A new technique for linear static state estimation based on weighted least absolute value approximations
This paper presents a new technique for solving the problem of linear static state estimation, based on weighted least absolute value (WLAV). A set ofm optimality equations is obtained, wherem=number of measurements, based on minimizing a WLAV performance index involvingn unknown state variables,m>n. These equations are solved using the left pseudo-inverse transformation, least-square sense, to obtain approximately the residual of each measurement.
Ifk is the rank of the matrixH,k=n, we choose among the optimality equations a number of equations equal to the rankk and having the smallest residuals. The solution of thesen equations inn unknowns yields the best WLAV estimation. A numerical example is reported; the results for this example are obtained by using both WLS and WLAV techniques. It is shown that the best WLAV approximation is superior to the best WLS approximation when estimating the true form of data containing some inaccurate observations.
Key WordsOptimal control linear estimation state estimation least absolute value optimal estimation
Unable to display preview. Download preview PDF.
- 1.Maybeck, P. S.,Stochastic Models Estimation and Control, Vol. 1, Academic Press, Orlando, Florida, 1979.Google Scholar
- 2.Bryson, A. E., andHo, Y. C.,Applied Optimal Control, Hemisphere Publishing Corporation, Washington, DC, 1975.Google Scholar
- 3.Stengel, R. F.,Stochastic Optimal Control, John Wiley and Sons, New York, New York, 1986.Google Scholar
- 4.Barrodale, I., andRoberts, F. D. K.,An Improved Algorithm for Discrete ℓ 1 Linear Approximation, SIAM Journal on Numerical Analysis, Vol. 10, No. 5, pp. 839–848, 1973.Google Scholar
- 5.Kotiuga, W. W., andVidyasagar, M.,Bad Data Rejection Properties of Weighted Least Absolute Value Techniques Applied to Static State Estimation, IEEE Transaction on Power Apparatus and Systems, Vol. PAS-101, No. 4, pp. 844–853, 1982.Google Scholar
- 6.Kotiuga, W. W.,Development of a Least Absolute Value Power System Tracking State Estimator, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 5, pp. 1160–1166, 1985.Google Scholar
- 7.Kotiuga, W. W.,Power System State Estimation Using Least Absolute Value Techniques, PhD Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1982.Google Scholar
- 8.Kotiuga, W. W.,Potential of Least Absolute Value Approximation in Solving Power System Planning and Operations Problems, Proceedings of the Spring Meeting of the Canadian Electrical Association, Montreal, Québec, Canada, 1986.Google Scholar
- 9.Lewis, F. L.,Optimal Estimation with an Introduction to Stochastic Control Theory, John Wiley and Sons, New York, New York, 1986.Google Scholar
- 10.Rosenberg, B., andCarlson, B.,A Simple Approximation of the Sampling Distribution of Least Absolute Residuals Regression Estimates, Communications in Statistics, Simulation, and Computation, Vol. B6, No. 4, pp. 421–437, 1977.Google Scholar
- 11.Sukov, A. N.,Comparison of the Median and the Mean in the Case of a Small Sample, Geodesy and Aerophotography, Vol. 13, pp. 326–329, 1971.Google Scholar