This psalm addresses God, acknowledging what God has done for us and what God knows about us. John H. Hayes, in Preaching through the Christian Year C, characterizes this knowledge as insight, oversight, and foresight.
The psalmist admits, and we admit when we pray this psalm, that the Lord knows everything about us whenever or wherever we are. The Lord knows what we are going to say before we say it.
Do we read these verses as reassurance, or are they unsettling to us? How comfortable is it for us to admit that God already knows what we have been doing today--and every day? For Arminians, are we bothered by the predestination element in verses 7 and 16?