Efficient moving horizon estimation and nonlinear model predictive control

State estimation from plant measurements should play an essential role in any advanced process control technology. Unlike the model predictive control (MPC) regulator, however, this area has received little attention. In this paper, we address the computational issues surrounding constrained moving horizon estimation (MHE) by presenting an algorithm for the efficient computation of moving horizon estimates. In our discussion, we present structured solvers for use with MHE, derive formulas for a nonlinear covariance smoothing update, and describe interactions between MHE and nonlinear target calculations. We conclude with relevant examples of MHE operating in a closed loop to remove non-zero mean disturbances, poor initial estimates, and random noise.