Technical:Accelerometer Fundamentals - Revision history

Kempelen: Category: -Hardware, (It's in sub 'Accelerometer')

2008-09-15T20:48:36Z

Category: -Hardware, (It's in sub 'Accelerometer')

C.M: Fixed spelling errors

2007-11-21T13:25:50Z

Fixed spelling errors

Speedevil: /* Results */ alter

2007-09-05T15:57:09Z

‎Results: alter

Speedevil: /* Results */ tidy

2007-08-31T15:00:03Z

‎Results: tidy

Speedevil: minor rewrite

2007-08-31T14:54:03Z

minor rewrite

Speedevil: merge in comments

2007-08-31T14:45:08Z

merge in comments

PTT: added link to magnetometer/compass page

2007-08-15T03:15:45Z

added link to magnetometer/compass page

PTT: /* What it can't do. */ added magnetometer reference

2007-08-14T23:44:57Z

‎What it can't do.: added magnetometer reference

Speedevil: /* Results */ add cases

2007-08-14T12:47:06Z

‎Results: add cases

Dion: Fixed definition of Acceleration.

2007-07-31T11:47:44Z

Fixed definition of Acceleration.

← Older revision		Revision as of 20:48, 15 September 2008
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	* [http://www.memsic.com/ Memsic accelerometers]*		* [http://www.memsic.com/ Memsic accelerometers]*

−	~~[[Category:Hardware]]~~
	[[Category:Accelerometer]]		[[Category:Accelerometer]]

@@ Line 18: / Line 18: @@
 ==What one three-axis accelerometer can do==
-*If the orientation of the phone is held constant - for example, clamped into a car holder, then you can make pretty good guesses about the correlation of aceleration and position.
+*If the orientation of the phone is held constant - for example, clamped into a car holder, then you can make pretty good guesses about the correlation of acceleration and position.
 **In normal driving, any lateral accelerations mean that the car is turning at a rate which can be computed if the speed of the car is known.
 **Accelerations in line with the course mean that the car is slowing up or down, and any vertical accelerations mean that there is a bump, or a rise or fall in the road.
@@ Line 31: / Line 31: @@
 ===What can be done with absolutely perfect devices?===
-Imagine two three axis accellerometers rigidly placed on each end of an arrow.
+Imagine two three axis accelerometers rigidly placed on each end of an arrow.
 How much information do you get out of these?
@@ Line 43: / Line 43: @@
 *What happens when we vary the orientation?
-**You can subtract any common accelleration that's measured by both sensors - this does not change the orientation.
+**You can subtract any common acceleration that's measured by both sensors - this does not change the orientation.
 *Remembering that we can skew the sensors against each other, and this has no effect, let's specify that they are oriented with X and Y lined up, and Z pointing in the direction of the arrow.
 *This reveals a problem.
-*Spin the arrow on its axis, and none of the accelererometers measure anything at all - they do not move, so they do not accelerate.
+*Spin the arrow on its axis, and none of the accelerometers measure anything at all - they do not move, so they do not accelerate.
 **(you can't get round this by moving them off-axis, as you can draw an imaginary arrow between the two accelerometers which has the same problem)
@@ Line 65: / Line 65: @@
 ===Numbers===
 I'm assuming specs similar to the ADXL330 - simplified a little.
-(The acceleometer mentioned on the mailing list as being included in GTA02 is significantly worse than this - some 20 times more noise)
+(The accelerometer mentioned on the mailing list as being included in GTA02 is significantly worse than this - some 20 times more noise)
 Assumptions:
@@ Line 102: / Line 102: @@
 *It will probably not be good enough for keeping a map aligned when you turn in place.
 **It may be adequate for some games, but again, the movements have to be sharp, it will false signal as you decrease the wanted signal.
-**The difference in accelleration when the device is swung like a baseball bat is fairly pronounced, and the speed of the swing can be accurately measured. Its exact path however cannot.
+**The difference in acceleration when the device is swung like a baseball bat is fairly pronounced, and the speed of the swing can be accurately measured. Its exact path however cannot.
 When in motion:
 *Improving the positioning of the GPS, it may give enough information to resolve sharp turns.
 *It can fill in _short_ - 3-5s gaps in GPS coverage, if the orientation of the phone is known.
-**In the best case - phone on its back, accelleration vector down, and turning in a vehicle, you may be able to tell sharp turns.
+**In the best case - phone on its back, acceleration vector down, and turning in a vehicle, you may be able to tell sharp turns.
 ***This is only useful if the phone is handheld, or not fixed in position to the vehicle, or if the vehicle does not go where it points.

@@ Line 112: / Line 112: @@
 In any condition:
 *Eliminating impossible points from the GPS data, if the maximum possible distance moved by the accelerometer over a time is under the difference between two GPS readings, then the GPS must be incorrect.
-*Recording taps on the case - the output will be broadly an intensity of tap, and the relative distance between the accelerometers and the tap.
+*Recording taps on the device - the output will be broadly an intensity of tap, and the relative distance between the accelerometers and the tap.
 And this is completely neglecting the temperature sensitivity.

@@ Line 91: / Line 91: @@
 ==Results==
 What does this mean though?
-Because the differential accelerations are so small, and comparable to the noise floor for gentle turning and twisting, there are basically two ways that they can be useful.
 When more or less stationary:
@@ Line 102: / Line 105: @@
 When in motion:
-*It may be adequate to improve positioning of the GPS, when sharply going round corners, or doing high-G aerobatics.
+*Improving the positioning of the GPS, it may give enough information to resolve sharp turns.
 *It can fill in _short_ - 3-5s gaps in GPS coverage, if the orientation of the phone is known.
 **In the best case - phone on its back, accelleration vector down, and turning in a vehicle, you may be able to tell sharp turns.

@@ Line 29: / Line 29: @@
 ==What two three axis accelerometers can do==
-==What can be done with absolutely perfect devices?==
+===What can be done with absolutely perfect devices?===
 Imagine two three axis accellerometers rigidly placed on each end of an arrow.
@@ Line 37: / Line 37: @@
 A few moments thought should reveal that the orientation of the sensors does not matter. You can resolve the three signals into one direction and size.
 This does not change however the devices are oriented - there is no benefit in for example skewing one 45 degrees.
-===In Space!===
+====Neglecting gravity====
 Considering the case in deep-space - the maths are simpler.
-(not a common use-case, but simpler to analyse)
+Holding the orientation steady, you can do perfect inertial navigation, and determine exactly where you are at all times.
-Holding the orientation steady, you can do perfect inertial navigation, and determine exactly where you are at all times. (in a flat space-time, but meh)
 *What happens when we vary the orientation?
@@ Line 53: / Line 52: @@
 *Spin the arrow around its centre (it must spin around its centre logically if you've subtracted the overall acceleration) you can pick up pitch and yaw.
-===With Gravity===
+====With Gravity====
 Now, what if we add gravity in?
@@ Line 66: / Line 65: @@
 ===Numbers===
 I'm assuming specs similar to the ADXL330 - simplified a little.
 Assumptions:
@@ Line 76: / Line 76: @@
 For interactive use.
-High-pass filtering the accelerometer with a bandwidth of 10Hz - you can't filter it much more than that or you lose important 'wobbles', because you need to integrate them to come up with a position - leads to a noise floor of 300uG/sqrt(Hz) *sqrt(10Hz) = 1mG. (RMS (No, not that RMS))
+High-pass filtering the accelerometer with a bandwidth of 10Hz - you can't filter it much more than that or you lose important 'wobbles', because you need to integrate them to come up with a position - leads to a noise floor of 300uG/sqrt(Hz) *sqrt(10Hz) = 1mG. (RMS)
 Neglecting roll for the moment.
@@ Line 89: / Line 89: @@
 Well - the velocity reads out as 6cm/s^2 wrong, which means that the position is now out by 3cm, or 10 degrees.
-===Results===
+==Results==
 What does this mean though?
 Because the differential accelerations are so small, and comparable to the noise floor for gentle turning and twisting, there are basically two ways that they can be useful.
@@ Line 113: / Line 113: @@
 And this is completely neglecting the temperature sensitivity.
-===What it can't do.===
+==What it can't do.==
 Inertial navigation or rotation over more than several seconds. For big movements the GPS could be used, for smaller movements in the Z direction (> 25 cm) a pressure sensor could be added, see [[Wish List - Hardware - Atmospheric]], and for inertial rotation a magnetometer (digital compass) can be used, see [[Wishlist - Hardware: Digital compass]].
-===References===
+=References=
 * [http://www.freescale.com/webapp/sps/site/overview.jsp?nodeId=0112690EFA4082&tid=tshbMERC Freescale products]
 * [http://www.freescale.com/files/sensors/doc/app_note/AN3107.pdf Measuring Tilt with low-g accelerometers (Freescale doc)]*

@@ Line 19: / Line 19: @@
 *If the orientation of the phone is held constant - for example, clamped into a car holder, then you can make pretty good guesses about the correlation of aceleration and position.
-**In normal driving, the ground track of the car is some function of the position of the steering wheel. Any lateral accelerations against the current known course mean that the steering wheel has been applied, and the car is turning at a rate which can be computed by calculating it with the cars known speed.
+**In normal driving, any lateral accelerations mean that the car is turning at a rate which can be computed if the speed of the car is known.
-**Accelerations in line with the course mean that the car is slowing up or down, and any vertical accelerations mean that the car is going up or down a hill.
+**Accelerations in line with the course mean that the car is slowing up or down, and any vertical accelerations mean that the car is going over a bump on the road.
-**Errors build up, but it's not bad for short periods.
+**Errors build up, but it's not bad for short periods, 1cm/s^2 of error, with a car going in a straight line at 20m/s, takes a bit over a minute to move from a true direction of northeast - say, to a false direction of northnortheast. (the position is off after this period by a hundred metres or two)
-**1cm/s^2 of error, with a car going in a straight line at 20m/s, takes a bit over a minute to move from a true direction of northeast - say, to a false direction of northnortheast. (the position is off after this period by a hundred metres or two)
 *When hand-held, and stationary, the phone has quite accurate (better than a degree) knowledge of where 'down' is.
@@ Line 30: / Line 29: @@
 ==What two three axis accelerometers can do==
-===What can be done with absolutely perfect devices?===
+*Better detection of fast rotations, especially around the Z axis (if the device isn't held vertically with the sensors above each other)
 Imagine two three axis accellerometers rigidly placed on each end of an arrow.
@@ Line 121: / Line 123: @@
 * [http://www.analog.com/en/cat/0,2878,764,00.html Analog Devices  MEMS and Sensors]
-* [http://www.analog.com/en/prod/0,2877,ADXL330,00.html Analog Devices  ADXL330] ([http://www.wiili.org/index.php/Motion_analysis the sensor used in the Wiimote])
+* [http://www.analog.com/en/prod/0,2877,ADXL330,00.html Analog Devices  ADXL330] ([http://www.wiili.org/index.php/Motion_analysis the sensor used in the Wiimote (only one sensor)])
 * [http://www.st.com/stonline/products/literature/ds/12094/lis3lv02dl.pdf ST Inertial Sensor]*

@@ Line 2: / Line 2: @@
 An accelerometer simply measures acceleration, either due to motion or due to gravity.
-Acceleration is measured in 'G' - the acceleration of an object falling near earths surface.
+Acceleration is measured in m/s<sup>2</sup>.
-G is an acceleration of around 9.8m/s<sup>2</sup> (or 32ft/s<sup>2</sup>).
+The acceleration at near the surface of the earth is around 9.8m/s<sup>2</sup> (or 32ft/s<sup>2</sup>), which can be an unwieldy number, so 9.8m/s<sup>2</sup>  is often labeled 1G.
 This means that if you drop an object from some height (assuming a vacuum), after 1 second it will be falling at 9.8m/s, a speed of 19.6m/s after 2 seconds, and so on.