Recuperación de los registros más recientes dentro de una consulta

MySQL no tiene funcionalidad de clasificación/analítica/ventana.

SELECT tl.locationid, tl.timestamp, tp.name, X, Y, Z
  FROM tblPerson tp
  JOIN tblLocation tl ON tl.personid = tp.personid
  JOIN (SELECT t.personid,
               MAX(t.timestamp) AS max_date
          FROM tblLocation t
      GROUP BY t.personid) x ON x.personid = tl.personid
                            AND x.max_date = tl.timestamp

SQL Server 2005+ y Oracle 9i+ admiten análisis, por lo que podría usar:

SELECT x.locationid, x.timestamp, x.name, x.X, x.Y, x.Z
  FROM (SELECT tl.locationid, tl.timestamp, tp.name, X, Y, Z,
               ROW_NUMBER() OVER (PARTITION BY tp.name ORDER BY tl.timestamp DESC) AS rank
          FROM tblPerson tp
          JOIN tblLocation tl ON tl.personid = tp.personid) x
WHERE x.rank = 1

Usar una variable para obtener la misma funcionalidad que ROW_NUMBER en MySQL:

SELECT x.locationid, x.timestamp, x.name, x.X, x.Y, x.Z
  FROM (SELECT tl.locationid, tl.timestamp, tp.name, X, Y, Z,
               CASE
                 WHEN @name != t.name THEN
                   @rownum := 1
                 ELSE @rownum := @rownum + 1
               END AS rank,
               @name := tp.name
          FROM tblLocation tl
          JOIN tblPerson tp ON tp.personid = tl.personid
          JOIN (SELECT @rownum := NULL, @name := '') r
      ORDER BY tp.name, tl.timestamp DESC) x
WHERE x.rank = 1