Estimation of a system pulse transfer function in the presence of noise

Levin, M.

doi:10.1109/tac.1964.1105690

Cited by 150 publications

(28 citation statements)

References 10 publications

(1 reference statement)

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“…In this case, the OLS solution is identical to the maximum likelihood one (Mendel 1987). If the errors have a different distribution, this approach leads to a biased estimate of the solution vector (Levin 1964). The use of the Euclidean norm relates to the S in OLS: the sum of squares of residuals is minimized.…”

Section: The Solution Of An Over-determined System Of Equationsmentioning

confidence: 99%

Toward a solution of allocation in life cycle inventories: the use of least-squares techniques

Marvuglia

Cellura

Heijungs

2010

Int J Life Cycle Assess

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Purpose The matrix method for the solution of the socalled inventory problem in LCA generally determines the inventory vector related to a specific system of processes by solving a system of linear equations. The paper proposes a new approach to deal with systems characterized by a rectangular (and thus non-invertible) coefficients matrix. The approach, based on the application of regression techniques, allows solving the system without using computational expedients such as the allocation procedure. Methods The regression techniques used in the paper are (besides the ordinary least squares, OLS) total least squares (TLS) and data least squares (DLS). In this paper, the authors present the application of TLS and DLS to a case study related to the production of bricks, showing the differences between the results accomplished by the traditional matrix approach and those obtained with these techniques. The system boundaries were chosen such that the resulting technology matrix was not too big and thus easy to display, but at the same time complex enough to provide a valid demonstrative example for analyzing the results of the application of the above-described techniques. Results and discussion The results obtained for the case study taken into consideration showed an obvious but not overwhelming difference between the inventory vectors obtained by using the least-squares techniques and those obtained with the solutions based upon allocation. The inventory vectors obtained with the DLS and TLS techniques are closer to those obtained with the physical rather than with the economic allocation. However, this finding most probably cannot be generalized to every inventory problem. Conclusions Since the solution of the inventory problem in life cycle inventory (LCI) is not a standard forecasting problem because the real solution (the real inventory vector related to the investigated functional unit) is unknown, we are not able to compute a proper performance indicator for the implemented algorithms. However, considering that the obtained least squares solutions are unique and their differences from the traditional solutions are not overwhelming, this methodology is worthy of further investigation. Recommendations In order to make TLS and DLS techniques a valuable alternative to the traditional allocation procedures, there is a need to optimize them for the very particular systems that commonly occur in LCI, i.e., systems with sparse coefficients matrices and a vector of constants whose entries are almost always all null but one. This optimization is crucial for their applicability in the LCI context.

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Section: The Solution Of An Over-determined System Of Equationsmentioning

confidence: 99%

Toward a solution of allocation in life cycle inventories: the use of least-squares techniques

Marvuglia

Cellura

Heijungs

2010

Int J Life Cycle Assess

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“…The relations (11) and (12) are the basis for the Frisch method. They constitute a system of 2n + 1 equations in 2n + 2 unknowns.…”

Section: Three Variants Of the Frisch Schemementioning

confidence: 99%

“…One of the first solutions for the identification of dynamic EIV models was given in [11] and [1]. After these pioneer works, this topic has been reproposed by several authors with different approaches.…”

Section: Introductionmentioning

confidence: 99%

Comparison of three Frisch methods for errors-in-variables identification

Mei

Söderström

Soverini

et al. 2008

IFAC Proceedings Volumes

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The errors-in-variables framework concerns static or dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors-invariables models. One of the more promising approaches is the so-called Frisch scheme. This report decribes three different estimation criteria within the Frisch context and compares their estimation accuracy on the basis of the asymptotic covariance matrices of the estimates. Some final numerical examples support the theoretical results and analyze the behaviour of the methods in case of finite number of data.

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“…Fourier series techniques involve compounded approximations and do not afford a clear picture of the errors involved (3,4). Sampled-data techniques involve aliasing problems which also make errors difficult to evaluate (5)(6)(7)(8)(9)(10). None of these methods clearly shows how close the result is to the best (in some prescribed sense) n th order rational function.…”

Section: Introductionmentioning

confidence: 99%

Rational transform approximation via the Laguerre spectrum

Steiglitz

1965

Journal of the Franklin Institute

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Estimation of a system pulse transfer function in the presence of noise

Cited by 150 publications

References 10 publications

Toward a solution of allocation in life cycle inventories: the use of least-squares techniques

Toward a solution of allocation in life cycle inventories: the use of least-squares techniques

Comparison of three Frisch methods for errors-in-variables identification

Rational transform approximation via the Laguerre spectrum

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