Search

Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSMs), which allow a range of statistical distributions to inform innovations and errors. In many applications, the main goal is to identify not only the hidden state, but also additional unknown model parameters (e.g., AR coefficients or unknown dynamics). We show how to efficiently optimize over model parameters in SSM that use smooth process and measurement losses. Our approach is to project out state variables, obtaining a value function that only depends on the parameters of interest, and derive analytical formulas for first and second derivatives that can be used by many types of optimization methods. We illustrate this by implementing Newton, Gauss–Newton, and quasi-Newton algorithms on a numerical example. The approach can be used with smooth robust penalties such as Hybrid and the Student's T, in addition to classic least squares. We use the approach to estimate robust AR models and long-run unemployment rates with sudden changes. [ABSTRACT FROM AUTHOR]

We develop a family of Fenchel dual gradient methods for solving constrained, strongly convex, but not necessarily smooth multi-agent optimization problems over time-varying networks. The proposed algorithms are constructed on the basis of weighted Fenchel dual gradients and can be implemented in a fully decentralized fashion. We show that the proposed algorithms drive all the agents to both primal and dual optimality at sublinear rates under a standard connectivity condition. Compared with the existing distributed optimization methods that also have convergence rate guarantees over time-varying networks, our algorithms are able to address constrained problems and have better scalability with respect to network size and time for reaching connectivity. The competent performance of the Fenchel dual gradient methods is demonstrated via simulations. [ABSTRACT FROM AUTHOR]

In this note, we extend the accurate continuous-discrete extended-cubature Kalman filter and continuous-discrete cubature Kalman filter to deal with the problem of Bayesian optimal smoothing in nonlinear dynamic systems. The dynamics can be modeled with nonlinear stochastic differential equations (SDEs) and the noise corrupted measurements are obtained at discrete time instants. To be consistent with the literature, the resulting nonlinear smoothers are referred to as the accurate continuous-discrete extended-cubature Kalman smoother and the continuous-discrete cubature Kalman smoother, respectively. We first present two approximation methodologies to solve the SDE encountered in the prediction step of continuous-discrete filter. Then, two types of novel Gaussian approximation smoothing methods are derived based on the fixed-interval Rauch–Tung–Striebel smoother, which computes the smoothing solution according to the stored filtering results. The performances of the proposed smoothing methods are demonstrated in a simulated application and the numerical results show that the newly presented approaches are more flexible and robust than other smoothing algorithms with lower computational cost. [ABSTRACT FROM AUTHOR]

This note considers the problem of Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Sigma-point approximations to the general Gaussian Rauch-Tung-Striebel smoother are widely used methods to tackle this problem. These algorithms perform statistical linear regression (SLR) of the nonlinear functions considering only the previous measurements. We argue that SLR should be done taking all measurements into account. We propose the iterated posterior linearization smoother (IPLS), which is an iterated algorithm that performs SLR of the nonlinear functions with respect to the current posterior approximation. The algorithm is demonstrated to outperform conventional Gaussian nonlinear smoothers in two numerical examples. [ABSTRACT FROM AUTHOR]

In this note, a new type of L2 - E performance criterion for a fixed-lag smoother is introduced, which is given by a gain between the energy of the external disturbances during the recent time horizon and the estimation error at the fixed-delayed time from the current one. By minimizing the maximum value of the L2 - E performance criterion, the L2 - E finite impulse response (FIR) smoother (LEFS) is obtained for a deterministic discrete-time state space signal model. The LEFS is designed to meet requirements such as linearity and FIR structure with respect to measured inputs and outputs, unbiased property in the deterministic sense, and independence of any state information simultaneously. The proposed LEFS is represented in a batch form for simplicity. The LEFS is compared with a conventional H∞ Infinite Impulse Response (IIR) smoother via simulation. [ABSTRACT FROM AUTHOR]

Examines some of the relationships between optimal control and statistics. Method used to produce generalized, smoothing splines; Proof of the convergence result for the smoothing splines.

A notable difference between the H[sup2] and H∞ smoothing is that the achievable performance in the latter problem might "saturate" as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag. In this note, necessary and sufficient conditions under which such a saturation occurs are derived. In particular, it is shown that the H[sup2] performance saturates only if the H[sup2] norm of the optimal error system is achieved at the infinite frequency, i.e., if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable. [ABSTRACT FROM AUTHOR]