Emil David - 4 months ago 19

iOS Question

So I embarked on a quest to calculate the number of steps taken by a user by using the data I get from the accelerometer i.e **x**, **y** and **z** coordinates.

I am trying to implement this algorithm but I am currently stuck at the local maxima portion. Matlab has a built in

`findpeaks()`

Below is my attempt at implementing the algorithm but I still get extremely enormous results from it.

At first, using a data set which consisted of

`20`

`990+`

`660`

`110`

`45`

`findpeaks()`

This is my class implementation

`import Foundation`

class StepCounter

{

private var xAxes: [Double] = [Double]()

private var yAxes: [Double] = [Double]()

private var zAxes: [Double] = [Double]()

private var rmsValues: [Double] = [Double]()

init(graphPoints: GraphPoints)

{

xAxes = graphPoints.xAxes

yAxes = graphPoints.yAxes

zAxes = graphPoints.zAxes

rmsValues = graphPoints.rmsValues

}

func numberOfSteps()-> Int

{

var pointMagnitudes: [Double] = rmsValues

removeGravityEffectsFrom(&pointMagnitudes)

let minimumPeakHeight: Double = standardDeviationOf(pointMagnitudes)

let peaks = findPeaks(&pointMagnitudes)

var totalNumberOfSteps: Int = Int()

for thisPeak in peaks

{

if thisPeak > minimumPeakHeight

{

totalNumberOfSteps += 1

}

}

return totalNumberOfSteps

}

// TODO: dummy method for the time being. replaced with RMS values from controller itself

private func calculateMagnitude()-> [Double]

{

var pointMagnitudes: [Double] = [Double]()

for i in 0..<xAxes.count

{

let sumOfAxesSquare: Double = pow(xAxes[i], 2) + pow(yAxes[i], 2) + pow(zAxes[i], 2)

pointMagnitudes.append(sqrt(sumOfAxesSquare))

}

return pointMagnitudes

}

private func removeGravityEffectsFrom(inout magnitudesWithGravityEffect: [Double])

{

let mean: Double = calculateMeanOf(rmsValues)

for i in 0..<magnitudesWithGravityEffect.count

{

magnitudesWithGravityEffect[i] -= mean

}

}

// Reference: https://en.wikipedia.org/wiki/Standard_deviation

private func standardDeviationOf(magnitudes: [Double])-> Double

{

var sumOfElements: Double = Double()

var mutableMagnitudes: [Double] = magnitudes

// calculates the numerator of the equation

/* no need to do (mutableMagnitudes[i] = mutableMagnitudes[i] - mean)

* because it has already been done when the gravity effect was removed

* from the dataset

*/

for i in 0..<mutableMagnitudes.count

{

mutableMagnitudes[i] = pow(mutableMagnitudes[i], 2)

}

// sum the elements

for thisElement in mutableMagnitudes

{

sumOfElements += thisElement

}

let sampleVariance: Double = sumOfElements/Double(mutableMagnitudes.count)

return sqrt(sampleVariance)

}

// Reference: http://www.mathworks.com/help/signal/ref/findpeaks.html#examples

private func findPeaks(inout magnitudes: [Double])-> [Double]

{

var peaks: [Double] = [Double]()

// ignore the first element

peaks.append(max(magnitudes[1], magnitudes[2]))

for i in 2..<magnitudes.count

{

if i != magnitudes.count - 1

{

peaks.append(max(magnitudes[i], magnitudes[i - 1], magnitudes[i + 1]))

}

else

{

break

}

}

// TODO:Does this affect the number of steps? Are they clumsly lost or foolishly added?

peaks = Array(Set(peaks)) // removing duplicates.

return peaks

}

private func calculateMeanOf(magnitudes: [Double])-> Double

{

var sumOfElements: Double = Double()

for thisElement in magnitudes

{

sumOfElements += thisElement

}

return sumOfElements/Double(magnitudes.count)

}

}`

With this datasheet, the actual number of steps taken was

`20`

`45`

`30`

`100s.`

Any assistance/guidance will be greatly appreciated

Answer

This function works with the example you provided. It treats plateaus as one peak, and allows for multiple peaks of the same value. The only problem is as — @user3386109 points outs — if there are lots of little oscillations in the data you will get more peaks than are really there. You might want to implement variance of the dataset in this calculation if you will be dealing with data like that.

Also, since you aren't changing the variable you pass in there is no need to use `inout`

```
private func findPeaks(magnitudes: [Double]) -> [Double] {
var peaks = [Double]()
// Only store initial point, if it is larger than the second. You can ignore in most data sets
if max(magnitudes[0], magnitudes[1]) == magnitudes[0] { peaks.append(magnitudes[0]) }
for i in 1..<magnitudes.count - 2 {
let maximum = max(magnitudes[i - 1], magnitudes[i], magnitudes[i + 1])
// magnitudes[i] is a peak iff it's greater than it's surrounding points
if maximum == magnitudes[i] && magnitudes[i] != magnitudes[i+1] {
peaks.append(magnitudes[i])
}
}
return peaks
}
```