Calculating user's distance and duration from GPS logs

Question

I am working with a GPS datasets of people's mobility for Beijing city. In my raw GPS table trajectories is the sequence of GPS for all users:

CREATE TABLE trajectories
(
    user_id integer,
    session_id bigint NOT NULL,
    "timestamp" timestamp with time zone NOT NULL,
    lat double precision NOT NULL,
    lon double precision NOT NULL,
    alt double precision,
    CONSTRAINT trajectories_pkey PRIMARY KEY (session_id, "timestamp")
);

SELECT * FROM trajectories ORDER BY user_id, timestamp LIMIT 10;
 user_id |   session_id   |       timestamp        |    lat    |    lon     | alt 
---------+----------------+------------------------+-----------+------------+-----
       1 | 20081023025304 | 2008-10-23 02:53:04+01 | 39.984702 | 116.318417 | 492
       1 | 20081023025304 | 2008-10-23 02:53:10+01 | 39.984683 |  116.31845 | 492
       1 | 20081023025304 | 2008-10-23 02:53:15+01 | 39.984686 | 116.318417 | 492
       1 | 20081023025304 | 2008-10-23 02:53:20+01 | 39.984688 | 116.318385 | 492
       1 | 20081023025304 | 2008-10-23 02:53:25+01 | 39.984655 | 116.318263 | 492
       1 | 20081023025304 | 2008-10-23 02:53:30+01 | 39.984611 | 116.318026 | 493
       1 | 20081023025304 | 2008-10-23 02:53:35+01 | 39.984608 | 116.317761 | 493
       1 | 20081023025304 | 2008-10-23 02:53:40+01 | 39.984563 | 116.317517 | 496
       1 | 20081023025304 | 2008-10-23 02:53:45+01 | 39.984539 | 116.317294 | 500
       1 | 20081023025304 | 2008-10-23 02:53:50+01 | 39.984606 | 116.317065 | 505
(10 rows)

The SELECT query above shows the sequence of GPS points for user 1, from the starting point for the current trip (session_id=20081023025304). I want to use the raw data in this table to insert calculated trip metrics into a new table I defined as:

CREATE TABLE trip_metrics(
  user_id INT,
  session_id BIGINT,
  lat_start DOUBLE PRECISION,
  lat_end DOUBLE PRECISION,
  lon_start DOUBLE PRECISION,
  lon_end DOUBLE PRECISION,
  trip_starttime timestamp,
  trip_endtime timestamp,
  trip_duration DOUBLE PRECISION,
  trip_distance DOUBLE PRECISION,
  PRIMARY KEY (user_id, session_id, trip_starttime)
  );

The point of this trip_metrics TABLE is to store results for analysis, so that lat_start, lon_start take the values of lat, lon of starting position (in the given example: 39.984702, 116.318417), trip_starttimestamp takes starting time (in this case 2008-10-23 02:53:04+01) and so the lat_end, lon_end, trip_endtime respectively.

And finally using lat_start/end, lon_start/end to compute the distance covered by this user in this trip. The final result should be like:

+---------+----------------+-----------+-----------+------------+------------+------------------------+------------------------+---------------+---------------+
| user_id |   session_id   | lat_start |  lat_end  | lon_start  |  lon_end   |     trip_starttime     |      trip_endtime      | trip_duration | trip_distance |
+---------+----------------+-----------+-----------+------------+------------+------------------------+------------------------+---------------+---------------+
|       1 | 20081023025304 | 39.984702 | 39.984606 | 116.318417 | 116.317065 | 2008-10-23 02:53:04+01 | 2008-10-23 02:53:50+01 |               |               |
+---------+----------------+-----------+-----------+------------+------------+------------------------+------------------------+---------------+---------------+

With the values of trip_duration and trip_distance calculated (of course the value of trip_duration would be trip_endtime - trip_starttime).

I have been stuck in my research for a couple of days thinking about how to do this in PostgrSQL database filtering only trips within Beijing city latitude (39.85 - 40.05) and longitude (116.25 - 116.5) as some trips spanned beyond the city. I created a db-fiddle here containing GPS points of 2 trips for this user (10 points each).

I would appreciate any guide to work around this to make a progress in my current research.

EDIT

Come across this function to calculate distance using haversine formula. I created this function but I'm not sure how to use it to get trip_distance value.

CREATE OR REPLACE FUNCTION distance(
    lat1 double precision,
    lon1 double precision,
    lat2 double precision,
    lon2 double precision)
  RETURNS double precision AS
$BODY$
DECLARE
    R integer = 6371e3; -- Meters
    rad double precision = 0.01745329252;

    φ1 double precision = lat1 * rad;
    φ2 double precision = lat2 * rad;
    Δφ double precision = (lat2-lat1) * rad;
    Δλ double precision = (lon2-lon1) * rad;

    a double precision = sin(Δφ/2) * sin(Δφ/2) + cos(φ1) * cos(φ2) * sin(Δλ/2) * sin(Δλ/2);
    c double precision = 2 * atan2(sqrt(a), sqrt(1-a));    
BEGIN                                                     
    RETURN R * c;        
END  
$BODY$
  LANGUAGE plpgsql VOLATILE
  COST 100;

Add postgis to your database then read more about geometry/geography functions in it. You can easily calculate distances (st_distance(geom, geom) or store paths as single records with it. More you will find here postgis.net/docs/ST_MakeLine.html — Grzegorz Grabek

Jim Jones Jim Jones · Accepted Answer · 2020-06-17T13:25:48

To compute distances more easily you have to install the PostGIS extension, as you already suggest in your tags:

CREATE EXTENSION postgis;

The function ST_Distance is what you're looking for, e.g (quick&dirty):

WITH j AS (
  SELECT user_id, session_id, 
    max(timestamp ORDER BY timestamp),
    min(timestamp ORDER BY timestamp) 
  FROM trajectories t
  GROUP BY user_id,session_id  
) 
SELECT 
  s.user_id,s.session_id, 
  lat_start,lon_start, 
  lat_end,lon_end, 
  trip_starttime, 
  trip_endtime,
  age(trip_endtime,trip_starttime),
  ST_Distance(
    ST_MakePoint(lon_start,lat_start)::geography,
    ST_MakePoint(lon_end,lat_end)::geography) AS trip_distance
FROM 
  (SELECT 
    j.user_id, j.session_id, 
    t.timestamp AS trip_starttime,
    lat AS lat_start, lon AS lon_start FROM j
   JOIN trajectories t ON t.timestamp = j.min 
     AND t.session_id = j.session_id AND t.user_id = j.user_id) s,
  (SELECT 
    j.user_id, j.session_id, 
    t.timestamp AS trip_endtime,
    lat AS lat_end,lon AS lon_end FROM j
   JOIN trajectories t ON t.timestamp = j.max 
     AND t.session_id = j.session_id AND t.user_id = j.user_id) e
WHERE s.user_id = e.user_id AND s.session_id = e.session_id;

 user_id |   session_id   | lat_start | lon_start |  lat_end  |  lon_end   |     trip_starttime     |      trip_endtime      |   age    |  trip_distance   
---------+----------------+-----------+-----------+-----------+------------+------------------------+------------------------+----------+------------------
       1 | 20081023025304 | 39.984702 | 16.318417 | 39.984606 | 116.317065 | 2008-10-23 03:53:04+02 | 2008-10-23 03:53:50+02 | 00:00:46 | 8012597.30391588

On a side note: Storing longitude and latitude in separated columns is almost always a bad idea. If possible store them into a geometry or geography column. It might seem necessary at first, but PostGIS offers a ton of really kickass functions!

Calculating user's distance and duration from GPS logs

1 Answers