Calculating distance using Linear acceleration android

Question

Possible Duplicate:
Android accelerometer accuracy (Inertial navigation)

I am using the following code to calculate the distance. tnew and anew are arraylists containing timestamps and accelerations respectively.

 double distance=0;
 double init_vel=0;
long time_prev=tnew.next();
   while(anew.hasNext())
   {
    float temp_acc=anew.next();
    long temp_time=tnew.next();

    interval=(temp_time-time_prev)/1000f;   //milliseconds to seconds
    double fin_vel=init_vel+(temp_acc*interval);
    distance+=(init_vel*interval)+0.5f*temp_acc*interval*interval;

    init_vel=fin_vel;
    time_prev=temp_time;
   }

Is there any logical mistake in the code? Because I am getting values much smaller than the actual length.

Output of LogCat :

--------- beginning of /dev/log/system

--------- beginning of /dev/log/main

V/PhonetapeActivity( 8842): Sensor Listener Registered

V/PhonetapeActivity( 8842): Sensor Unregistered

V/PhonetapeActivity( 8842): No. of Iterations : 49

V/PhonetapeActivity( 8842): Value of acceleration : 3.5762787E-7

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665585965

V/PhonetapeActivity( 8842): Value of acceleration : -0.15275347

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586017

V/PhonetapeActivity( 8842): Value of acceleration : 0.15585232

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586077

V/PhonetapeActivity( 8842): Value of acceleration : 1.075269

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586138

V/PhonetapeActivity( 8842): Value of acceleration : 3.6529458

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586199

V/PhonetapeActivity( 8842): Value of acceleration : 9.645137

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586257

V/PhonetapeActivity( 8842): Value of acceleration : 17.022213

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586316

V/PhonetapeActivity( 8842): Value of acceleration : 9.721476

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586376

V/PhonetapeActivity( 8842): Value of acceleration : -18.729362

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586437

V/PhonetapeActivity( 8842): Value of acceleration : -22.868385

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586497

V/PhonetapeActivity( 8842): Value of acceleration : -16.777517

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586557

V/PhonetapeActivity( 8842): Value of acceleration : -7.0492268

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586617

V/PhonetapeActivity( 8842): Value of acceleration : -3.860828

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586677

V/PhonetapeActivity( 8842): Value of acceleration : 1.7244682

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586737

V/PhonetapeActivity( 8842): Value of acceleration : 5.0734243

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586797

V/PhonetapeActivity( 8842): Value of acceleration : 6.4193974

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586857

V/PhonetapeActivity( 8842): Value of acceleration : 2.739545

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586917

V/PhonetapeActivity( 8842): Value of acceleration : 5.559997

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665586977

V/PhonetapeActivity( 8842): Value of acceleration : 4.2290807

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587037

V/PhonetapeActivity( 8842): Value of acceleration : 5.0012918

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587097

V/PhonetapeActivity( 8842): Value of acceleration : 5.9317436

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587157

V/PhonetapeActivity( 8842): Value of acceleration : 5.20226

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587217

V/PhonetapeActivity( 8842): Value of acceleration : 7.1381693

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587276

V/PhonetapeActivity( 8842): Value of acceleration : 7.6460614

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587337

V/PhonetapeActivity( 8842): Value of acceleration : 5.566694

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587396

V/PhonetapeActivity( 8842): Value of acceleration : 3.355657

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587457

V/PhonetapeActivity( 8842): Value of acceleration : 1.8876343

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587517

V/PhonetapeActivity( 8842): Value of acceleration : -0.8815446

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587577

V/PhonetapeActivity( 8842): Value of acceleration : -0.9595623

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587646

V/PhonetapeActivity( 8842): Value of acceleration : -4.233544

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587697

V/PhonetapeActivity( 8842): Value of acceleration : -1.9580669

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587765

V/PhonetapeActivity( 8842): Value of acceleration : -1.4569702

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587822

V/PhonetapeActivity( 8842): Value of acceleration : -0.6058636

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587876

V/PhonetapeActivity( 8842): Value of acceleration : -0.21207428

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587937

V/PhonetapeActivity( 8842): Value of acceleration : 0.5068469

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665587997

V/PhonetapeActivity( 8842): Value of acceleration : 5.614555

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588057

V/PhonetapeActivity( 8842): Value of acceleration : -4.5297813

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588122

V/PhonetapeActivity( 8842): Value of acceleration : -0.29250193

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588178

V/PhonetapeActivity( 8842): Value of acceleration : -2.4922757

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588237

V/PhonetapeActivity( 8842): Value of acceleration : -1.7652755

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588297

V/PhonetapeActivity( 8842): Value of acceleration : -2.3279366

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588357

V/PhonetapeActivity( 8842): Value of acceleration : -1.8127642

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588419

V/PhonetapeActivity( 8842): Value of acceleration : -1.956768

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588477

V/PhonetapeActivity( 8842): Value of acceleration : -0.8337221

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588537

V/PhonetapeActivity( 8842): Value of acceleration : -0.24841261

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588601

V/PhonetapeActivity( 8842): Value of acceleration : 0.23997736

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588657

V/PhonetapeActivity( 8842): Value of acceleration : 0.14441395

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588723

V/PhonetapeActivity( 8842): Value of acceleration : 0.23150349

V/PhonetapeActivity( 8842): Value of timestamp(milli) : 1350665588777

V/PhonetapeActivity( 8842):  1st while loop ended

V/PhonetapeActivity( 8842): 2nd while loop ended

V/PhonetapeActivity( 8842): Avg value : 0.4006781578063965

V/PhonetapeActivity( 8842): Max Value : 17.022213

V/PhonetapeActivity( 8842): Min Value : -22.868385

V/PhonetapeActivity( 8842): Standard Deviation : -0.0031174493

V/PhonetapeActivity( 8842): 3rd while loop started

V/PhonetapeActivity( 8842): startpos=3 endpos=8

V/PhonetapeActivity( 8842): acceleration=0.1558523178100586 interval=0.061000000685453415

V/PhonetapeActivity( 8842): distance=5.799264876044276E-4

V/PhonetapeActivity( 8842): next init velocity=0.009506991493243078

V/PhonetapeActivity( 8842): acceleration=1.0752689838409424 interval=0.061000000685453415

V/PhonetapeActivity( 8842): distance=0.005160928954000712

V/PhonetapeActivity( 8842): next init velocity=0.07509840024458736

V/PhonetapeActivity( 8842): acceleration=3.6529457569122314 interval=0.057999998331069946

V/PhonetapeActivity( 8842): distance=0.021805144861910285

V/PhonetapeActivity( 8842): next init velocity=0.2869692480489858

V/PhonetapeActivity( 8842): acceleration=9.645136833190918 interval=0.05900000035762787

V/PhonetapeActivity( 8842): distance=0.07231105232279186

V/PhonetapeActivity( 8842): next init velocity=0.8560323246566197

V/PhonetapeActivity( 8842): acceleration=17.022212982177734 interval=0.05999999865889549

V/PhonetapeActivity( 8842): distance=0.18495295465057213

V/PhonetapeActivity( 8842): next init velocity=1.8773650807587172

V/PhonetapeActivity( 8842): 3rd while loop ended

V/PhonetapeActivity( 8842): final distance=0.18495295465057213

V/PhonetapeActivity( 8842): values of acceleration, timestamp, distance, start_time and calibrating reset

If you observe the logcat, first it iterates through 49 values of acceleration and their respective time stamps in milliseconds. Then there is a avg, sum, max, min etc.
Then if you see there is a startpos=3 and endpos=8. This is the iteration number range, I am using to calculate the distance .i.e I am using the values of acceleration and timestamp only from iteration 3 to 8.
This is because, I detect the start of distance calculation from a rise in acceleration to a sudden change in the opposite direction. You can see that the values from 3-8 fit into the logic. From 3 there is a considerable rise in acceleration and after 8 there is a sudden decrease.

Solution 1

Accelerometers are very precise but bad at dead-reckoning. Gyroscopes are good at that but they "drift" over time. "Sensor-fusion" is the process of using accel/gyro data in tandem to correct one's deficiency using the other. AFAIR, "sensor-fusion" is NOT enabled on Galaxy Ace. LINEAR_ACCELERATION is nothing but ACCELEROMETER - gravity component. On devices without gyroscope, fusion is not possible by definition it requires accel+gyro.

The accelerometer data contains the gravity component of 9.8. This is filtered out by simply determining the difference between 2 consecutive samples of accelerometer data. This gives us the LINEAR_ACCELERATION data.

Check this out for actual internal code :
frameworks/base/services/sensorservice/LinearAccelerationSensor.cpp
The function LinearAccelerationSensor::process() is of interest in the above file.

Also rudimentary operations like filtering/averaging that the above link and video talk about, need to performed on the accel data obtained in your app. The processed values obtained in this manner will be better(though not as good as the ones that would have been obtaioned had sensor fusion been present on your device) than the raw values. These can then be used to calculate the velocity and position more accurately.

That said, 16 samples a second (@poll-rate=60ms) is relatively inaccurate in itself. You might want to try registering the sensorEventListner using SENSOR_DELAY_FASTEST to see the maximum number of samples that you can obtain on you device.

Also note that the accelerometers on phones are clamped to certain MAX sensitivity (usually -/+ 2/4/8 G range). While normal walking/running might operate under these ranges, a sudden impulse in acceleration (for example on a bike) will definitely be clamped to the MAX and you will lose sync in dead-reckoning. This can be checked by noting the number of samples that are very close to the -/+MAX. Lot of samples at -/+MAX imply that you would have most certainly lost sync with the actual position.

Solution 2

The first thing I would check is your time interval. I am not certain it is being converted properly. The timestamp is listed as:

public long timestamp The time in nanosecond at which the event happened

And so in the documentation we see the conversion is done by dividing by 1 billion instead of 1 thousand.

float dT = (event.timestamp - timestamp) / 1000000000.0f;
timestamp = event.timestamp;

That said I think that change will just shrink the values but to calculate real world distance you need to watch your units.

Next, when reading about these things people are always going on about how you need to know your initial position for each reading to make any sense with respect to real world linear measurements. I do not see you tracking your previous acceleration which will make each following measurement's integration based on instantaneous acceleration, or the change in acceleration, instead of full acceleration.

Try something like this:

final int X = 0;
double distance[];
double init_vel[];
double total_Accel[];

void dblIntegrate(SensorEvent event){
    double data[] = new double[3];
    for(int i = 0; i < event.lenght; i++){
        data[i] = (double)event[i];
        total_Accel[i] += data[i];
        vel[i] = init_vel[i] + (total_Accel[i] * dt);
        init_vel[i] = vel[i];

        ....rinse and repeate to get distance
        (not using the accel data of course)
    }
}

I realize you understand this but for anyone else is reading this => remember you can't have the counting vars total_Accel or init_vel re-instantiated each time you call dblIntegrate().

If you are doing it right you should see total_Accel go from zero to some max value then back to zero every time you move the device. This means you are adding equal parts positive and negative acceleration each time the device moves in any direction.

I believe this is the property of acceleration that is the hardest to understand properly because for the device to go from resting state to resting state your total_acceleration will go from zero to a max pos/neg value back to zero to the oppposite max value and then back to zero.

For example, if I move a phone resting on its back on a table with the bottom facing my chest to the right for one meter you will get something like this:

total_Accel = 0.0 (0 Meters)

total_Accel = 0.5

total_Accel = 1.0

total_Accel = 1.5 (approx .25 Meters)

total_Accel = 1.0

total_Accel = 0.5

total_Accel = 0.0 (if accel is perfectly distributed, .5 Meters)

total_Accel = -0.5

total_Accel = -1.0

total_Accel = -1.5 (approx .75 Meters)

total_Accel = -1.0

total_Accel = -0.5

total_Accel = 0.0 (1 Meter)

In the example you can start to see why simply doubly integrating the change in acceleration isn't going to give you the real change in velocity/displacement.

I hope so anyway because writing this took a lot longer than I had thought it would! :)

Solution 3

This is an answer to your question:

why I need to track my previous acceleration. onSensorChanged(MotionEvent event){} is called when there is a change in acceleration. It provides the new acceleration and not the change in acceleration.

The short answer is, integrating the reading w/o including the initial condition (your total previous acceleration) you will end up with a value that does not include all the information. Plus, the longer you go the further your value gets from the real value because you are losing more and more information.

I do not think you want an explanation of acceleration, velocity and displacement (and this is not the place for that) so maybe I can show it by expanding the example I included above.

A phone resting on its back on a table with the bottom facing my chest is moved to the right for an arbitrary distance and stops. If you look at your data you will get something like this. Of course the actual numbers will vary widely but their signs will be the same and the proportions will be kind of the same but will start smaller than they peak like you would expect (unless you fired it out of a gun at a wall or whatever).:

Time...........Accel Reading...........Total Accel........Total Velocity

00ms.............. 0.0......................0.0.......................0.000..

10ms.............. 0.5......................0.5.......................0.005 m/s..

20ms.............. 0.5......................1.0.......................0.015 m/s..

30ms............. 0.5......................1.5.......................0.030 m/s..

40ms............. -0.5......................1.0.......................0.040 m/s..

50ms............. -0.5......................0.5.......................0.045 m/s..

60ms............. -0.5......................0.0.......................0.045 m/s..

70ms............. -0.5.....................-0.5.......................0.040 m/s..

80ms............. -0.5.....................-1.0.......................0.030 m/s..

90ms............. -0.5.....................-1.5.......................0.015 m/s..

100ms............. 0.5.....................-1.0.......................0.005 m/s..

110ms............. 0.5.....................-0.5.......................0.000 m/s..

120ms............. 0.5......................0.0.......................0.000 m/s..

You can see that if you do not track total acceleration your total velocity would be the column marked Total Accel above. That would mean your phone would be moving in the positive direction of the x-axis the whole time but your velocity would be negative (moving backwards) the last half of the movement.

I hope this proves my case even if it does not explain the mechanics behind acceleration or accelerometers.

If you wanted to look-up how the accelerometer works they are MEMS type sensors and I think they use a suspended cantilever beam with a weighted end to measure the force of acceleration.

Comments

[Ashwin]

I have not yet finished reading the post fully. But about the timestamp, I used System.currentMillis(). I am getting a time interval of 60ms as specified in the android documentation for delay_sensor_ui.

[Ashwin]

I don't understand why I need to track my previous acceleration. onSensorChanged(MotionEvent event){} is called when there is a change in acceleration. It provides the new acceleration and not the change in acceleration. So all I need is the acceleration between x ms and x + 60ms and the velocity at x(i.t initial velocity after every 60 ms)

[BluMo.us]

Sorry about the timeStamp info. I have been sloging through this stuff for the last month or so and I think I assumed all the sensors were reporting time in the same unit. I should have double checked my facts before giving a bad answer. I did double check the SensorEvent event.timestamp doc and it is saying it is in nanoseconds but this is for API Level 3 so maybe that is where the confusion is coming from. I apologize I can't be more definitive but hopefully someone else can weigh in.

[BluMo.us]

I have to log off but I'll get back to you on your second question tomorrow. Basically it has to do with the way the sensor works. This is the reason why RC airplane pilots say you can't use the accelerometer alone to track position because acceleration is only useful if you know what has happened since it started moving from a resting state. If you haven't already maybe you want to google a linear acceleration tutorial. Until you really wrap your mind around acceleration none of this will make sense.

[Ashwin]

I agree than you need to have knowledge of the prevous state or initial state to calculate position. But I am starting from REST, so initial velocity is zero. What else do I need? I have taken care of all the parameters, I think.

[Ashwin]

thanks for posting the comments as an answer. But you said that sensor fusion was not enabled on galaxy ACE. But LINEAR_ACCELERATION works in my phone(ACE). LINEAR_ACCELERATION is a result of sensor fusion. It uses two or more sensors to give the linear acceleration.

[TheCodeArtist]

LINEAR_ACCELERATION is nothing but ACCELEROMETER - gravity component. On devices without gyroscope, fusion is not possible as by definition it requires accel+gyro.

[Ashwin]

please correct me if I am wrong. To find out the gravity component, you need a gyro. It gives the orientation of the phone and accordingly the gravity component is removed

[TheCodeArtist]

No, gyro is not absolutely essential for that. Updated answer to describe internals of LINEAR_ACCELERATION sensor. i.e. what is done to accelerometer data before reporting it as linear-acceleration.

[BluMo.us]

I struggled with this for a long time and it wasn't until I started tracking total accumulated acceleration that it started working properly. If you would like I can post some of my output data.

[BluMo.us]

Are you outputing your data, each measurement, to a csv file? It would be a big help if I could see an output of all your variables (sensor reading, velocity, dT, & displacement) before and after any filtering. I have spent many hours looking at mine :) and I might see something that will help.

[Ashwin]

yeah sure. just give me some time.

[Ashwin]

What do you mean by "clamped to the MAX and lose sync in dead reckoning"? Will it start displaying random data once max value has reached?

[BluMo.us]

:) you are on! I realized yesterday we are living in opposite time zones and I was thinking I checked this too late.

[Ashwin]

which country are you from? your profile doesn't say much! Anyway, is it okay If I paste the output of my log cat in the question itself?

[BluMo.us]

FYI: Clamped to the max from above is just the max value the sensor can read. So if it maxes out at 2G it will read 2G even if it is accelerating at 10G.

[BluMo.us]

I'm in the US, in Texas. Sure anywhere is OK. Put it in a code block if the formatting is ugly. :)

[Ashwin]

posted the logcat in the question.

[Ashwin]

oh and I forgot to mention - I have not applied and filter(I want to). And the data is raw data from accelerometer. I get the same distance and similar data even when using linear_acceleration.

[BluMo.us]

I have to step away but will try to post w/in 2 hours. Sorry, B

[BluMo.us]

You really need to increase your sampling speed. You are losing a lot of data. one interval goes from 9.7 to -17.7. I do not know how you can have nearly 30Gs of force in such a short time but you should see it somewhere. But my biggest concern is why your values are so large. Are you manipulating them before you send them to the log? If you aren't there is possibly something wrong with your sensor or the software reading from it because when I am shaking my phone I rarely see values above 3-3.5G. That said, I will work with the data and put into another answer later (6-7 hours).

[BluMo.us]

One last thing, this is going to take a lot of time. You will be testing and testing again because understanding the sensor output is counter-intuitive so you really need to add a FileWriter to capture the data in a csv file. I'll add the code into the answer I'll add later. Please do yourself a favor and use this tool because there is nothing as helpful as seeing a graph of your values after you test when you are debugging.

[TheCodeArtist]

Lets say you accelerate very quickly for a brief moment to the order of +3g. But the accelerometer is configured to the range of -/+2g, his means that it will report +2g(whereas you were actually at +3g). So you actual position and calculated position will differ and there si non real way to correct this. Just possible to detect it; coz if you get a lot of values at the MAX limit, then chances of you having gone over it are more. Then again such "large" acceleration is not really common when the device is in hand and the user is on foot. But, nevertheless you need to be aware of this pitfall.

[Ashwin]

Th difference between the the interval 9.7 and -17.7 is 3G of force. And I start and end with a sudden jerk. That is the reason for high acceleration. I have kept the sampling rate low so that you understand easily. I have also tried with keeping the interval to SENSOR_DELAY_FASTEST. I get similar results to to the one you see now.

[BluMo.us]

Here is one half second of data from my sensor reading (one half of the movement forward): 0.991026819 1.181484699 0.553365707 0.344187886 0.281776369 0.71893096 0.184576452 0.422301173 -0.188359618 -0.216263115 -0.412414134 -0.374867082 -0.048857689 -0.168574631 -0.378953457 -0.148276091 -0.375006378 -0.500817239 -0.71646446 -1.089801431 -1.36315012 -1.086476803 -0.640532315 -0.35008955 -0.394858718 These are raw readings. Maybe every phone is different but I have never seen anything that says so. I do not think I can be of any help since we are working with totally different readings. gl.

[Ashwin]

So is everything alright with the equations?

[erik]

hey guys, chiming in late here.. but could someone explain the last part where he says "rinse and repeat with out accelerometer data"?

[Gevaria Purva]

May I have some code implementation please ?