A new conditional posterior Cramér-Rao lower bound for a class of nonlinear systems

References

• Arasaratnam, I., & Haykin, S. (2009). Cubature Kalman filter. IEEE Transactions on Automatic Control, 54, 1254–1269.
   Web of Science ®Google Scholar
• Arulampalam, S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50, 174–189.
   Web of Science ®Google Scholar
• Bar-Shalom, Y., Li, X.R., & Kirubarajan, T. (2001). Estimation with applications to tracking and navigation: Theory algorithms and software. New York, NY: Wiley-Interscience.
   Google Scholar
• Christian, M., Nadia, O., & Francois, L.G. (2001). Improving regularized particle filters in sequential Monte Carlo method in practice. New York, NY: Springer-Verlag.
   Google Scholar
• Desbouvries, F., Petetin, Y., & Ait-El-Fquih, B. (2011). Direct, prediction-and smoothing-based Kalman and particle filter algorithms. Signal Processing, 91, 2064–2077.
   Web of Science ®Google Scholar
• Duník, J., Straka, O., & Šimandl, M. (2013). Stochastic integration filter. IEEE Transactions on Automatic Control, 58, 1561–1566.
   Web of Science ®Google Scholar
• Guo, D., & Wang, X.D. (2006). Quasi-Monte Carlo filtering in nonlinear dynamic systems. IEEE Transactions on Signal Processing, 54, 2087–2098.
   Web of Science ®Google Scholar
• Han, H., Ding, Y.S., Hao, K.R., & Hu, L.J. (2013). Particle filter for state estimation of jump Markov nonlinear system with application to multi-targets tracking. International Journal of Systems Science, 44, 1333–1343.
   Web of Science ®Google Scholar
• Hernandez, M.L., Kirubarajan, T., & Bar-Shalom, Y. (2004). Multisensor resource deployment using posterior Cramér-Rao bounds. IEEE Transactions on Aerospace and Electronic Systems, 40, 399–416.
   Web of Science ®Google Scholar
• Horn, R., & Johnson, C.R. (1985). Matrix analysis. New York, NY: Cambridge University Press.
   Google Scholar
• Hurtado, M., Zhao, T., & Nehorai, A. (2008). Adaptive polarized waveform design for target tracking based on sequential Bayesian inference. IEEE Transactions on Signal Processing, 56, 1120–1133.
   Web of Science ®Google Scholar
• Jia, B., Xin, M., & Cheng, Y. (2013). High-degree cubature Kalman filter. Automatica, 49, 510–518.
   Web of Science ®Google Scholar
• Kadirkamanathan, V., Li, P., Jaward, M.H., & Fabri, S.G. (2002). Particle filtering-based fault detection in non-linear stochastic systems. International Journal of Systems Science, 33, 259–265.
   Web of Science ®Google Scholar
• Kotecha, J.H., & Djurić, P.M. (2003a). Gaussian particle filtering. IEEE Transactions on Signal Processing, 51, 2592–2601.
   Web of Science ®Google Scholar
• Kotecha, J.H., & Djurić, P.M. (2003b). Gaussian sum particle filtering. IEEE Transactions on Signal Processing, 51, 2602–2612.
   Web of Science ®Google Scholar
• Lei, M., Wyk van, B.J., & Qi, Y. (2011). Online estimation of the approximate posterior Cramer-Rao lower bound for discrete-time nonlinear filtering. IEEE Transactions on Aerospace and Electronic Systems, 47, 37–57.
   Web of Science ®Google Scholar
• Mohammadi, A., & Asif, A. (2013). Decentralized conditional posterior Cramér-Rao lower bound for nonlinear distributed estimation. IEEE Signal Processing Letters, 20, 165–168.
   Web of Science ®Google Scholar
• Saha, S., & Gustafsson, F. (2012). Particle filtering with dependent noise processes. IEEE Transactions on Signal Processing, 60, 4497–4508.
   Web of Science ®Google Scholar
• Šimandl, M., Królovec, J., & Tichavskó, P. (2001). Filtering, predictive, & smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic systems. Automatica, 37, 1703–1716.
   Web of Science ®Google Scholar
• Šimandl, M., Królovec, J., & Soderstorm, T. (2006). Advanced point-mass method for nonlinear state estimation. Automatica, 42, 1133–1145.
   Web of Science ®Google Scholar
• Simon, D. (2006). Optimal state estimation: Kalman, H∞, and nonlinear approaches. New Jersey, NJ: A John Wiley & Sons.
   Google Scholar
• Tichavsky, P., Muravchik, C.H., & Nehorai, A. (1998). Posterior Cramér-Rao bounds for discrete-time nonlinear filtering. IEEE Transactions on Signal Processing, 46, 1386–1396.
   Web of Science ®Google Scholar
• van der Merwe, R., Doucet, A., de Freitas, J.F.G., & Wan, E. (2000). The unscented particle filter. In Proceedings of the Advances in Neural Information Processing Systems (pp. 584–590). Denver, CO.
   Google Scholar
• Wang, S.Y., Feng, J.C., & Tse, C.K. (2014). Spherical simplex-radial cubature Kalman filter. IEEE Signal Processing Letters, 21, 43–46.
   Web of Science ®Google Scholar
• Wang, X.X., Liang, Y., Pan, Q., Zhao, C.H., & Li, H.Z. (2012). Unscented Kalman filter for nonlinear systems with colored measurement noise. Acta Automatica Sinica, 38, 986–998.
   Google Scholar
• Wang, X.X., Liang, Y., Pan, Q., Zhao, C.H., & Yang, F. (2015). Nonlinear Gaussian smoothers with colored measurement noise. IEEE Transactions on Automatic Control, 60, 870–876.
   Web of Science ®Google Scholar
• Wang, X.X., & Pan, Q. (2014). Nonlinear Gaussian filter with the colored measurement noise. In Proceedings of the 17th International Conference on Information Fusion (pp. 1–7). Salamanca.
   Google Scholar
• Wu, Y.X., Hu, D.W., Wu, M.P., & Hu, X.P. (2006). A numerical-integration perspective on Gaussian filters. IEEE Transactions on Signal Processing, 54, 2910–2921.
   Web of Science ®Google Scholar
• Zhang, Y.G., Huang, Y.L., Li, N., & Zhao, L. (2015a). Interpolatory cubature Kalman filters. IET Control Theory & Applications, 9, 1731–1739.
   Web of Science ®Google Scholar
• Zhang, Y.G., Huang, Y.L., Li, N., & Zhao, L. (2015b). Embedded cubature Kalman filter with adaptive setting of free parameter. Signal Processing, 114, 112–116.
   Web of Science ®Google Scholar
• Zheng, Y.J., Ozdemir, O., Niu, R.X., & Varshney, P.K. (2012). New conditional posterior Cramér-Rao lower bounds for nonlinear sequential Bayesian estimation. IEEE Transactions on Signal Processing, 60, 5549–5556.
   Web of Science ®Google Scholar
• Zuo, L. (2010). Conditional PCRLB for target tracking in sensor networks. (PhD dissertation). Syracuse University, Department of Electrical Engineering and Computer Science, Syracuse, NY, Dec. 2010.
   Google Scholar
• Zuo, L., Niu, R.X., & Varshney, P.K. (2011). Conditional posterior Cramér-Rao lower bounds for nonlinear sequential Bayesian estimation. IEEE Transactions on Signal Processing, 59, 1–14.
   Web of Science ®Google Scholar