Numerically stable algorithm for combining census and sample estimates with the multivariate composite estimator

The minimum variance multivariate composite estimator is a relatively simple sequential estimator for complex sampling designs (Czaplewski 2009). Such designs combine a probability sample of expensive field data with multiple censuses and/or samples of relatively inexpensive multi-sensor, multi-resolution remotely sensed data. Unfortunately, the multivariate composite estimator is vulnerable to numerical errors, which can cause infeasible or unreliable estimates (Grewal and Andrews 2001:Chapter 6). Numerical errors can exceed random estimation errors, which is especially dangerous if undetected (Bierman 1977:97). These problems are well known in the Kalman filter literature (e.g., Maybeck 1979), which is a generalization of the multivariate composite estimator. U-D factorization is a numerically robust solution (Bierman 1977).