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Add exact distance to GPS coordinates

I want to be able to add an exact distance to some GPS coordinates.
I have a longitude and a latitude and I want to add a distance, let's say 30 meters.
I found below formula but when I test it, it does not seem to be that accurate because the resulting long and lat are 37m away from the beginning coords.
public static Coordinates addDistanceToCoordinates(String lat, String lon, double distance) {
Double latitude = Double.valueOf(lat);
Double longitude = Double.valueOf(lon);
double lat0 = cos(Math.PI / 180.0 * latitude);
double x = longitude + (180/Math.PI)*(distance/6378137)/cos(lat0);
double y = latitude + (180/Math.PI)*(distance/6378137);
return Coordinates.builder().lon(x).lat(y).build();
}

If you have a center (x,y) and you move on the x axis by 30 meters and on the y axis by another 30 meters your distance from the center won't be 30.
It will be Math.sqrt( Math.pow(x, 2) + Math.pow(y, 2) );.
Specifically, there are an infinite number of points that are 30 meters distant from the center (or your initial coordinates).
If you want to move in only one direction, then you can simply add/subtract 30 meters in either of your axis.
As you already did:
double x = longitude + (180/Math.PI)*(distance/6378137)/cos(lat0);
or
double y = latitude + (180/Math.PI)*(distance/6378137);
but not both...
You are still better off by using angles in your calculations, which will turn handy when you move on both axis.
By knowing which direction you are headed to, for example 50° from the x axis,
double a = Math.toRadians(50); // degrees
double x = longitude + (180/Math.PI) * (30 / 6378137)/cos(lat0) * Math.cos(a);
double y = latitude + (180/Math.PI) * (30 / 6378137) * Math.sin(a);
Coming back to your question, if you want to move on the x axis and the y axis by the same distance and end up exactly 30 meters away from the center, then your angle will be double a = Math.toRadians(45); (if you head North-East) *
In fact you will obtain for both (30 / 6378137) * Math.cos(a) and (30 / 6378137) * Math.sin(a) a result of x1 = y1 = 3.325924707417923e-06.
If you then apply Pythagoras
double finalDistance = Math.sqrt(Math.pow(x1, 2) + Math.pow(y1, 2)) * 6378137;
you will find finalDistance to be 30 meters from your initial coordinates.
*
The correct calculation would be Math.toRadians(45 * (2 * n - 1)); | where n = [1, 2, 3, 4]

Your code adds 30 meters north and 30 meters east, resulting in 42.4 meters northeast.
The calculation is assuming earth as a sphere instead of an ellipsoid, but that's mostly OK, can make a difference of max. 0.2 percent. It uses the biggest earth diameter (equator - equator) instead of some mean value, which will result in points too close to the starting point most of the time, but agian, taht can give an error of maybe 0.2 percent.
The calculation assumes the lat/lon grid to be rectangular, which is OK as long as the distances are short and you stay away from north or south pole.
So, all of this doesn't explain the 20 percent error you are reporting. The problem must be outside of the code you showed us.
The most suspicious remaining aspect is the string conversion. You'll need at least 5 decimal places for lat / lon degree values to get a 1 meter resolution.
Or maybe the tool that told you about the 37 meters isn't correct or somehow incompatible with the data...

Calculating speed from set of longitude and latitudes values obtained in one minute?

I need to calculate speed after each 10 seconds or less (currently i am using fused location api to get the location after each 10 seconds). The problem is that the equipment is too slow and sometimes it gives the distance covers equal to zero.
I have tried using Location.distanceBetween() but it also produces zeros even when the equipment is moving. I have tried to calculate distance by a formula but sometimes distance is too small that it gives zero.
Now i want to calculate average speed. I want to save the points obtained in 1 minute (6 lat long values). And then after each 10 seconds, i want to calculate average speed between them. Thus after each 10 seconds I will add one points at the end and remove one point from the start. That will remove the possibility of zero.
Now is there any formula that can calculate speed or distance from set of lat long values or any better approach will be highly appreciated.

You can calculate distance between two point, that are close enough, using simple geometry
deltaLngMeters = R * cos(latitude) * deltaLongitudeRadians;
deltaLatMeters = R * deltaLatitudeRadians;
whereas deltas are in radians, deltaLatitudeRadians = deltaLatitudeDegrees * pi / 180
Hence distance = sqrt(deltaLngMeters ^2 + deltaLatMeters ^ 2).
To sum up
function distance(point1, point2) {
var degToRad = Math.PI / 180;
return R * degToRad * Math.sqrt(Math.pow(Math.cos(point1.lat * degToRad ) * (point1.lng - point2.lng) , 2) + Math.pow(point1.lat - point2.lat, 2));
}
If you have array of six points, you can calculate average speed.
points = [{lat: .., lng: ..}, ... ]; // 6 points
distancesSum = 0;
for(i = 0; i < distances.length - 1; i++) {
distancesSum += distance(points[i], points[i + 1]);
}
return (distancesSum / (points.length - 1));
Yes, R is for the Earth radius, R = 6371000;// meters

You can use multi threading(Thread.sleep()) to calculate a formula repeatedly for every 10 seconds. You can verify it here https://beginnersbook.com/2013/03/multithreading-in-java/.

For small distances(hope the device won't move at speeds above 1 km/s), earth's surface can be treated as a plane. Then the latitude and longitude will be the coordinates of the device on the Cartesian plane attached to earth. Hence you can calculate the distance by this formula:
√(delta(longitude)^2 + delta(latitude)^2)
delta: difference

How to use Math.PI and Math.pow [duplicate]

This question already has an answer here:
Division between integers in Java
(1 answer)
Closed 8 years ago.
I am doing an assignment for my first JAVA programming. So far it has been going well but I am stuck at the last part with using math functions.
double radius;
double diameter;
double volume;
System.out.print("Enter a diameter of a sphere: ");
diameter = keyboard.nextDouble();
radius = diameter / 2;
volume = (4 / 3) * Math.PI * Math.pow(radius, 3.0);
System.out.print("Volume of the sphere is " + volume + ".");
I am trying to use the formula for finding a volume of a sphere using diameter input variable. But I keep getting just the PI as an output.
This is what I am supposed to do.
Add a line that prompts the user to enter the diameter of a sphere.
Read in and store the number into a variable called diameter (you will need to
declare any variables that you use).
The diameter is twice as long as the radius, so calculate and store the radius in an
appropriately named variable.
The formula for the volume of a sphere is
V = 4/3 * PI * radius^3
Convert the formula to Java and add a line which calculates and stores the value
of volume in an appropriately named variable. Use Math.PI for PI and Math.pow
to cube the radius.
Print your results to the screen with an appropriate message.
What am I doing wrong ? Also how do I make it so the volume displays with E notation?

I think you might be getting an incorrect ans because of 4/3 in Integer Math give 1 and not 1.33 Try changing you code to what is give below. I tried and worked fine for me.
radius = diameter / 2.0d;
volume = (4.0d / 3.0d) * Math.PI * Math.pow(radius, 3);

Calculating distance between two points represented by lat,long upto 15 feet accuracy

I have converted the formula into Java provided here. But accuracy is a problem. We are using GPS coordinates.
We are using iPhone provided GPS location that is upto 10 decimal point accuracy.
/*
* Latitude and Longitude are in Degree
* Unit Of Measure : 1 = Feet,2 = Kilometer,3 = Miles
*/
//TODO 3 Change Unit of Measure and DISTANCE_IN_FEET constants to Enum
public static Double calculateDistance(double latitudeA,double longitudeA,double latitudeB,double longitudeB,short unitOfMeasure){
Double distance;
distance = DISTANCE_IN_FEET *
Math.acos(
Math.cos(Math.toRadians(latitudeA)) * Math.cos(Math.toRadians(latitudeB))
*
Math.cos(Math.toRadians(longitudeB) - Math.toRadians(longitudeA))
+
Math.sin(Math.toRadians(latitudeA))
*
Math.sin(Math.toRadians(latitudeB))
);
return distance;
}
FYI : public static final int DISTANCE_IN_FEET = 20924640;
And then I use Math.round(distance); to convert to long.
For actual 25 feet, I am getting 7 feet output.

You need the haversine formula.
Here's my java implementation:
/**
* Calculates the distance in km between two lat/long points
* using the haversine formula
*/
public static double haversine(
double lat1, double lng1, double lat2, double lng2) {
int r = 6371; // average radius of the earth in km
double dLat = Math.toRadians(lat2 - lat1);
double dLon = Math.toRadians(lng2 - lng1);
double a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
Math.cos(Math.toRadians(lat1)) * Math.cos(Math.toRadians(lat2))
* Math.sin(dLon / 2) * Math.sin(dLon / 2);
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
double d = r * c;
return d;
}

According to Wikipedia, 10 feet is close to the limit of what you can expect from normal GPS accuracy. (And that assumes you are getting a good GPS signal.) This post on http://gis.stackexchange.com provides more detailed numbers. It basically says that 3 meter horizontal resolution is the best you are likely to get with an ordinary GPS receiver.
So if you are comparing locations provided by two different (ordinary) receivers with best case ( 3 meter / 10 feet ) resolution on each, you are still not going to be able to tell reliably if one receiver is within 10 feet of the other.
(Note your 10 digits of "precision" may well be illusory. The real issue is how accurate the locations are; i.e. how big the error bars are ... on two different devices.)
So in that case what other alternatives I have?
The linked articles mention WAAS and Carrier Phase GPS (CPGPS). Another option is WPS.

SQlite Getting nearest locations (with latitude and longitude)

I have data with latitude and longitude stored in my SQLite database, and I want to get the nearest locations to the parameters I put in (ex. My current location - lat/lng, etc.).
I know that this is possible in MySQL, and I've done quite some research that SQLite needs a custom external function for the Haversine formula (calculating distance on a sphere), but I haven't found anything that is written in Java and works.
Also, if I want to add custom functions, I need the org.sqlite .jar (for org.sqlite.Function), and that adds unnecessary size to the app.
The other side of this is, I need the Order by function from SQL, because displaying the distance alone isn't that much of a problem - I already did it in my custom SimpleCursorAdapter, but I can't sort the data, because I don't have the distance column in my database. That would mean updating the database every time the location changes and that's a waste of battery and performance. So if someone has any idea on sorting the cursor with a column that's not in the database, I'd be grateful too!
I know there are tons of Android apps out there that use this function, but can someone please explain the magic.
By the way, I found this alternative: Query to get records based on Radius in SQLite?
It's suggesting to make 4 new columns for cos and sin values of lat and lng, but is there any other, not so redundant way?

1) At first filter your SQLite data with a good approximation and decrease amount of data that you need to evaluate in your java code. Use the following procedure for this purpose:
To have a deterministic threshold and more accurate filter on data, It is better to calculate 4 locations that are in radius meter of the north, west, east and south of your central point in your java code and then check easily by less than and more than SQL operators (>, <) to determine if your points in database are in that rectangle or not.
The method calculateDerivedPosition(...) calculates those points for you (p1, p2, p3, p4 in picture).
/**
* Calculates the end-point from a given source at a given range (meters)
* and bearing (degrees). This methods uses simple geometry equations to
* calculate the end-point.
*
* #param point
* Point of origin
* #param range
* Range in meters
* #param bearing
* Bearing in degrees
* #return End-point from the source given the desired range and bearing.
*/
public static PointF calculateDerivedPosition(PointF point,
double range, double bearing)
{
double EarthRadius = 6371000; // m
double latA = Math.toRadians(point.x);
double lonA = Math.toRadians(point.y);
double angularDistance = range / EarthRadius;
double trueCourse = Math.toRadians(bearing);
double lat = Math.asin(
Math.sin(latA) * Math.cos(angularDistance) +
Math.cos(latA) * Math.sin(angularDistance)
* Math.cos(trueCourse));
double dlon = Math.atan2(
Math.sin(trueCourse) * Math.sin(angularDistance)
* Math.cos(latA),
Math.cos(angularDistance) - Math.sin(latA) * Math.sin(lat));
double lon = ((lonA + dlon + Math.PI) % (Math.PI * 2)) - Math.PI;
lat = Math.toDegrees(lat);
lon = Math.toDegrees(lon);
PointF newPoint = new PointF((float) lat, (float) lon);
return newPoint;
}
And now create your query:
PointF center = new PointF(x, y);
final double mult = 1; // mult = 1.1; is more reliable
PointF p1 = calculateDerivedPosition(center, mult * radius, 0);
PointF p2 = calculateDerivedPosition(center, mult * radius, 90);
PointF p3 = calculateDerivedPosition(center, mult * radius, 180);
PointF p4 = calculateDerivedPosition(center, mult * radius, 270);
strWhere = " WHERE "
+ COL_X + " > " + String.valueOf(p3.x) + " AND "
+ COL_X + " < " + String.valueOf(p1.x) + " AND "
+ COL_Y + " < " + String.valueOf(p2.y) + " AND "
+ COL_Y + " > " + String.valueOf(p4.y);
COL_X is the name of the column in the database that stores latitude values and COL_Y is for longitude.
So you have some data that are near your central point with a good approximation.
2) Now you can loop on these filtered data and determine if they are really near your point (in the circle) or not using the following methods:
public static boolean pointIsInCircle(PointF pointForCheck, PointF center,
double radius) {
if (getDistanceBetweenTwoPoints(pointForCheck, center) <= radius)
return true;
else
return false;
}
public static double getDistanceBetweenTwoPoints(PointF p1, PointF p2) {
double R = 6371000; // m
double dLat = Math.toRadians(p2.x - p1.x);
double dLon = Math.toRadians(p2.y - p1.y);
double lat1 = Math.toRadians(p1.x);
double lat2 = Math.toRadians(p2.x);
double a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.sin(dLon / 2)
* Math.sin(dLon / 2) * Math.cos(lat1) * Math.cos(lat2);
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
double d = R * c;
return d;
}
Enjoy!
I used and customized this reference and completed it.

Chris's answer is really useful (thanks!), but will only work if you are using rectilinear coordinates (eg UTM or OS grid references). If using degrees for lat/lng (eg WGS84) then the above only works at the equator. At other latitudes, you need to decrease the impact of longitude on the sort order. (Imagine you're close to the north pole... a degree of latitude is still the same as it is anywhere, but a degree of longitude may only be a few feet. This will mean that the sort order is incorrect).
If you are not at the equator, pre-calculate the fudge-factor, based on your current latitude:
<fudge> = Math.pow(Math.cos(Math.toRadians(<lat>)),2);
Then order by:
((<lat> - LAT_COLUMN) * (<lat> - LAT_COLUMN) +
(<lng> - LNG_COLUMN) * (<lng> - LNG_COLUMN) * <fudge>)
It's still only an approximation, but much better than the first one, so sort order inaccuracies will be much rarer.

I know this has been answered and accepted but thought I'd add my experiences and solution.
Whilst I was happy to do a haversine function on the device to calculate the accurate distance between the user's current position and any particular target location there was a need to sort and limit the query results in order of distance.
The less than satisfactory solution is to return the lot and sort and filter after the fact but this would result in a second cursor and many unnecessary results being returned and discarded.
My preferred solution was to pass in a sort order of the squared delta values of the long and lats:
((<lat> - LAT_COLUMN) * (<lat> - LAT_COLUMN) +
(<lng> - LNG_COLUMN) * (<lng> - LNG_COLUMN))
There's no need to do the full haversine just for a sort order and there's no need to square root the results therefore SQLite can handle the calculation.
EDIT:
This answer is still receiving love. It works fine in most cases but if you need a little more accuracy, please check out the answer by #Teasel below which adds a "fudge" factor that fixes inaccuracies that increase as the latitude approaches 90.

In order to increase performance as much as possible I suggest improve #Chris Simpson's idea with the following ORDER BY clause:
ORDER BY (<L> - <A> * LAT_COL - <B> * LON_COL + LAT_LON_SQ_SUM)
In this case you should pass the following values from code:
<L> = center_lat^2 + center_lon^2
<A> = 2 * center_lat
<B> = 2 * center_lon
And you should also store LAT_LON_SQ_SUM = LAT_COL^2 + LON_COL^2 as additional column in database. Populate it inserting your entities into database. This slightly improves performance while extracting large amount of data.

Try something like this:
//locations to calculate difference with
Location me = new Location("");
Location dest = new Location("");
//set lat and long of comparison obj
me.setLatitude(_mLat);
me.setLongitude(_mLong);
//init to circumference of the Earth
float smallest = 40008000.0f; //m
//var to hold id of db element we want
Integer id = 0;
//step through results
while(_myCursor.moveToNext()){
//set lat and long of destination obj
dest.setLatitude(_myCursor.getFloat(_myCursor.getColumnIndexOrThrow(DataBaseHelper._FIELD_LATITUDE)));
dest.setLongitude(_myCursor.getFloat(_myCursor.getColumnIndexOrThrow(DataBaseHelper._FIELD_LONGITUDE)));
//grab distance between me and the destination
float dist = me.distanceTo(dest);
//if this is the smallest dist so far
if(dist < smallest){
//store it
smallest = dist;
//grab it's id
id = _myCursor.getInt(_myCursor.getColumnIndexOrThrow(DataBaseHelper._FIELD_ID));
}
}
After this, id contains the item you want from the database so you can fetch it:
//now we have traversed all the data, fetch the id of the closest event to us
_myCursor = _myDBHelper.fetchID(id);
_myCursor.moveToFirst();
//get lat and long of nearest location to user, used to push out to map view
_mLatNearest = _myCursor.getFloat(_myCursor.getColumnIndexOrThrow(DataBaseHelper._FIELD_LATITUDE));
_mLongNearest = _myCursor.getFloat(_myCursor.getColumnIndexOrThrow(DataBaseHelper._FIELD_LONGITUDE));
Hope that helps!