Abstract
Evidence filtering is a promising approach to infer the “frequency” characteristics of various events of interest from temporally and spatially distributed sensor data based on Dempster–Shafer evidence theory. The design of evidence filters has several challenges due to the nonnegativity of the filters’ coefficients. This paper presents an iterative constrained minimax method for the magnitude response design of finite impulse response evidence filters with a prescribed transition-band magnitude drop. The method iteratively converts the problem into a sequence of minimax magnitude error subproblems of the evidence filters with given minimum stopband attenuations. The convergence of the global solutions of these subproblems to the global solution of the original problem is established. By using a recently published algorithm to solve the subproblems, the proposed method has obtained better magnitude responses than existing methods in design examples of this paper.
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B. Anderson, M. Deistler, L. Farina, L. Benvenuti, Nonnegative realization of a linear system with nonnegative impulse response. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 43(2), 134–142 (1996)
A. Antoniou, W.-S. Lu, Practical Optimization: Algorithms and Engineering Applications (Springer, New York, 2007)
D.A. Dewasurendra, P. Bauer, K. Premaratne, Evidence filtering. IEEE Trans. Signal Process. 55(12), 5796–5805 (2007)
L. Farina, S. Rinaldi, Positive Linear Systems: Theory and Applications (Wiley Interscience, New York, 2000)
D.L. Hall, J. Llinas, Handbook of Multisensor Data Fusion (CRC Press, Boca Raton, 2001)
C.Y.F. Ho, B.W.K. Ling, H.H.H. Dam, K.L. Teo, Minimax passband group delay nonlinear phase peak constrained FIR filter design without imposing desired phase response. Int. J. Innov. Comput. Inf. Control 8(5(B)), 3863–3874 (2012)
J.R. Howell, Some classes of step-response models without extrema. Automatica 33(7), 1427–1428 (1997)
X. Lai, Optimal design of nonlinear-phase FIR filters with prescribed phase error. IEEE Trans. Signal Process. 57(9), 3399–3410 (2009)
X. Lai, Projected least-squares algorithms for constrained FIR filter design. IEEE Trans. Circuits Syst. I: Regular Pap. 52(11), 2436–2443 (2005)
X. Lai, Z. Lin, Optimal design of constrained FIR filters without phase response specifications. IEEE Trans. Signal Process. 62(17), 4532–4546 (2014)
X. Lai, A. Xue, Z. Lin, C. Lai, Minimax design of nonnegative finite impulse response filters, In: Proceedings the 15th International Conference on Information Fusion, Singapore, pp. 441–1446, 2012
B.A. Leon de la Barra, On undershoot in SISO systems. IEEE Trans. Autom. Control 39(3), 578–581 (1994)
Y. Liu, Analysis and Design of Systems with a Nonnegative Impulse Response (University of Notre Dame, PhD dissertation) (2011)
Y. Liu, P.H. Bauer, On the non-negative impulse response of multi-dimensional systems. Multidimension. Syst. Signal Process. 25(1), 95–114 (2014)
Y. Liu, P.H. Bauer, A new approach to designing high performance non-negative finite-impulse response filters, In: Proceedings of 2010 IEEE Workshop on Signal Processing Systems, Cupertino, pp. 444–449, 2010
Y. Liu, P.H. Bauer, Frequency domain limitations in the design of non-negative impulse response filters. IEEE Trans. Signal Process. 58(9), 4535–4546 (2010)
Y. Liu, P.H. Bauer, Fundamental properties of non-negative impulse response filters. IEEE Trans. Circuits Syst. I: Regular Pap. 57(6), 1338–1347 (2010)
S.C. Pei, C.C. Tseng, W.S. Yang, FIR filter designs with linear constraints using the eigenfilter approach. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 45(2), 232–237 (1998)
K. Premaratne, D.A. Dewasurendra, P.H. Bauer, Evidence combination in an environment with heterogeneous sources. IEEE Trans. Syst. Man Cybern. Part A 37(3), 298–309 (2007)
A. Rachid, Some conditions on zeros to avoid step-response extrema. IEEE Trans. Autom. Control 40(8), 1501–1503 (1995)
G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976)
P.P. Vaidyanathan, Eigenfilters: a new approach to least-squares FIR filter design and applications including Nyquist filters. IEEE Trans. Circuits Syst. 34(1), 11–23 (1987)
R.R. Yager, J. Kacprzyk, M. Fedrizzi, Advances in the Dempster-Shafer Theory of Evidence (Wiley, New York, 1994)
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This work was supported in part by the National Nature Science Foundation of China under Grants 61175001 and 61333009 and in part by the National Basic Research Program of China under Grants 2012CB821200.
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Liu, J., Guo, Y., Xue, A. et al. An Iterative Constrained Minimax Approach to Magnitude Response Design of FIR Evidence Filters. Circuits Syst Signal Process 34, 3559–3572 (2015). https://doi.org/10.1007/s00034-015-0019-3
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DOI: https://doi.org/10.1007/s00034-015-0019-3