Abstract: The present disclosure provides a system and a method for monitoring an operation of a vapor compression cycle. The method comprises collecting digital representation of observed variables of the operation of the vapor compression cycle over multiple instances of time and executing a constrained ensemble Kalman smoother for each instance of time to estimate the state variables of the vapor compression cycle for each instance of time. The constrained ensemble Kalman smoother updates the state variables over a sequence of time instances within a smoothing window by solving a series of constrained optimization problems in a range of a covariance, for which constraints are enforced for every variable in the smoothing window for every instance of the constrained optimization problems. The method further comprises outputting, based on the estimates of the state variables, estimates of variables of the vapor compression cycle at each instance of time.