I am developing an android application to calculate position based on Sensor’s Data
Accelerometer –> Calculate Linear Acceleration
Magnetometer + Accelerometer –> Direction of movement
The initial position will be taken from GPS (Latitude + Longitude).
Now based on Sensor’s Readings i need to calculate the new position of the Smartphone:
My Algorithm is following - (But is not calculating Accurate Position): Please help me improve it.
Note: My algorithm Code is in C# (I am sending Sensor Data to Server - Where Data is stored in the Database. I am calculating the position on Server)
All DateTime Objects have been calculated using TimeStamps - From 01-01-1970
var prevLocation = ServerHandler.getLatestPosition(IMEI); var newLocation = new ReceivedDataDTO() { LocationDataDto = new LocationDataDTO(), UsersDto = new UsersDTO(), DeviceDto = new DeviceDTO(), SensorDataDto = new SensorDataDTO() }; //First Reading if (prevLocation.Latitude == null) { //Save GPS Readings newLocation.LocationDataDto.DeviceId = ServerHandler.GetDeviceIdByIMEI(IMEI); newLocation.LocationDataDto.Latitude = Latitude; newLocation.LocationDataDto.Longitude = Longitude; newLocation.LocationDataDto.Acceleration = float.Parse(currentAcceleration); newLocation.LocationDataDto.Direction = float.Parse(currentDirection); newLocation.LocationDataDto.Speed = (float) 0.0; newLocation.LocationDataDto.ReadingDateTime = date; newLocation.DeviceDto.IMEI = IMEI; // saving to database ServerHandler.SaveReceivedData(newLocation); return; } //If Previous Position not NULL --> Calculate New Position **//Algorithm Starts HERE** var oldLatitude = Double.Parse(prevLocation.Latitude); var oldLongitude = Double.Parse(prevLocation.Longitude); var direction = Double.Parse(currentDirection); Double initialVelocity = prevLocation.Speed; //Get Current Time to calculate time Travelling - In seconds var secondsTravelling = date - tripStartTime; var t = secondsTravelling.TotalSeconds; //Calculate Distance using physice formula, s= Vi * t + 0.5 * a * t^2 // distanceTravelled = initialVelocity * timeTravelling + 0.5 * currentAcceleration * timeTravelling * timeTravelling; var distanceTravelled = initialVelocity * t + 0.5 * Double.Parse(currentAcceleration) * t * t; //Calculate the Final Velocity/ Speed of the device. // this Final Velocity is the Initil Velocity of the next reading //Physics Formula: Vf = Vi + a * t var finalvelocity = initialVelocity + Double.Parse(currentAcceleration) * t; //Convert from Degree to Radians (For Formula) oldLatitude = Math.PI * oldLatitude / 180; oldLongitude = Math.PI * oldLongitude / 180; direction = Math.PI * direction / 180.0; //Calculate the New Longitude and Latitude var newLatitude = Math.Asin(Math.Sin(oldLatitude) * Math.Cos(distanceTravelled / earthRadius) + Math.Cos(oldLatitude) * Math.Sin(distanceTravelled / earthRadius) * Math.Cos(direction)); var newLongitude = oldLongitude + Math.Atan2(Math.Sin(direction) * Math.Sin(distanceTravelled / earthRadius) * Math.Cos(oldLatitude), Math.Cos(distanceTravelled / earthRadius) - Math.Sin(oldLatitude) * Math.Sin(newLatitude)); //Convert From Radian to degree/Decimal newLatitude = 180 * newLatitude / Math.PI; newLongitude = 180 * newLongitude / Math.PI;
This is the Result I get –> Phone was not moving. As you can see speed is 27.3263111114502 So there is something wrong in calculating Speed but I don’t know what
ANSWER:
I found a solution to calculate position based on Sensor: I have posted an Answer below.
If you need any help, please leave a comment
this is The results compared to GPS ( Note: GPS is in Red)
As some of you mentioned you got the equations wrong but that is just a part of the error.
Newton - D’Alembert physics for non relativistic speeds dictates this:
// init values
double ax=0.0,ay=0.0,az=0.0; // acceleration [m/s^2] double vx=0.0,vy=0.0,vz=0.0; // velocity [m/s] double x=0.0, y=0.0, z=0.0; // position [m]
// iteration inside some timer (dt [seconds] period) … ax,ay,az = accelerometer values vx+=axdt; // update speed via integration of acceleration vy+=aydt; vz+=azdt; x+=vxdt; // update position via integration of velocity y+=vydt; z+=vzdt;
the sensor can rotate so the direction must be applied:
double gx=0.0,gy=-9.81,gz=0.0; // [edit1] background gravity in map coordinate system [m/s^2] double ax=0.0,ay=0.0,az=0.0; // acceleration [m/s^2] double vx=0.0,vy=0.0,vz=0.0; // velocity [m/s] double x=0.0, y=0.0, z=0.0; // position [m] double dev[9]; // actual device transform matrix … local coordinate system (x,y,z) <- GPS position;
// iteration inside some timer (dt [seconds] period) … dev <- compass direction ax,ay,az = accelerometer values (measured in device space) (ax,ay,az) = dev(ax,ay,az); // transform acceleration from device space to global map space without any translation to preserve vector magnitude ax-=gx; // [edit1] remove background gravity (in map coordinate system) ay-=gy; az-=gz; vx+=axdt; // update speed (in map coordinate system) vy+=aydt; vz+=azdt; x+=vxdt; // update position (in map coordinate system) y+=vydt; z+=vz*dt;
gx,gy,gz
~9.81 m/s^2
Y
gy=-9.81
0.0
Accelerometer must be checked as often as possible (second is a very long time). I recommend not to use timer period bigger than 10 ms to preserve accuracy also time to time you should override calculated position with GPS value. Compass direction can be checked less often but with proper filtration
Compass values should be filtered for some peak values. Sometimes it read bad values and also can be off by electro-magnetic polution or metal enviroment. In that case the direction can be checked by GPS during movement and some corrections can be made. For example chech GPS every minute and compare GPS direction with compass and if it is constantly of by some angle then add it or substract it.
Hate on-line waste of traffic. Yes you can log data on server (but still i think file on device will be better) but why to heck limit position functionality by internet connection ??? not to mention the delays …
[Edit 1] additional notes
Edited the code above a little. The orientation must be as precise as it can be to minimize cumulative errors.
Gyros would be better than compass (or even better use them both). Acceleration should be filtered. Some low pass filtering should be OK. After gravity removal I would limit ax,ay,az to usable values and throw away too small values. If near low speed also do full stop (if it is not a train or motion in vacuum). That should lower the drift but increase other errors so an compromise has to be found between them.
Add calibration on the fly. When filtered acceleration = 9.81 or very close to it then the device is probably stand still (unless its a flying machine). Orientation/direction can be corrected by actual gravity direction.
acceleration = 9.81
