Accurate　real-time　state　estimation　is　fundamental　to　process　control　and　optimization.　Many　dynamic　systems,　including　chemical　batches　and　traffic　flow,　operate　cyclically.　Traditional　approaches　isolate　individual　cycles,　ignoring　inter-cycle　relationships　-　a　one-dimensional　limitation.　This　research　introduces　a　two-dimensional　estimation　methodology　capturing　both　temporal　dynamics　and　cycle-to-cycle　patterns,　integrating　historical　measurements　across　multiple　cycles.　Using　a　two-dimensional　state-space　model,　we　derive　Bayesian　filtering　equations　for　three　scenarios:　fully　two-dimensional,　time-dominant,　and　cycle-dominant　systems.　For　nonlinear　and　non-Gaussian　processes,　we　develop　a　particle　filtering　algorithm　that　propagates　particles　simultaneously　through　time　and　cycle　dimensions.　We　validate　our　methodology　through　simulation　of　an　uneven-length　batch　process,　demonstrating　significant　performance　improvements　over　conventional　techniques.　　©　Published　under　licence　by　IOP　Publishing　Ltd.