Related papers: Least-Squares Parameter Estimation for State-Space…

Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…

Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…

Although the theory of constrained least squares (CLS) estimation is well known, it is usually applied with the view that the constraints to be imposed are unavoidable. However, there are cases in which constraints are optional. For…

In this paper we investigate a problem of state estimation for the dynamical system described by the linear operator equation with unknown parameters in Hilbert space. We present explicit expressions for linear minimax estimation and error…

This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…

This paper presents a new robust fault and state estimation based on recursive least square filter for linear stochastic systems with unknown disturbances. The novel elements of the algorithm are : a simple, easily implementable, square…

Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…

Parameter reconstructions are indispensable in metrology. Here, the objective is to to explain $K$ experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined…

The least squares (LS) estimator and the best linear unbiased estimator (BLUE) are two well-studied approaches for the estimation of a deterministic but unknown parameter vector. In many applications it is known that the parameter vector…

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…

This paper deals with the state estimation of linear time-invariant systems using distributed observers with local sampled-data measurement and aperiodic communication. Each observer agent perceives partial information of the system to be…

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…

Recurrent State-space models (RSSMs) are highly expressive models for learning patterns in time series data and system identification. However, these models assume that the dynamics are fixed and unchanging, which is rarely the case in…

This study shows how to obtain least-squares solutions to initial and boundary value problems to nonhomogeneous linear differential equations with nonconstant coefficients of any order. However, without loss of generality, the approach has…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…

Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…

In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…

This work provides a theoretical framework for the pose estimation problem using total least squares for vector observations from landmark features. First, the optimization framework is formulated with observation vectors extracted from…

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…