Sequential Least Squares Estimation Research Articles

Bayesian sequential least-squares estimation for the drift of a Wiener process

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known “prior” distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.

New Algorithm of GPS Rapid Positioning Based on Double-k-Type Ridge Estimation

In this paper, a new algorithm is employed in global positioning system (GPS) rapid positioning using several-epoch single-frequency phase data. First, we define the double- k -type ridge estimator (DKRE) based on the structure characteristics of multicollinearities of the normal equations matrix in the double-difference (DD) model, and prove when the DKRE is not worse than the least-squares estimator (LSE) in the sense of a reduced MSEM. Taking into account how the ridge parameter in the ordinary ridge estimator is confirmed based on the generalized ridge estimator (GRE), we propose a method of estimating two ridge parameters for the DKRE. Second, we improve the LAMBDA method through replacing the cofactor matrix computed by the LSE with the cofactor matrix computed by the DKRE. The ambiguities-fixed solution is found by the sequential LSE. A theorem stating that the success rate of the improved LAMBDA method is bigger than the original LAMBDA method is given. Finally, through the GPS positioning tests, ...

Sequential point estimation of parameters in a threshold AR(1) model

We show that if an appropriate stopping rule is used to determine the sample size when estimating the parameters in a stationary and ergodic threshold AR(1) model, then the sequential least-squares estimator is asymptotically risk efficient. The stopping rule is also shown to be asymptotically efficient. Furthermore, non-linear renewal theory is used to obtain the limit distribution of appropriately normalized stopping rule and a second-order expansion for the expected sample size. A central result here is the rate of decay of lower-tail probability of average of stationary, geometrically β-mixing sequences.

Kalman Filter—Finite Element Method in Identification

The extended Kalman filter, which is essentially a method of sequential least-squares estimation, has been applied not only for dynamic parameter identification but also for static or dynamic system identification problems. In order to obtain the stable and convergent estimation in dynamic or static parameter identification problems, an extended Kalman filter-weighted local iteration procedure with an objective function (EK-WLI procedure) is previously proposed by writers. This paper investigates the procedure in geotechnical engineering problems, where the EK-WLI procedure is incorporated with the finite element method in order to identify unknown parameters. For the effectiveness of this proposed procedure, parameter identification problems are numerically analyzed for an elastic plain strain field represented by finite element models under several conditions. And numerical examples show the usefulness of this method in parameter identification of a plain strain field.

On-Line Algorithms for Forecasting Hourly Loads of an Electric Utility

A method which lends itself to online forecasting of hourly electric loads is presented and the results of its use are compared to models developed using the Box-Jenkins method. The method consits of processing the historical hourly loads with a sequential least-squares estimator to identify a finite order autoregressive model which in turn is used to obtain a parsimnious autoregressive-moving average model.

周波数応答のシーケンシャルな多点同時最小2乗推定

周波数応答のシーケンシャルな多点同時最小2乗推定

Sequential least-squares estimation and the electrical-network problem

Fundamental relationships existing between the electrical-network problem and least-squares estimation theory are illustrated, and the theorems of least power associated with the equilibrium conditions of physical systems are shown to correspond to the mathematical concepts of least-squares theory. The solution of the electrical-network problem based on Kron's method of tearing and interconnection is considered, and is shown to incorporate an iterative technique which also forms the basis for sequential least-squares data fitting.

Sequential Estimation of States and Parameters in Noisy Nonlinear Dynamical Systems

The problem considered is the sequential estimation of states and parameters in noisy nonlinear systems. The class of systems considered is those in which the dynamical behavior is described by an ordinary differential equation. No statistical assumptions are required concerning the nature of the unknown inputs to the system or the measurement errors on the output. For estimation purposes, a least-squares criterion is used. The new feature of the approach presented is that a sequential least-squares estimator is obtained for the class of problems considered. This estimator could be implemented in real time. Experimental results from several examples indicate that the proposed estimation scheme is feasible.