Those who call upon the Lord according to His covenant are those who have been redeemed by God in Christ, typified by the sacrifices.
Verse 2 says, "Out of Zion, the perfection of beauty,/God shines forth." Just as the shining of the sun is a dispensing of the sun's goodness, so the shining forth of God out of His house is a dispensing of His goodness. Under such a shining, such a dispensing, we enjoy God in Christ.
This is the second category of persons regarding the enjoyment of God in Christ. I believe that most of us are in this category.
In Psalm 51 we have the third categorya person repenting, confessing his sins to God, and asking God for His purging. In the life of each one of us, there needs to be a period of time, perhaps lasting for several days, in which we thoroughly repent, confess our sins to God, and plead with Him to deal with our sins and with our sinful nature. Furthermore, day by day we need to repent and confess.
The title of Psalm 51 is significant: "A Psalm of David, when Nathan the prophet came to him, after he had gone in to Bath-sheba" (2 Sam. 11:112:14). This indicates that this psalm was composed after David's great sin in murdering Uriah and robbing him of his wife Bath-sheba and then being rebuked by the prophet Nathan.
In verses 3 through 5 and 17 David repented and confessed his sins to God.