Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (6): 1142-1157.doi: 10.21629/JSEE.2018.06.04
收稿日期:
2016-12-11
出版日期:
2018-12-25
发布日期:
2018-12-26
Mahmoudreza HADAEGH1(), Hamid KHALOOZADEH2,*()
Received:
2016-12-11
Online:
2018-12-25
Published:
2018-12-26
Contact:
Hamid KHALOOZADEH
E-mail:mr_hadaegh@yahoo.com;h_khaloozadeh@kntu.ac.ir
About author:
HADAEGH Mahmoudreza received his B.S. degree in electronics engineering from Shiraz University, Shiraz, Iran, in 1999, M.S. degree in control engineering from K. N. Toosi University of Technology, Tehran, in 2001. He is currently a Ph.D. student in control engineering with the Department of Electrical and Computer Engineering, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran. Now he is an instructor in Islamic Azad University and his interests include target tracking for single and multiple targets and wireless sensor networks. E-mail: . [J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1142-1157.
Mahmoudreza HADAEGH, Hamid KHALOOZADEH. Modified switched IMM estimator based on autoregressive extended Viterbi method for maneuvering target tracking[J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1142-1157.
"
Initialization (for j = 1, 2, ..., n) |
n: the number of parallel models in IMM. |
M: the number of AR model coefficients. |
N: the highest degree of polynomial used to approximate the range. |
Attention: M >N + 1. |
m: the most probable paths used in the EV algorithm. |
Attention: 1≤m ﹤ n (m = 1 in EV1 and m = 2 in EV2). |
x0jandP0jare initial estimate and initial covariance; |
The process noise covariance: Q = qrTI (T is sampling time, and Iis identity matrix; |
Initial model probability: μ0(j) = 1/n; |
Model transition probability: P = {pij}, i, j = 1, 2, ..., n. |
Step 1 Calculation of transition matrix (for j = 1, 2, ..., n) |
In every time step, the convex quadratic programming problem (25) should be solved, and the transition matrix Aj k|k?1 is obtained by (5) in every AR model. |
Attention: It is the special part of the proposed method in which the AR idea is incorporated. |
Step 2 Model-conditioned re-initialization (for j = 1, 2, ..., n & s = 1, 2, ..., m) |
$\mu_{k-1}(l_{sj}|j) = \dfrac{\max^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}}{{ }\sum^m_{s = 1}{\max}^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}}$ |
$\mu_{k-1}(l_{sj}|j) = \dfrac{\max^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}}{{ }\sum^m_{s = 1}{\max}^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}}$ |
Mixing estimate: $\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{0j}_{k-1} = { }\sum^m_{s = 1}\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{l_{sj}}_{k-1}\mu_{k-1}(l_{sj}|j)$ |
Mixing covariance: ${{{\mathit{\boldsymbol{P}}}}}^{0j}_{k-1} = { }\sum^m_{s = 1}\mu_{k-1}(l_{sj}|j)\{{{{\mathit{\boldsymbol{P}}}}}^{l_{sj}}_{k-1}+ [\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{l_{sj}}_{k-1}-\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{0j}_{k-1}]\times[\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{l_{sj}}_{k-1}-\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{0j}_{k-1}]'\}$. |
Step 3 Model-conditioned filtering (for j = 1, 2, ..., n) |
Predicted state: $\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{j}_{k|k-1} = {{{\mathit{\boldsymbol{A}}}}}^{j}_{k|k-1}\widehat{{{{\mathit{\boldsymbol{x}}}}}}^{0j}_{k-1|k-1}$ |
Predicted covariance: ${{{\mathit{\boldsymbol{P}}}}}^j_{k|k-1}\! = \!{{{\mathit{\boldsymbol{A}}}}}^j_{k|k-1}{{{\mathit{\boldsymbol{P}}}}}^{0j}_{k-1|k-1}({{{\mathit{\boldsymbol{A}}}}}^j_{k|k-1})^{{{\rm{T}}}}\!+\!{{{\mathit{\boldsymbol{Q}}}}}^j$ |
Filter gain: ${{{\mathit{\boldsymbol{K}}}}}^j_{k} = {{{\mathit{\boldsymbol{P}}}}}^j_{k|k-1}({{{\mathit{\boldsymbol{H}}}}}^j_k)^{{{\rm{T}}}}({{{\mathit{\boldsymbol{S}}}}}^j_k)^{-1}$ |
${{{\mathit{\boldsymbol{S}}}}}^j_k = {{{\mathit{\boldsymbol{H}}}}}^j_k{{{\mathit{\boldsymbol{P}}}}}^j_{k|k-1}({{{\mathit{\boldsymbol{H}}}}}^j_k)^{{{\rm{T}}}}+{{{\mathit{\boldsymbol{R}}}}}^j_k$ |
Updated state: $\widehat{{{{\mathit{\boldsymbol{x}}}}}}^j_{k|k} = \widehat{{{{\mathit{\boldsymbol{x}}}}}}^j_{k|k-1}+{{{\mathit{\boldsymbol{K}}}}}^j_k{{{\mathit{\boldsymbol{d}}}}}^j_k$, where ${{{\mathit{\boldsymbol{d}}}}}^j_k = {{{\mathit{\boldsymbol{z}}}}}_j-{{{\mathit{\boldsymbol{H}}}}}^j_k\widehat{{{{\mathit{\boldsymbol{x}}}}}}^j_{k|k-1}$ |
Updated covariance: ${{{\mathit{\boldsymbol{P}}}}}^j_{k|k} = [{{{\mathit{\boldsymbol{I}}}}}^j-{{{\mathit{\boldsymbol{K}}}}}^j_k{{{\mathit{\boldsymbol{H}}}}}^j_k]{{{\mathit{\boldsymbol{P}}}}}^j_{k|k-1}$ |
Step 4 Model probability update (for $j = 1, 2, \ldots, n$) |
Model probability update (for $j = 1, 2, \ldots, n$) |
Model likelihood: ${\it\Lambda}^j_k = N({{{\mathit{\boldsymbol{d}}}}}^j_k; 0, {{{\mathit{\boldsymbol{S}}}}}^j_k)$ Model probability: $\mu_k(j) = \dfrac{{ }{\it\Lambda}_k\sum^m_{s = 1}{\max}^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}} {{ }\sum^n_{j = 1}{\it\Lambda}_k(j)\sum^m_{s = 1}{\max}^s_{1{\leqslant} i{\leqslant} n}\{p_{ij}\mu_{k-1}(i)\}}$ |
Step 5 Calculation of m largest model probabilities (for $r = 1, 2, \ldots, m$) |
$\widetilde{\mu}_k(\widetilde{l}_r) = \dfrac{\max^r_{1{\leqslant} i{\leqslant} n}\{\mu_{k}(j)\}}{{ }\sum^m_{r = 1}{\max}^r_{1{\leqslant} i{\leqslant} n}\{\mu_{k-1}(j)\}'}$ |
$\widetilde{l}_{r} = \arg\{\max^r_{1{\leqslant} i{\leqslant} n}\{\mu_{k}(j)\}\}$ |
Step 6Estimate fusion |
Overall estimate: $\widehat{{{{\mathit{\boldsymbol{x}}}}}}_k = { }\sum^m_{r = 1}\widetilde{\mu}_k(\widetilde{l}_r)\widehat{{{{\mathit{\boldsymbol{x}}}}}}_k^{\widetilde{l}_r}$ |
"
Comparison of position estimations for different algorithms according to (56) | Time interval/s | $C\!M\!P_{p\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{p\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm AR}}$ | $C\!M\!P_{p\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EV2}}$ | $C\!M\!P_{p\mbox{-}{\rm AR}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{p\mbox{-}{\rm EV2}\; {\rm vs}\; {\rm CA}}$ |
0–200 | 5.423 | 7.558 | 8.165 | 0.978 | 1.235 | |
200–400 | 12.165 | 10.125 | 19.267 | 13.836 | 2.030 3 | |
400–600 | 11.433 | 2.158 7 | 9.346 9 | 2.899 | 1.469 | |
600–800 | 66.229 | 1.785 | 85.719 | 24.919 | 2.443 | |
800–1000 | 23.154 | 3.458 | 35.746 | 19.743 | 1.584 | |
Comparison ofx-velocity estimationsfor differentalgorithmsaccording to (57) | Time interval/s | $C\!M\!P_{vx\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{vx\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm AR}}$ | $C\!M\!P_{vx\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EV2}}$ | $C\!M\!P_{vx\mbox{-}{\rm AR}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{vx\mbox{-}{\rm EV2}\; {\rm vs}\; {\rm CA}}$ |
0–200 | 1.068 | 1.584 | 1.021 | 0.877 | 1.005 | |
200–400 | 1.055 | 1.615 | 1.051 | 0.915 | 1.154 | |
400–600 | 5.401 | 1.159 | 5.491 | 2.651 | 1.166 | |
600–800 | 1.255 | 1.687 | 1.548 | 1.054 | 1.114 | |
800–1000 | 9.762 | 8.746 | 9.154 | 7.119 | 7.256 | |
Comparison of y-velocity estimations for different algorithms according to (57) | Time interval/s | $C\!M\!P_{vy\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{vy\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm AR}}$ | $C\!M\!P_{vy\mbox{-}{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EV2}}$ | $C\!M\!P_{vy\mbox{-}{\rm AR}\; {\rm vs}\; {\rm CA}}$ | $C\!M\!P_{vy\mbox{-}{\rm EV2}\; {\rm vs}\; {\rm CA}}$ |
0–200 | 1.178 | 1.072 | 0.987 | 0.824 | 0.912 | |
200–400 | 1.101 | 1.856 | 1.142 | 0.826 | 1.151 | |
400–600 | 6.455 | 1.106 | 9.852 | 2.954 | 1.002 | |
600–800 | 1.167 | 2.065 | 1.507 | 1.007 | 1.523 | |
800–1000 | 10.875 | 8.166 | 8.462 | 8.463 | 5.451 |
"
Time interval/s | $C\!M\!P_{p-{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EKF}}$ | $C\!M\!P_{vx-{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EKF}}$ | $C\!M\!P_{vy-{\rm S\mbox{-}AREV}\; {\rm vs}\; {\rm EKF}}$ |
0–200 | 36.32 | –5.760 | –7.180 |
200–400 | 43.06 | 1.013 | 0.963 |
400–600 | 52.20 | 12.02 | 19.490 |
600–800 | 67.16 | 0.897 | 0.388 |
800–1000 | 85.18 | 7.020 | 3.260 |
1 | LI X R, JILKOV V P. A survey of maneuvering target tracking. Part IV: decision-based methods. Proc. of SPIE Conference on Signal and Data Processing of Small Targets, 2002: 4728-4760. |
2 | BAR-SHALOM Y, BIRMIWAL K. Variable dimension filter for maneuvering target tracking. IEEE Trans. on Aerospace Electronics Systems, 1982, 18 (5): 621- 629. |
3 |
ZHANG Z, WU Y, SUN W. Modeling and adaptive motion/force tracking for vertical wheel on rotating table. Journal of Systems Engineering and Electronics, 2015, 26 (5): 1060- 1069.
doi: 10.1109/JSEE.2015.00115 |
4 |
WANG S, DA X, LI M, et al. Adaptive back-tracking search optimization algorithm with pattern search for numerical optimization. Journal of Systems Engineering and Electronics, 2016, 27 (2): 395- 406.
doi: 10.1109/JSEE.2016.00041 |
5 |
YANG J, LI P, LI Z, et al. Multiple extended target tracking algorithm based on Gaussian surface matrix. Journal of Systems Engineering and Electronics, 2016, 27 (2): 279- 289.
doi: 10.1109/JSEE.2016.00028 |
6 | KHALOOZADEH H, KARSAZ A. Modified input estimation technique for tracking maneuvering targets. IET Radar Sonar & Navigation, 2009, 3 (1): 30- 41. |
7 |
MAZOR E, AVERBUCH A, BAR-SHALOM Y, et al. Interacting multiple model methods in target tracking: a survey. IEEE Trans. on Aerospace Electronics Systems, 1998, 34 (1): 103- 123.
doi: 10.1109/7.640267 |
8 |
FU X, JIA Y, DU J, et al. New interacting multiple model algorithms for the tracking of the maneuvering target. IET Control Theory Applications, 2010, 4 (10): 2184- 2194.
doi: 10.1049/iet-cta.2009.0583 |
9 |
HO T J. A switched IMM-extended Viterbi estimator-based algorithm for maneuvering target tracking. Automatica, 2011, 47, 92- 98.
doi: 10.1016/j.automatica.2010.10.005 |
10 | FOO P H, NG G W. Combining the interacting multiple model method with particle filters for maneuvering target tracking. IET Radar Sonar & Navigation, 2011, 5 (3): 234- 255. |
11 |
BOERS Y, DRIESSEN J N. Interacting multiple model particle filter. IEE Proceeding of Radar, Sonar and Navigation, 2003, 150 (5): 344- 349.
doi: 10.1049/ip-rsn:20030741 |
12 | LANEUVILLE D, BAR-SHALOM Y. Maneuvering target tracking: a Gaussian mixture based IMM estimator. Proc. of IEEE/AIAA Aerospace Conference, 2012: 1-12. |
13 |
LAN J, LI X R, JILKOV V P, et al. Second-order Markov chain based multiple-model algorithm for maneuvering target tracking. IEEE Trans. on Aerospace Electronics Systems, 2013, 49 (1): 3- 19.
doi: 10.1109/TAES.2013.6404088 |
14 |
LI X R. Multiple-model estimation with variable structure. IEEE Trans. on Automatic Control, 2000, 45 (11): 2047- 2060.
doi: 10.1109/9.887626 |
15 | YU C H, CHOI J W. Interacting multiple model filter-based distributed target tracking algorithm in underwater wireless sensor networks. International Journal of Control, Automation and Systems, 2014, 12 (3): 618- 627. |
16 |
LI X R, JILKOV V P. Survey of maneuvering target tracking. IEEE Trans. on Aerospace Electronics Systems, 2005, 41 (4): 1255- 1321.
doi: 10.1109/TAES.2005.1561886 |
17 |
JING L, VADAKKEPAT P. Interacting MCMC particle filter for tracking maneuvering target. Digital Signal Processing, 2010, 20, 561- 574.
doi: 10.1016/j.dsp.2009.08.011 |
18 | SINGIRESU S R. Engineering optimization: theory and practice. 4th ed New York: Wiley, 2009. |
19 |
LI X R, JILKOV V P. Survey of maneuvering target tracking. IEEE Trans. on Aerospace Electronics Systems, 2003, 39 (4): 1333- 1364.
doi: 10.1109/TAES.2003.1261132 |
20 |
SESHADRI N, SUNDBERG C E W. List Viterbi decoding algorithms with applications. IEEE Trans. on Communications, 1994, 42 (2/3/4): 313- 323.
doi: 10.1109/TCOMM.1994.577040 |
21 | JIN B, JIU B, SU T, et al. Switched Kalman filter-interacting multiple model algorithm based on optimal autoregressive model for maneuvering target tracking. IET Radar, Sonar & Navigation, 2014, 9 (2): 199- 209. |
22 |
HO T J. A switched IMM-extended Viterbi estimator-based algorithm for maneuvering target tracking. Automatica, 2011, 47 (1): 92- 98.
doi: 10.1016/j.automatica.2010.10.005 |
23 |
VÄLIVIITA S, OVASKA S J, VAINIO O. Polynomial predictive filtering in control instrumentation: a review. IEEE Trans. on Industrial Electronics, 1999, 46 (5): 876- 888.
doi: 10.1109/41.793335 |
24 |
XU L, LI X R, DUAN Z, et al. Modelling and state estimation for dynamic systems with linear equality constraints. IEEE Trans. on Signal Processing, 2013, 61 (11): 2927- 2939.
doi: 10.1109/TSP.2013.2255045 |
25 | MEYER C D. Matrix analysis and applied linear algebra. Philadelphia: SIAM, 2000. |
26 | BAR-SHALOM Y, LI X R. Estimation and tracking, principle, techniques and software. Boston: Artech House, 1993. |
27 |
HO T J, CHEN B S. Novel extended Viterbi-based multiplemodel algorithms for state estimation of discrete-time systems with Markov jump parameters. IEEE Trans. on Signal Processing, 2006, 54 (2): 393- 404.
doi: 10.1109/TSP.2005.861753 |
28 | HERAB H M, KHALOOZADEH H. Extended input estimation method for tracking non-linear maneuvering targets with multiplicative noises. IET Radar, Sonar & Navigation, 2016, 10 (9): 1683- 1690. |
29 | RAHMATI H, KHALOOZADEH H, AYATI M. Novel approach for nonlinear maneuvering target tracking based on input estimation. Proc. of the International Conference on Mechanical and Aerospace Engineering, 2012: 4415-4423 |
No related articles found! |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||