Righteousness is that order/right standing/alignment with the one in authority. In righteousness you shall be established (Isaiah 54:14). But in whose righteousness are you established? The scripture says that Abraham believed God and it was credited to him as righteousness.
Our righteousness is in Christ Jesus who is the author and finisher of our faith. This is a higher righteousness and is a gift from God. We should be confident of our position of righteousness. Christ carried away all our sins to the cross and by His stripes we are healed.
He who knew no sin became sin that we might become the righteousness of God. All our righteousness is like filthy rags. May the Spirit of God help us to be established in the righteousness of God.