If you use Android we have done something similar on Smarter Time, which saves everything on the phone and also can receive apps from the computer. For now the event log export is quite crude, but all the data is here and it can be made more readable very easily. What my log looks like, in semi readable format:
13:43:08 MOVE_STOP 1470138188271 0
13:41:41 MOVE_START MOVE_WALK 0
13:41:09 NEW_PLACE 0 > Tue Aug 02 13:41:09 GMT+02:00 2016 0
13:40:07 ACTION_SCREEN_OFF 1470138007545 0
13:39:49 NEW_PLACE 621 > Tue Aug 02 13:38:59 GMT+02:00 2016 0
13:39:07 APP_L gmail > 13:38:21 - 13:39:07 0
13:39:07 ACTION_SCREEN_OFF 1470137947528 0
13:38:59 MOVE_STOP 1470137939279 0
13:38:46 NEW_PLACE 0 > Tue Aug 02 13:38:46 GMT+02:00 2016 0
13:38:30 MOVE_START MOVE_WALK 0
13:38:29 NEW_PLACE 621 > Tue Aug 02 13:38:29 GMT+02:00 2016 0
Edit : if you are looking for a higher-level log, it can also be exported from the app, example (raw csv):
Day,Timestamp,Time,Place,Room,Activity,Activity Category,Duration ms,Steps,Move,Device
20160314,1457910000000,Mon Mar 14 00:00:00 GMT+01:00 2016,home,office,video games,Art & Entertainment,2561989,50,still,
20160314,1457912561989,Mon Mar 14 00:42:41 GMT+01:00 2016,home,bedroom,sleep,Resting,26591266,19,still,
20160314,1457939153255,Mon Mar 14 08:05:53 GMT+01:00 2016,home,office,news browsing,Professional Life,4704415,51,still,
20160314,1457943857670,Mon Mar 14 09:24:17 GMT+01:00 2016,walk,Transport,683646,0,walk,
20160314,1457944541316,Mon Mar 14 09:35:41 GMT+01:00 2016,phone : pocket,Professional Life,1084440,0,vehicle,Nexus 5
20160314,1457945625756,Mon Mar 14 09:53:45 GMT+01:00 2016,walk,Transport,683096,2123,walk,
20160314,1457946308852,Mon Mar 14 10:05:08 GMT+01:00 2016,Incubateur Telecom,bureau d11,news browsing,Professional Life,1610014,46,still,
20160314,1457947918866,Mon Mar 14 10:31:58 GMT+01:00 2016,Incubateur Telecom,bureau d11,com,Professional Life,7509205,49,still,
20160314,1457955428071,Mon Mar 14 12:37:08 GMT+01:00 2016,walk,Transport,472838,526,walk,
20160314,1457955900909,Mon Mar 14 12:45:00 GMT+01:00 2016,Chef asie,eating out,Social,152010,0,still,
20160314,1457956052919,Mon Mar 14 12:47:32 GMT+01:00 2016,walk,Transport,337434,606,walk,
20160314,1457956390353,Mon Mar 14 12:53:10 GMT+01:00 2016,Incubateur Telecom,cafet,eating out,Social,1846493,19,still,
20160314,1457958236846,Mon Mar 14 13:23:56 GMT+01:00 2016,Incubateur Telecom,bureau d11,programming,Professional Life,7007803,81,still,
20160314,1457965244649,Mon Mar 14 15:20:44 GMT+01:00 2016,walk,Transport,389305,452,walk,
20160314,1457965633954,Mon Mar 14 15:27:13 GMT+01:00 2016,vehicle,Transport,222149,0,vehicle,
20160314,1457965856103,Mon Mar 14 15:30:56 GMT+01:00 2016,walk,Transport,666776,1066,walk,
20160314,1457966522879,Mon Mar 14 15:42:02 GMT+01:00 2016,Fitness Price,sport,Sport & Fitness,3399231,0,still,
20160314,1457969922110,Mon Mar 14 16:38:42 GMT+01:00 2016,walk,Transport,180966,268,walk,
20160314,1457970103076,Mon Mar 14 16:41:43 GMT+01:00 2016,Incubateur Telecom,bureau d11,programming,Professional Life,6363264,44,still,
20160314,1457976466340,Mon Mar 14 18:27:46 GMT+01:00 2016,Incubateur Telecom,salle 4,fundraising,Professional Life,918238,5,still,
20160314,1457977384578,Mon Mar 14 18:43:04 GMT+01:00 2016,Incubateur Telecom,bureau d11,fundraising,Professional Life,3184032,128,still,
20160314,1457980387474,Mon Mar 14 19:33:07 GMT+01:00 2016,Incubateur Telecom,salle b,phone : chrome,Art & Entertainment,181136,4,still,Nexus 5
20160314,1457980568610,Mon Mar 14 19:36:08 GMT+01:00 2016,Incubateur Telecom,bureau d14,meeting,Professional Life,148695,4,still,
20160314,1457980748620,Mon Mar 14 19:39:08 GMT+01:00 2016,walk,Transport,668355,0,walk,
20160314,1457981416975,Mon Mar 14 19:50:16 GMT+01:00 2016,vehicle,Transport,984152,1159,vehicle,
20160314,1457982401127,Mon Mar 14 20:06:41 GMT+01:00 2016,walk,Transport,622240,872,walk,
20160314,1457983023367,Mon Mar 14 20:17:03 GMT+01:00 2016,home,office,news browsing,Professional Life,5080122,24,still,
20160314,1457984906192,Mon Mar 14 20:48:26 GMT+01:00 2016,home,office,video games,Art & Entertainment,3197297,24,still,
20160314,1457988103489,Mon Mar 14 21:41:43 GMT+01:00 2016,home,kitchen,cooking,Chores,1075625,18,still,
20160314,1457989179114,Mon Mar 14 21:59:39 GMT+01:00 2016,home,living,phone : le monde,Art & Entertainment,129637,28,still,Nexus 5
20160314,1457989308751,Mon Mar 14 22:01:48 GMT+01:00 2016,home,living,television,Art & Entertainment,146674,0,still,
20160314,1457989455425,Mon Mar 14 22:04:15 GMT+01:00 2016,home,living,phone : le monde,Art & Entertainment,2381913,0,still,Nexus 5
20160314,1457991837338,Mon Mar 14 22:43:57 GMT+01:00 2016,home,living,television,Art & Entertainment,273571,7,still,
20160314,1457991837338,Mon Mar 14 22:43:57 GMT+01:00 2016,home,living,phone : pocket,Professional Life,2795012,7,still,Nexus 5
20160314,1457994632350,Mon Mar 14 23:30:32 GMT+01:00 2016,home,living,television,Art & Entertainment,230980,0,still,
20160314,1457994863330,Mon Mar 14 23:34:23 GMT+01:00 2016,home,office,video games,Art & Entertainment,1536670,0,still,