The algorithms in this data release implement a State-Space Model (SSM) of vertical infiltration through the unsaturated zone and recharge to the water table. These algorithms build on previous investigations available at https://doi.org/10.1029/2020WR029110 and https://doi.org/10.1111/gwat.13206. The SSM is defined by observed states (i.e., the water-table altitude) and unobserved states (i.e., fluxes through the unsaturated zone and recharge to the water table)and interprets time-series data for observations of water-table altitude and meteorological inputs (i.e., the liquid precipitation rate and the Potential Evapotranspiration (PET) rate). The algorithms first perform the estimation of the SSM parameters from the time-series data over a Parameter-Estimation Window (PEW). The estimated model parameters are then used in a subsequent State-Estimation Window (SEW) to estimate the observed and unobserved systems states of the SSM using the Kalman Filter (KF). The application of the KF to the SSM facilitates the assimilation of the recently available observations of the water-table altitude in the estimation of the observed and unobserved system states over the SEW. An additional outcome of applying the KF is the calculation of the time-varying error covariance of the system states over the SEW. The algorithms are used to demonstrate a comparison of the model outcomes for forecasting, filtering, and fixed-lag smoothing (FLS) using data for water-table altitude and meteorological inputs available from the Masser Recharge Site, which was operated by the U.S. Department of Agriculture, Agricultural Research Service. The algorithms were prepared and executed using the computational software MATLAB to meet the needs of the investigation presented in https://doi.org/10.1111/gwat.13349. MATLAB is a proprietary software, and thus, an executable version of the software cannot be supplied with this data release. The MATLAB files comprising the algorithms are included in this data release. The interested user would need to secure the appropriate versions of MATLAB and the associated MATLAB toolboxes. This USGS data release contains all of the input and output files for the simulations described in the associated journal article (https://doi.org/10.1111/gwat.13349).