AP_GPS: use mktime for NMEA and MTK time conversion

this fixes NMEA time handling, which was off by 3 days

libraries/AP_GPS/GPS_Backend.cpp

@@ -16,6 +16,8 @@
 #include "AP_GPS.h"
 #include "GPS_Backend.h"
 #include <AP_Logger/AP_Logger.h>
+#include <time.h>
+#include <AP_RTC/AP_RTC.h>
 
 #define GPS_BACKEND_DEBUGGING 0
 
@@ -76,34 +78,25 @@ int16_t AP_GPS_Backend::swap_int16(int16_t v) const
  */
 void AP_GPS_Backend::make_gps_time(uint32_t bcd_date, uint32_t bcd_milliseconds)
 {
-    uint8_t year, mon, day, hour, min, sec;
-    uint16_t msec;
+    struct tm tm {};
 
-    year = bcd_date % 100;
-    mon  = (bcd_date / 100) % 100;
-    day  = bcd_date / 10000;
+    tm.tm_year = 100U + bcd_date % 100U;
+    tm.tm_mon  = ((bcd_date / 100U) % 100U)-1;
+    tm.tm_mday = bcd_date / 10000U;
 
     uint32_t v = bcd_milliseconds;
-    msec = v % 1000; v /= 1000;
-    sec  = v % 100; v /= 100;
-    min  = v % 100; v /= 100;
-    hour = v % 100;
-
-    int8_t rmon = mon - 2;
-    if (0 >= rmon) {    
-        rmon += 12;
-        year -= 1;
-    }
+    uint16_t msec = v % 1000U; v /= 1000U;
+    tm.tm_sec = v % 100U; v /= 100U;
+    tm.tm_min = v % 100U; v /= 100U;
+    tm.tm_hour = v % 100U;
 
-    // get time in seconds since unix epoch
-    uint32_t ret = (year/4) - (GPS_LEAPSECONDS_MILLIS / 1000UL) + 367*rmon/12 + day;
-    ret += year*365 + 10501;
-    ret = ret*24 + hour;
-    ret = ret*60 + min;
-    ret = ret*60 + sec;
+    // convert from time structure to unix time
+    time_t unix_time = AP::rtc().mktime(&tm);
 
     // convert to time since GPS epoch
-    ret -= 272764785UL;
+    const uint32_t unix_to_GPS_secs = 315964800UL;
+    const uint16_t leap_seconds_unix = GPS_LEAPSECONDS_MILLIS/1000U;
+    uint32_t ret = unix_time + leap_seconds_unix - unix_to_GPS_secs;
 
     // get GPS week and time
     state.time_week = ret / AP_SEC_PER_WEEK;