256
I. A. Kudryavtseva and K. A. Rybakov
References
1. Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, New York (1970)
2. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with Applications to Tracking and
Navigation. Wiley, New York (2001)
3. Bain, A., Crisan, D.: Fundamentals of Stochastic Filtering. Springer, New York (2009)
4. Crisan, D.: The stochastic filtering problem: A brief historical account. Appl. Probab. Index
51(A), 13–22 (2014)
5. Gustafsson, F., Gunnarsson, F., Bergman, N., Forssell, U., Jansson, J., Karlsson, R., Nordlund,
P.-J.: Particle filters for positioning, navigation and tracking. IEEE Trans. Signal Process. 50(2),
425–437 (2002)
6. Arasaratnam, I., Haykin, S., Hurd, T.R.: Cubature Kalman filtering for continuous-discrete
systems: theory and simulations. IEEE Trans. Signal Process. 58(10), 4977–4993 (2010)
7. Chari, V., Jawahar, C.: Multiple plane tracking using unscented Kalman filter. In: Proceedings of
50th IEEE Conference on Decision and Control and European Control Conference, pp. 2914–
2919 (2011)
8. Jeon, D., Eun, Y., Bang, H., Yeom, C.: Nonlinear aircraft tracking filter utilizing a point mass
flight dynamics model. J. Aerosp. Eng. 227(11), 1795–1810 (2012)
9. Song, H., Shin, V., Jeon, M.: Mobile node localization using fusion prediction-based interacting
multiple model in cricket sensor network. IEEE Trans. Ind. Electron. 59(11), 4349–4359 (2012)
10. Cook, B., Arnett, T., Macmann, O., Kumar, M.: Real-time radar-based tracking and state
estimation of multiple non-conformant aircraft. In: Proceedings of 55th AIAA Aerospace
Sciences Meeting (2017)
11. Zorina, O.A., Izmailov, E.A., Kukhtevich, S.E., Portnov, B.I., Fomichev, A.V., Vavilova,
N.B., Golovan, A.A., Papusha, I.A., Parusnikov, N.A.: Enhancement of INS/GNSS integration
capabilities for aviation-related applications. Gyroscopy Navig. 8(4), 248–258 (2017)
12. Rudenko, E.A.: Autonomous path estimation for a descent vehicle using recursive Gaussian
filters. J. Comput. Sys. Sc. Int. 57(5), 695–712 (2018)
13. Rudenko, E.A.: Optimal recurrent nonlinear filter of a large order for jump diffusion Markov
signals. J. Comput. Sys. Sc. Int. 59(1), 49–62 (2020)
14. Chugai, K.N., Kosachev, I.M., Rybakov, K.A.: Approximate Filtering Methods in ContinuousTime Stochastic Systems. In: Jain, L.C., Favorskaya, M.N., Nikitin, I.S., Reviznikov, D.L.
(eds.) Advances in Computational Mechanics and Numerical Simulation. Smart Innovation,
Systems and Technologies, vol. 173, pp. 351–371. Springer, Singapore (2020)
15. Tupysev, V.A., Litvinenko, Yu.A.: Application of polynomial-type filters to integrated navigation systems with modular architecture. In: Proceedings of 26th Saint Petersburg International
Conference on Integrated Navigation Systems (ICINS) (2019)
16. Stepanov, O.A., Vasiliev, V.A., Toropov, A.B., Loparev, A.V., Basin, M.V.: Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial
measurements. J. Franklin Inst. 356(10), 5573–5591 (2019)
17. Hazewinkel, M.: Lectures on linear and nonlinear filtering. In: Schiehlen, W.O., Wedig, W.
(eds.) Analysis and Estimation of Stochastic Mechanical Systems. International Centre for
Mechanical Sciences (Courses and Lectures), vol. 303, pp. 103–136. Springer, Vienna (1988)
18. Averina, T.A., Rybakov, K.A.: Using maximum cross section method for filtering jumpdiffusion random processes. Rus. J. Numer. Anal. Math. Modelling 35(2), 55–67 (2020)
19. Lototsky, S., Mikulevicius, R., Rozovskii, B.L.: Nonlinear filtering revisited: a spectral
approach. SIAM J. Control Optim. 35(2), 435–461 (1997)
20. Ahmed, N.U., Radaideh, S.M.: A powerful numerical technique solving Zakai equation for
nonlinear filtering. Dyn. Control 7(3), 293–308 (1997)
21. Gobet, E., Pagès, G., Pham, H., Printemps, J.: Discretization and simulation of Zakai equation.
SIAM J. Numer. Anal. 44(6), 2505–2538 (2006)
22. Luo, X., Yau, S.S.-T.: Complete real time solution of the general nonlinear filtering problem
without memory. IEEE Trans. Autom. Control 58(10), 2563–2578 (2013)
I. A. Kudryavtseva and K. A. Rybakov
References
1. Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, New York (1970)
2. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with Applications to Tracking and
Navigation. Wiley, New York (2001)
3. Bain, A., Crisan, D.: Fundamentals of Stochastic Filtering. Springer, New York (2009)
4. Crisan, D.: The stochastic filtering problem: A brief historical account. Appl. Probab. Index
51(A), 13–22 (2014)
5. Gustafsson, F., Gunnarsson, F., Bergman, N., Forssell, U., Jansson, J., Karlsson, R., Nordlund,
P.-J.: Particle filters for positioning, navigation and tracking. IEEE Trans. Signal Process. 50(2),
425–437 (2002)
6. Arasaratnam, I., Haykin, S., Hurd, T.R.: Cubature Kalman filtering for continuous-discrete
systems: theory and simulations. IEEE Trans. Signal Process. 58(10), 4977–4993 (2010)
7. Chari, V., Jawahar, C.: Multiple plane tracking using unscented Kalman filter. In: Proceedings of
50th IEEE Conference on Decision and Control and European Control Conference, pp. 2914–
2919 (2011)
8. Jeon, D., Eun, Y., Bang, H., Yeom, C.: Nonlinear aircraft tracking filter utilizing a point mass
flight dynamics model. J. Aerosp. Eng. 227(11), 1795–1810 (2012)
9. Song, H., Shin, V., Jeon, M.: Mobile node localization using fusion prediction-based interacting
multiple model in cricket sensor network. IEEE Trans. Ind. Electron. 59(11), 4349–4359 (2012)
10. Cook, B., Arnett, T., Macmann, O., Kumar, M.: Real-time radar-based tracking and state
estimation of multiple non-conformant aircraft. In: Proceedings of 55th AIAA Aerospace
Sciences Meeting (2017)
11. Zorina, O.A., Izmailov, E.A., Kukhtevich, S.E., Portnov, B.I., Fomichev, A.V., Vavilova,
N.B., Golovan, A.A., Papusha, I.A., Parusnikov, N.A.: Enhancement of INS/GNSS integration
capabilities for aviation-related applications. Gyroscopy Navig. 8(4), 248–258 (2017)
12. Rudenko, E.A.: Autonomous path estimation for a descent vehicle using recursive Gaussian
filters. J. Comput. Sys. Sc. Int. 57(5), 695–712 (2018)
13. Rudenko, E.A.: Optimal recurrent nonlinear filter of a large order for jump diffusion Markov
signals. J. Comput. Sys. Sc. Int. 59(1), 49–62 (2020)
14. Chugai, K.N., Kosachev, I.M., Rybakov, K.A.: Approximate Filtering Methods in ContinuousTime Stochastic Systems. In: Jain, L.C., Favorskaya, M.N., Nikitin, I.S., Reviznikov, D.L.
(eds.) Advances in Computational Mechanics and Numerical Simulation. Smart Innovation,
Systems and Technologies, vol. 173, pp. 351–371. Springer, Singapore (2020)
15. Tupysev, V.A., Litvinenko, Yu.A.: Application of polynomial-type filters to integrated navigation systems with modular architecture. In: Proceedings of 26th Saint Petersburg International
Conference on Integrated Navigation Systems (ICINS) (2019)
16. Stepanov, O.A., Vasiliev, V.A., Toropov, A.B., Loparev, A.V., Basin, M.V.: Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial
measurements. J. Franklin Inst. 356(10), 5573–5591 (2019)
17. Hazewinkel, M.: Lectures on linear and nonlinear filtering. In: Schiehlen, W.O., Wedig, W.
(eds.) Analysis and Estimation of Stochastic Mechanical Systems. International Centre for
Mechanical Sciences (Courses and Lectures), vol. 303, pp. 103–136. Springer, Vienna (1988)
18. Averina, T.A., Rybakov, K.A.: Using maximum cross section method for filtering jumpdiffusion random processes. Rus. J. Numer. Anal. Math. Modelling 35(2), 55–67 (2020)
19. Lototsky, S., Mikulevicius, R., Rozovskii, B.L.: Nonlinear filtering revisited: a spectral
approach. SIAM J. Control Optim. 35(2), 435–461 (1997)
20. Ahmed, N.U., Radaideh, S.M.: A powerful numerical technique solving Zakai equation for
nonlinear filtering. Dyn. Control 7(3), 293–308 (1997)
21. Gobet, E., Pagès, G., Pham, H., Printemps, J.: Discretization and simulation of Zakai equation.
SIAM J. Numer. Anal. 44(6), 2505–2538 (2006)
22. Luo, X., Yau, S.S.-T.: Complete real time solution of the general nonlinear filtering problem
without memory. IEEE Trans. Autom. Control 58(10), 2563–2578 (2013)