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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def NESS(xs, est_xs, ps):
 """ Computes the normalized estimated error squared test on a sequence of estimates. The estimates are optimal if the mean error is zero and the covariance matches the Kalman filter's covariance. If this holds, then the mean of the NESS should be equal to or less than the dimension of x. Examples -------- .. code-block: Python xs = ground_truth() est_xs, ps, _, _ = kf.batch_filter(zs) NESS(xs, est_xs, ps) Parameters xs : list-like sequence of true values for the state x est_xs : list-like sequence of estimates from an estimator (such as Kalman filter) ps : list-like sequence of covariance matrices from the estimator Returns ------- ness : list of floats list of NESS computed for each estimate """


    est_err = xs - est_xs
    ness = []
    for x, p in zip(est_err, ps):
        ness.append(np.dot(x.T, linalg.inv(p)).dot(x))
    return ness