iOS: Swift: Combine Accelerometer and Attitude data for comparable results - ios

Question

Idea
My idea is to write a little application for my iOS-Device to record a motion after start recording by touching an UIButton and save the data from the accelerometer for this motion. After the recording, I can save this data to use it in the finished Application to detect this motion again.
So, what I'm looking for is a way to compare two NSMutableArrays, each as a set of motion data, and want to check if the current NSMutableArray is the same motion as the recorded one.
Problems
To realize this idea, I found three problems, which I can't solve myself:
How to compare two NSMutableArrays and get e.g. an index-level of the similarity or a percentage e.g. 97.32% equivalent.
What if the user makes the motion in different speeds? E.g. slowly or fast.
The last problem: How to handle different device-orientations? Is there a way to calculate the data from the accelerometer to a neutral level in any orientation? I think I have a solution approach for this last problem, but don't know how to bring this to code: We have the attitude data for pitch, roll and yaw. Maybe we can calculate with these values the neutral data for the accelerometer?
Code
At this moment, I only have the code to get the data from the accelerometer and the attitude data, both from the MotionManager. I played multiple hours with my code and searched a lot on Google, but can't find the right way...
import UIKit
import CoreMotion
var motionManager = CMMotionManager()
var x:Float = 0.0
var y:Float = 0.0
var z:Float = 0.0
var roll:Float = 0.0
var pitch:Float = 0.0
var yaw:Float = 0.0
class FirstViewController: UIViewController {
override func viewDidLoad() {
super.viewDidLoad()
motionManager.accelerometerUpdateInterval = 1
motionManager.deviceMotionUpdateInterval = 1
}
#IBAction func startRecording() {
accelerometerData = NSMutableArray()
motionManager.startDeviceMotionUpdates(using: CMAttitudeReferenceFrame.xMagneticNorthZVertical, to:
OperationQueue.current!, withHandler: {
(deviceMotion, error) -> Void in
let attitude = deviceMotion?.attitude
let roll = self.degrees(radians: attitude!.roll)
let pitch = self.degrees(radians: attitude!.pitch)
let yaw = self.degrees(radians: attitude!.yaw)
self.roll = Float(roll)
self.pitch = Float(pitch)
self.yaw = Float(yaw)
let accX = deviceMotion?.userAcceleration.x
let accY = deviceMotion?.userAcceleration.y
let accZ = deviceMotion?.userAcceleration.z
self.x = Float(accX!)
self.y = Float(accY!)
self.z = Float(accZ!)
})
}
}
Update
I will update this question, when I know more.
Problem 2: Solution:
With the Attribute CMAttitudeReferenceFrame.xMagneticNorthZVertical for the motionManager.startDeviceMotionUpdates-Method you can neutralize all sensors data to a defined orientation. You can access the accelerometer-data here too. I've updated the code above, too.