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The En KF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.En KF is related to the particle filter (in this context, a particle is the same thing as ensemble member) but the En KF makes the assumption that all probability distributions involved are Gaussian; when it is applicable, it is much more efficient than the particle filter.The Ensemble Kalman Filter (En KF) is a Monte Carlo implementation of the Bayesian update problem: given a probability density function (pdf) of the state of the modeled system (the prior, called often the forecast in geosciences) and the data likelihood, the Bayes theorem is used to obtain the pdf after the data likelihood has been taken into account (the posterior, often called the analysis). The Bayesian update is combined with advancing the model in time, incorporating new data from time to time.

However, maintaining the covariance matrix is not feasible computationally for high-dimensional systems. En KFs represent the distribution of the system state using a collection of state vectors, called an ensemble, and replace the covariance matrix by the sample covariance computed from the ensemble.

The ensemble is operated with as if it were a random sample, but the ensemble members are really not independent – the En KF ties them together.

In order to project a better representation of the territory, the samples were mined from ten cites each.

The mined clay samples from the ten cites were mixed properly and a representative specimen for test from that location was produced using the cone and quartering system as recommended by the American Society of Testing Materials (ASTM).

introduce the joint position-amplitude adjustment model using ensembles, and systematically derive a sequential approximation which can be applied to both En KF and other formulations.