Inferring device position from acceleration

so getting device position from an accelerometer and gyroscope is, like, nontrivial, due to noise and very severe error propagation in double-integrating the sensor data. here is a good answer that will smash your dreams.

but i'm just lookin for somethin very very rough..... like, oh, you moved the phone upwards.

runge-kutta would be better than euler integration: python, javascript.

and a kalman filter might help clean up the sensor data.

ugh : )

gnight for now

<!DOCTYPE html>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">

<style>

* {
	box-sizing: border-box;
}

html, body {
	margin: 0;
	width: 100%;
	height: 100%;
	position: relative;
}

body {
	perspective: 100px;
	padding: 100px;
}

svg {
	position: absolute;
	width: 100%;
	height: 100%;
	top: 0;
	left: 0;
}

path {
	stroke: black;
	stroke-width: 1;
	fill: none;
}

#phone {
	border: 5px solid black;
	width: 100%;
	height: 100%;
}

</style>

</body>

// store current rotation in euler angles
var rotation = {
	alpha: 0, beta: 0, gamma: 0
};

// store whole history of acceleration and implied velocity and position,
// starting from these initial conditions
var z = [
	{
		position: 0,
		velocity: 0,
		acceleration: 0,
		time: undefined
	}
];

// visualize motion through a box
var phone = d3.select('#phone');

window.addEventListener('devicemotion', handleMotion);
window.addEventListener('deviceorientation', handleOrientation);
window.addEventListener('mousemove', handleMousemove);

d3.timer(renderState);
d3.interval(renderHistory, 500);

// not the focus here, but it also shows rotation!
function handleOrientation(e) {
	if(e.gamma === null || e.beta === null || e.alpha === null) return;
	rotation = {
		gamma: e.gamma || 0,
		beta: e.beta || 0,
		alpha: e.alpha || 0
	}
}

// accelerate according to z-axis device motion
function handleMotion(e) {
	if(e.acceleration.x === null || e.acceleration.y === null || e.acceleration.z === null) return;
	accelerate(e.acceleration.z, e.timeStamp);
}

// for testing on desktop, basically: map horizontal mouse position to acceleration
function handleMousemove(e) {
	var mouseAccelerator = d3.scaleLinear()
		.domain([0,innerWidth])
		.range([-.2,.2]);
	accelerate(mouseAccelerator(e.pageX), e.timeStamp);
	console.log(mouseAccelerator(e.pageX));
}

// step forward with new acceleration, applying some very crude filtering & friction
function accelerate(a, t) {

var newZ = Object.assign({}, z[0]);

newZ.acceleration = Math.abs(a) > .1 ? a : 0; // noise filter
	newZ.time = t;
	newZ = eulerStep(z[0], newZ);

newZ.velocity *= .9; // friction
	newZ.velocity = Math.abs(newZ.velocity) < .01 ? 0 : newZ.velocity; // noise filter
	newZ.position *= .999; // tend back to zero

z.unshift(newZ);
}

// euler double integration
function eulerStep(state0, state1) {
	var interval = (state1.time - state0.time) / 1000; // convert ms to s
	if(interval) {
		state1.position = state0.position + state0.velocity * interval;
		state1.velocity = state0.velocity + state0.acceleration * interval;
	}
	return Object.assign({}, state1);
}

// transform lil box representing your phone
function renderState() {
	phone.style('transform', ''
		// + 'rotateZ('+rotation.alpha+'deg) '
		+ 'rotateX('+rotation.beta+'deg) '
		+ 'rotateY('+rotation.gamma+'deg) '
		+ 'translate3d('+0+'px,'+0+'px,'+(-z[0].position*1000)+'px)'
		);
}

// draw graph
function renderHistory() {

// draw three lines: x, dx, ddx
	var data = ['position','velocity','acceleration'].map(function(d,i) {
		return z.filter(function(dd) { return dd.time; }).map(function(dd,ii) {
			return {
				'value': dd[d],
				'time': dd.time
			}
		});
	});

var svg = d3.select('svg');

var x = d3.scaleLinear()
		.domain(d3.extent(d3.merge(data), function(d) { return d.time; }))
		.range([0,svg.node().getBoundingClientRect().width]);

var y = d3.scaleLinear()
		.domain(d3.extent(d3.merge(data), function(d) { return d.value; }))
		.range([0,svg.node().getBoundingClientRect().height]);

var line = d3.line()
		.x(function(d,i) { return x(d.time); })
		.y(function(d,i) { return y(d.value); });

var path = svg.selectAll('path')
		.data(data);

path.enter().append('path')
		.style('stroke', function(d,i) {
			var colors = {
				0: 'red', 	//position
				1: 'green',	//velocity
				2: 'blue'		//acceleration
			}
			return colors[i];
		});

path.attr('d', line);

}

</script>

https://d3js.org/d3.v4.min.js