Getting Largest Distance from group of GPS Coordinates

Question

So I have a database with multiple rows of GPS coordinates. I know how to calculate the distance from a given lat/lng from any one of them in the database, but what I want to do basically is look at the coordinates of a set of rows and get the two rows that are farthest apart. I'd love it if I could do this in SQL, but if I have to do it in my application code that would work to. Here is what I am doing to calculate the distance between two points:

ROUND(( 3960 * acos( cos( radians( :lat ) ) *
cos( radians( p.latitude ) ) * cos( radians(  p.longitude  ) - radians( :lng ) ) +
sin( radians( :lat ) ) * sin( radians(  p.latitude  ) ) ) ),1) AS distance

What we are trying to do is, look at GPS data for a specific user and make sure they aren't moving wildly all over the country. All the coordinates for a user should be within a couple miles at most of each other. A flag that there is malicious activity in our system is if the coordinates are all over the country. So I'd like to be able to quickly run through the data for a spcicic user and know what is the max distance they have been.

I thought about just running a Max/Min on the lat and lng separately and set an internal threshold for what is acceptable. And maybe that is easier, but if what I asked in the first part is possible, that would be best.

Answer 1

If you have SQL Server 2008 or later then you can use GEOGRAPHY to calculate the distance, e.g.:

DECLARE @lat1 DECIMAL(19,6) = 44.968046;
DECLARE @lon1 DECIMAL(19,6) = -94.420307;
DECLARE @lat2 DECIMAL(19,6) = 44.33328;
DECLARE @lon2 DECIMAL(19,6) = -89.132008;
SELECT GEOGRAPHY::Point(@lat1, @lon1, 4326).STDistance(GEOGRAPHY::Point(@lat2, @lon2, 4326));

This makes the problem pretty trivial?

For a set of lats/ longs for a user you would need to calculate the distance between each set and then return the highest distance. Putting this all together, you could probably do something like this:

DECLARE @UserGPS TABLE (
    UserId INT, --the user
    GPSId INT, --the incrementing unique id associated with this GPS reading (could link to a table with more details, e.g. time, date)
    Lat DECIMAL(19,6), --lattitude
    Lon DECIMAL(19,6)); --longitude
INSERT INTO @UserGPS SELECT 1, 1, 44.968046, -94.420307; --User #1 goes on a very long journey
INSERT INTO @UserGPS SELECT 1, 2, 44.33328, -89.132008;
INSERT INTO @UserGPS SELECT 1, 3, 34.12345, -92.21369;
INSERT INTO @UserGPS SELECT 1, 4, 44.978046, -94.430307;
INSERT INTO @UserGPS SELECT 2, 1, 44.968046, -94.420307; --User #2 doesn't get far
INSERT INTO @UserGPS SELECT 2, 2, 44.978046, -94.430307;

--Make a working table to store the distances between each set of co-ordinates
--This isn't strictly necessary; we could change this into a common-table expression
DECLARE @WorkTable TABLE (
    UserId INT, --the user
    GPSIdFrom INT, --the id of the first set of co-ordinates
    GPSIdTo INT, --the id of the second set of co-ordinates being compared
    Distance NUMERIC(19,6)); --the distance

--Get the distance between each and every combination of co-ordinates for each user
INSERT INTO
    @WorkTable
SELECT
    c1.UserId,
    c1.GPSId,
    c2.GPSId,
    GEOGRAPHY::Point(c1.Lat, c1.Lon, 4326).STDistance(GEOGRAPHY::Point(c2.Lat, c2.Lon, 4326))
FROM
    @UserGPS c1
    INNER JOIN @UserGPS c2 ON c2.UserId = c1.UserId AND c2.GPSId > c1.GPSId;
--Note this is a self-join, but single-tailed.  So we compare each set of co-ordinates to each other set of co-ordinates for a user
--This is handled by the "c2.GPSID > c1.GPSId" in the JOIN clause
--As an example, say we have three sets of co-ordinates for a user
--We would compare set #1 to set #2
--We would compare set #1 to set #3
--We would compare set #2 to set #3
--We wouldn't compare set #3 to anything (as we already did this)

--Determine the maximum distance between all the GPS co-ordinates per user
WITH MaxDistance AS (
    SELECT
        UserId,
        MAX(Distance) AS Distance
    FROM
        @WorkTable
    GROUP BY
        UserId)
--Report the results
SELECT
    w.UserId,
    g1.GPSId,
    g1.Lat,
    g1.Lon,
    g2.GPSId,
    g2.Lat,
    g2.Lon,
    md.Distance AS MaxDistance
FROM 
    MaxDistance md
    INNER JOIN @WorkTable w ON w.UserId = md.UserId AND w.Distance = md.Distance
    INNER JOIN @UserGPS g1 ON g1.UserId = md.UserId AND g1.GPSId = w.GPSIdFrom
    INNER JOIN @UserGPS g2 ON g2.UserId = md.UserId AND g2.GPSId = w.GPSIdTo;

Results are:

UserId  GPSId   Lat Lon GPSId   Lat Lon MaxDistance
1   3   34.123450   -92.213690  4   44.978046   -94.430307  1219979.460185
2   1   44.968046   -94.420307  2   44.978046   -94.430307  1362.820895

Now I made a LOT of assumptions about what data you are holding as there was no information about the detail of this in your question. You would probably need to adapt this to some degree?