Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear pa...

AbstructA circuit implementation of the chaotic Lorenz system is described. The chaotic behavior of the circuit closely matches the results predicted by numerical experiments. Using the concept of synchronized chaotic systems (SCS’s), two possible approaches to secure communications are demonstrated with the Lorenz circuit implemented in both the transmitter and receiver. In the first approach,...

Linear and nonlinear optimal control have been investigated in transitional channel and boundary layer flows. The flow phenomena that we study are governed by the incompressible Navier–Stokes equations and the main aim with the control is to prevent transition from laminar to turbulent flows. A linear model-based feedback control approach, that minimizes an objective function which measures the...

This paper introduces and analyzes the asymptotic (large sample) performance of a family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of carrier phase, frequency offset, and Doppler rate for burst-mode phaseshift keying transmissions. An optimal or “matched” nonlinear estimator that exhibits the smallest asymptotic variance within the family of envisaged bl...

The Bayesian approach provides a rather powerful framework for handling nonlinear, as well as linear, estimation problems. We can in fact pose a general solution to the nonlinear estimation problem. However, in the general case there does not exist any closed-form solution and we are forced to use approximate techniques. In this thesis we will study one such technique, the sequential Monte Carl...

This paper is motivated by recent evidence that many univariate economic and …nancial time series have both nonlinear and long memory characteristics. Hence, this paper considers a general nonlinear, smooth transition regime autoregression which is embedded within a strongly dependent, long memory process. A time domainMLE with simultaneous estimation of the long memory, linear AR and nonlinear...

The search for conditions for the consistency of maximum likelihood estimators in nonlinear mixed effects models is difficult due to the fact that, in general, the likelihood can only be expressed as an integral over the random effects. For repeated measurements or clustered data, we focus on asymptotic theory for the maximum likelihood estimator for the case where the cluster sizes go to infin...

The error bound in probability between the approximate maximum likelihood estimator AMLE and the continuous maximum likelihood estimator MLE is investigated for nonlinear nonhomogenous stochastic system with unknown parameter. The rates of convergence of the approximations for Itô and ordinary integral are introduced under some regular assumptions. Based on these results, the in probability rat...

We characterize eecient estimators for the expectation of a function under the invariant distribution of a Markov chain and outline ways of constructing such estimators. We consider two models. The rst is described by a parametric family of constraints on the transition distribution; the second is the heteroscedastic nonlinear autoregressive model. The eecient estimator for the rst model adds a...

We consider finite-order moving average and nonlinear autoregressive processes with no parametric assumption on the error distribution, and present a kernel density estimator of a bootstrap series that estimates their marginal densities root-n consistently. This is equal to the rate of the best known convolution estimators, and faster than the standard kernel density estimator. We also conduct ...