Three data-driven assimilation algorithms are compared in the flow around a surface mounted prism at $ \mathit{\operatorname{Re}}=1000 $. All algorithms employ proper orthogonal decomposition (POD) for dimensionality reduction and synthesize linear estimators (Kalman filters). Two estimators are new and exploit past historical patterns of the training data. They are constructed from the singular vectors of the time-delayed Hankel matrix assembled from the signals of the POD coefficients. The two estimators differ on the forcing term of the linear system and its statistics. They can reconstruct (and also forecast) the instantaneous velocity field from sparse data. The third algorithm is based on the n4sid system identification method. The performance of the algorithms is compared with respect to the number of sensor points, model order, computational time for synthesis, and accuracy at reproducing the statistics of the flow (Reynolds stresses) at design and off-design conditions. For all criteria, it is found that the two new estimators were more robust and accurate compared to n4sid. Between the two, the estimator with random noise forcing was slightly more accurate. The future evolution of the flow was also accurately forecast over long time horizons using only one sensor. Application of the model trained at the reference Reynolds number to an off-design condition (at the nearby $ \mathit{\operatorname{Re}}=800 $) showed that very satisfactory results can be obtained with only very few sensors. The new estimators are scalable, easy to construct, and physically interpretable and can provide flow reconstruction (and, if needed, forecasting over a rolling time window) in almost real time.