Maximum Likelihood Based Joint Angle-Frequency Estimation Using QPSO Algorithm

Abstract:

In this paper, the Maximum Likelihood (ML) method using Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is applied to the problem of estimating the direction-of-arrival (DOA) and the Doppler frequency of multiple signal sources impinging on an antenna array simultaneously. The extended observability matrix containing the angle and frequency parameters is established using state-space model. The ML method is used to estimate the parameters accurately and convert the problem from parameter estimation to a nonlinear multidimensional function optimization. Then the DOA and Doppler frequency are estimated by optimizing the likelihood function using QPSO algorithm. The proposed method reserves the asymptotic unbiased estimation of the ML method and reduces the computational burden of calculating the solution. Besides, the estimated parameters can be paired automatically.

• Periodical: Applied Mechanics and Materials (Volumes 513-517)
• Pages: 1227-1232
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.513-517.1227
• Online since: February 2014
• Authors: Zhi Cheng Zhang*, Xiao Hui Yu, Yao Wu Shi
• Keywords: Direction-of-Arrival (DOA), Doppler Frequency, Maximum Likelihood, QPSO

References

[1] A. N. Lemma, A. J. van der Veen and E. F. Deprettere, Joint angle-frequency estimation using multi-resolution ESPRIT, IEEE International Conference on Acoustics, Speech and Signal Processing, Seattle, USA, pp.1957-1960, (1998).

DOI: 10.1109/icassp.1998.681447

[2] M. Haardt and J. A. Nossek, 3-D unitary ESPRIT for joint 2-D angle and carrier estimation, IEEE International Conference on Acoustics, Speech and Signal Processing, Munich, Germany, pp.255-258, (1997).

DOI: 10.1109/icassp.1997.599617

[3] A. N. Lemma, A. J. van der Veen and E. F. Deprettere, Analysis of ESPRIT Based joint angle-frequency estimation, IEEE International Conference on Acoustics, Speech and Signal Processing, Istanbul，Turkey, pp.3053-3056, (2000).

DOI: 10.1109/icassp.2000.861181

[4] A. N. Lemma, A. J. van der Veen and E. F. Deprettere, Analysis of joint angle-frequency estimation using ESPRIT, IEEE Transactions on Signal Processing, vol. 51, no. 5, pp.1264-1283, (2003).

DOI: 10.1109/tsp.2003.810306

[5] F. L. Liu, J. K Wang and R. Y. Du, Unitary-JAFE algorithm for joint angle–frequency estimation based on Frame–Newton method, Signal Processing, vol. 90, no. 3, pp.809-820, (2010).

DOI: 10.1016/j.sigpro.2009.08.013

[6] J. D. Lin, W. H. Fang, Y. Y. Wang and J. T. Chen, FSF MUSIC for Joint DOA and frequency estimation and its performance analysis, IEEE Transactions on Signal Processing, vol. 54, no. 12, pp.4529-4542, (2006).

DOI: 10.1109/tsp.2006.882112

[7] F. Atheley, Asymptotically decoupled angle-frequency estimation with sensor arrays, The Thirty-Third Asilomar Conference on Signal, Systems and Computers, Pacific Grove, USA, p.1098–1102, (1999).

DOI: 10.1109/acssc.1999.831879

[8] H. G. Wang and S. Kay, Maximum likelihood angle-Doppler estimator using importance sampling, IEEE Transactions on Aerospace and Electronics Systems, vol. 46, no. 2, pp.610-622, (2010).

DOI: 10.1109/taes.2010.5461644

[9] J. Sun, W. Fang and W. B. Xu, Particle swarm optimization with particles having quantum behavior, Congress on Evolutionary Computation, Portland, USA, pp.326-331, (2004).

DOI: 10.1109/cec.2004.1330875

[10] W. Fang, J. Sun and Z. P. Xie, Convergence analysis of quantum-behaved particle swarm optimization algorithm and study on its control parameter, Acta Physica Sinica, vol. 59, no. 6, pp.3686-3694, 2010. (in Chinese).

DOI: 10.7498/aps.59.3686

[11] L. Boccato, R. Krummenauer, R. Attux and A. Lopes, Application of natural computing algorithms to maximum likelihood estimation of direction of arrival, Signal Processing, vol. 92, no. 5, pp.1338-1352, (2012).

DOI: 10.1016/j.sigpro.2011.12.004