This paper reports a stable online adaptive identification technique for the identification of finite-dimensional dynamical models of dynamically positioned underwater robotic vehicles. Proofs for the identifier’s global stability, and for the input-tostate stability of this class of plants are reported. A direct comparison of the adaptive identification method to a conventional, offline, least...

In this paper we investigate least squares matching problems, extending the methods of our earlier paper 1] in such a way as to make them applicable to problems involving the sets of points that are so complex that approximate answers are of interest. These problems are formulated in terms of continuous descent equations, and lower bounds on the quality of the best match are obtained in terms o...

The least-squares νth-order polynomial filtering and fixed-point smoothing problems of uncertainly observed signals are considered. The proposed estimators do not require the knowledge of the state-space model generating the signal, but only the moments (up to the 2νth one) of the signal and the observation noise, as well as the probability that the signal exists in the observations.

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict su$cient assumptions which however does not include important model structures such as, e.g. Box}Jenkins. Based on a simple least-squares appro...

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of covariates. In a linear regression model with homoscedastic Normal noise, I consider shrinkage estimation of the nuisance parameters associated with control...

The problem of numerical analysis to which this study is directed is that of determining an optimum approximation (in the least squares sense) to a given function f by a function of the form p/q, where p and q are confined to certain prescribed linear spaces. The analogous approximation problem employing the uniform norm has received much recent attention. See, for example, [1, 2, 3, 4, 5, 9]. ...

The linear heteroskedastic regression model, for which the variance of the response is given by a suitable function of a set of linear exogenous variables, is very useful in econometric applications. We derive a simple matrix formula for the n biases of the maximum likelihood estimators of the parameters in the variance of the response, where n is the sample size. These biases are easily obtain...

This paper shows that the recursive least-squares (RLS) algorithm with forgetting factor is a special case of a varying-coe$cient model, and a model which can easily be estimated via simple local regression. This observation allows us to formulate a new method which retains the RLS algorithm, but extends the algorithm by including polynomial approximations. Simulation results are provided, whic...

The estimation of shaping filters with the `1-norm as opposed to the `2-norm leads to a proper attenuation of multiples when significant amplitude discrepancies exist between multiples and primaries. The actual method implemented is the fairly standard iteratively re-weighted least-squares method which is an excellent approximation to `1. Synthetic and field data results illustrate the advantag...