Incorporating　differentially　private　continuous　data　release　(DPCR)　into　private　federated　learning　(FL)　has　recently　emerged　as　a　powerful　technique　for　enhancing　accuracy.　Designing　an　effective　DPCR　model　is　the　key　to　improving　accuracy.　Still,　the　state-of-the-art　DPCR　models　hinder　the　potential　for　accuracy　improvement　due　to　insufficient　privacy　budget　allocation　and　the　design　only　for　specific　iteration　numbers.　To　boost　accuracy　further,　we　develop　an　augmented　BIT-based　continuous　data　release　(AuBCR)　model,　leading　to　demonstrable　accuracy　enhancements.　By　employing　a　dual-release　strategy,　AuBCR　gains　the　potential　to　further　improve　accuracy,　while　confronting　the　challenge　of　consistent　release　and　doubly-nested　complex　privacy　budget　allocation　problem.　Against　this,　we　design　an　efficient　optimal　consistent　estimation　algorithm　with　only　O(1)　complexity　per　release.　Subsequently,　we　introduce　the　(k,　N)-AuBCR　Model　concept　and　design　a　meta-factor　method.　This　innovation　significantly　reduces　the　optimization　variables　from　O(T)　to　O　(lg(2)T),　thereby　greatly　enhancing　the　solvability　of　optimal　privacy　budget　allocation　and　simultaneously　supporting　arbitrary　iteration　number　T　.　Our　experiments　on　classical　datasets　show　that　AuBCR　boosts　accuracy　by　4.9%　similar　to　18.1%　compared　to　traditional　private　FL　and　0.4%　similar　to　1.2%　compared　to　the　state-of-the-art　ABCRG　model.