 + [accel x] * 2.0;
    float yShift = [hv yShift] * 0.8 + [accel y] * 2.0;

    [hv setXShift:xShift];
    [hv setYShift:yShift];

    [hv setNeedsDisplay];
}

Fairly simple question: where do they get these values from? I've been looking through the documentation and I found something about low pass filters, which suggests the following code:

   #define kFilteringFactor 0.1

- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration {
    // Use a basic low-pass filter to keep only the gravity component of each axis.
    accelX = (acceleration.x * kFilteringFactor) + (accelX * (1.0 - kFilteringFactor));
    accelY = (acceleration.y * kFilteringFactor) + (accelY * (1.0 - kFilteringFactor));
    accelZ = (acceleration.z * kFilteringFactor) + (accelZ * (1.0 - kFilteringFactor));

   // Use the acceleration data.
}

However, I first tried with that code and I got an error (by analyzing my app) saying 'the left value of '*' is a garbage value'. My accelerometer tracking didn't work either.

I'm fairly confused as to what these values mean. For example, in the first part of the code, why do they multiply the acceleration values by 10? To get a 'bigger' movement? I could make some sense out of that, but the second code with the low pass filter makes absolutely no sense to me.

accelX = (acceleration.x * kFilteringFactor) + (accelX * (1.0 - kFilteringFactor));

Whats happening in this code you are multiplying the acceleration at the moment by the Filtering factor 0.1 and then adding it to the filtered acceleration of the last time an update was called by 0.9.

This is pretty much getting the new value and adding it as 10% of the total accelX the other 90% is made up of the previous value which depends on the value before that, which depends on the value before that and so on. This cuts out high frequency values as only allows 10% of any change to go through to the new accelX value.

The KFilteringFactor of 0.1 makes this filter cut out all high frequencies. You will definitely want to experiment by changing this value to suit your particular application.