Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

Errors of measurement and least squares estimation in a simple recursive model of dynamic equilibrium

Abstract: where Yt and Xt are subject to random errors of measurement ut and vt, respectively, with E(u) = E(vt) = 0, E(u2) = u, E(v2) = 2, E(utvt) = , and E(utu')E(vtsv) = 0 for t # t', is applied to a simple system of difference equations. The paper treats two such models, which differ in that one system is specified as deterministic except for measurement error, while the second model includes random "shocks" in the equations as well. The investigation focuses on the possible consistency of least squares estimates of structural parameters in both cases. Mann and Wald [3] have demonstrated the consistency property of least squares estimates in stochastic difference equations which contain a shock term, and T. W. Anderson [1] has more recently shown such estimates to possess asymptotic normal distributions. One way argue, and perhaps quite legitimately, against the inclusion of measurement errors and shocks as separate entities in systems such as those under consideration. This separation, however, does provide a useful contrast with regard to the consistency property of LS estimates as compared to the case when only shocks (which subsume measurement error) are present in the specification of the system. When measurement errors are separated from shocks, LS yields consistent estimates for the explosive case of cobweb equilibrium and inconsistent estimates under convergence. The above phenomenon rests on the perhaps more interesting results for a recursive model where only measurement errors are present. This change in how the random terms enter the system, as contrasted to the Mann and Wald or Anderson formulations, causes zero correlation between observed variables and inconsistent LS estimates in the equations under convergence. Again, under explosion, LS provides consistent estimators of structural parameters.

Recursive-Least-Squares-Based Real-Time Estimation of Supercapacitor Parameters

Abstract: The letter suggests utilizing a recursive-least-squares identification algorithm for real-time estimation of supercapacitor equivalent capacitance and resistance. Estimation is required since both parameters are subject to age, temperature, and terminal-voltage-based variations in addition to typical 20% tolerance of manufacturer provided values. The proposed approach allows calculating the device instantaneous state of energy used as a fuel gauge instead of the commonly adopted state of charge. Experimental results are given to verify the feasibility of the proposed method.

On the Convergence of the Partial Least Squares Path Modeling Algorithm

Abstract: This paper adds to an important aspect of Partial Least Squares (PLS) path modeling, namely the convergence of the iterative PLS path modeling algorithm. Whilst conventional wisdom says that PLS always converges in practice, there is no formal proof for path models with more than two blocks of manifest variables. This paper presents six cases of non-convergence of the PLS path modeling algorithm. These cases were estimated using Mode A combined with the factorial scheme or the path weighting scheme, which are two popular options of the algorithm. As a conclusion, efforts to come to a proof of convergence under these schemes can be abandoned, and users of PLS should triangulate their estimation results.

Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem

Abstract: In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured total least squares problem. Due to the low displacement rank of the involved matrices and the sparsity of the generators, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of our algorithm as compared to other algorithms for solving this type of structured total least squares problem. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least squares estimator.