© The Institution of Engineering and Technology
The digital filtering technology has been widely applied in a majority of signal processing applications. For the linear systems with state-space model, Kalman filter provides optimal state estimates in the sense of minimum-mean-squared errors and maximum-likelihood estimation. However, only with accurate system parameters and noise statistical properties, the estimation obtained by standard Kalman filter is the optimal state estimate. Most of time, the exact noise statistical properties could not be obtained as a priori information or even wrong statistical properties may be captured by the offline method. This may lead to a poor performance (even divergence) of Kalman filtering algorithm. In this study, a novel real-time filter, named as fast minimum norm filtering algorithm, has been proposed to deal with the case when the covariance matrices of the process and measurement noises were unknown in the linear time-invariant systems with state-space model. Tests have been performed on numerical examples to illustrate that the fast minimum norm filtering algorithm could be used to obtain acceptable precision state estimation in comparison with the standard Kalman filter for the discrete-time linear time-invariant systems.
References
-
-
1)
-
B. Hassibi ,
A. Sayed ,
T. Kailath
.
H infinity optimality of the LMS algorithm.
IEEE Trans. Signal Process.
,
267 -
279
-
2)
-
11. Carlson, N.: ‘Fast triangular formulation of the square root filter’, AIAA J., 1973, 11, (9), pp. 1259–1265 (doi: 10.2514/3.6907).
-
3)
-
3. Mehra, R.K.: ‘On the identification of variance and adaptive Kalman filtering’, IEEE Trans. Autom. Control, 1970, AC-15, (2), pp. 175–184 (doi: 10.1109/TAC.1970.1099422).
-
4)
-
22. Ra, W.S., Whang, I.H., Park, J.B.: ‘Non-conservative robust Kalman filtering using a noise corrupted measurement matrix’, IET Control Theory Appl., 2009, 3, (9), pp. 1226–1236 (doi: 10.1049/iet-cta.2008.0224).
-
5)
-
27. Azimi-Sadjadi, M.R., Xiao, R.R., Yu, X.: ‘Neural network decision directed edge-adaptive Kalman filter for image estimation’, IEEE Trans. Image Process., 1999, 8, (4), pp. 589–592 (doi: 10.1109/83.753746).
-
6)
-
S. Bhaumik ,
S. Sadhu ,
T.K. Ghoshal
.
Risk-sensitive formulation of unscented Kalman filter.
IET Control Theory Appl.
,
4 ,
375 -
382
-
7)
-
9. Khanesar, M.A., Kayacan, E., Teshnehlab, M., Kaynak, O.: ‘Extended Kalman filter based learning algorithm for type-2 fuzzy logic systems and its experimental evaluation’, IEEE Trans. Ind. Electron., 2012, 59, (11), pp. 4443–4455 (doi: 10.1109/TIE.2011.2151822).
-
8)
-
28. Xiao, X., Feng, B., Wang, B.: ‘On-line realization of SVM Kalman filter for MEMS gyro’. Proc. of the Third Int. Conf. on Measuring Technology and Mechatronics Automation, vol. 2., (IEEE Computer Society, Shanghai, China, 2011), pp. 768–770.
-
9)
-
13. Julier, S.J., Uhlmann, J.K.: ‘New extension of the Kalman filter to nonlinear systems’. Proc. of the Int. Society for Optical Engineering, vol 3068, (, Orlando, FL, USA, April 1997), pp. 182–193.
-
10)
-
K. Xiong ,
H. Zhang ,
L. Liu
.
Adaptive robust extended Kalman filter for nonlinear stochastic systems.
IET Control Theory Appl.
,
3 ,
239 -
250
-
11)
-
R.E. Kalman
.
A new approach to linear filtering and prediction problems.
Trans. ASME-J. Basic Eng.
,
35 -
45
-
12)
-
S. Jaferzadeh ,
S. Lascu ,
S. Fadali
.
State estimation of induction motor drives using the unscented Kalman Filter.
IEEE Trans. Ind. Electron.
,
99
-
13)
-
3. de Marina, H.G., Pereda, F.J., Giron-Sierra, J.M., Espinosa, F.: ‘UAV attitude estimation using unscented Kalman filter and TRIAD’, IEEE Trans. Ind. Electron., 2012, 59, (11), pp. 4465–4474 (doi: 10.1109/TIE.2011.2163913).
-
14)
-
18. Petersen, I.R., Savkin, A.V.: ‘Robust Kalman filtering for signals and systems with large uncertainties’ (BirkhauseBoston, 1999).
-
15)
-
4. Xu, H., Mannor, S.: ‘A Kalman filter design based on the performance/robustness tradeoff’, IEEE Trans. Autom. Control, 2009, 54, (5), pp. 1171–1175 (doi: 10.1109/TAC.2009.2017816).
-
16)
-
5. Bogosyan, S., Barut, M., Gokasan, M.: ‘Braided extended Kalman filters for sensorless estimation in induction motors at high-low/zero speed’, IET Control Theory Appl., 2007, 1, (4), pp. 987–998 (doi: 10.1049/iet-cta:20060329).
-
17)
-
R. Cui ,
B. Ren ,
S.S. Ge
.
Synchronised tracking control of multi-agent system.
IET Control Theory Appl.
,
5 ,
603 -
614
-
18)
-
2. Wu, W., Chen, S., Qin, A.Q.: ‘Online estimation of ship dynamic flexure model parameters for transfer alignment’, IEEE Trans. Control Syst. Technol., 2013, 21, (5), pp. 1666–1678 (doi: 10.1109/TCST.2012.2214778).
-
19)
-
24. Doucet, A., De Freitas, N., Gordon, N.: ‘Sequential Monte Carlo Methods in Practice’ (Springer, 2001).
-
20)
-
Y. Mostofi ,
R.M. Murray
.
To drop or not to drop: design principles for Kalman filtering over wireless fading channels.
IEEE Trans. Autom. Control
,
2 ,
376 -
381
-
21)
-
R. Kalman ,
R. Bucy
.
New results in linear filtering and prediction theory.
ASME Trans. Part D (J. Basic Eng.)
,
95 -
108
-
22)
-
S. Schmidt
.
Kalman filter: its recognition and development for aerospace applications.
J. Guid. Control
,
1 ,
4 -
7
-
23)
-
N.A. Carlson
.
Federated square root filter for decentralized parallel processes.
IEEE Trans. Aerosp. Electron. Syst.
,
3 ,
517 -
525
-
24)
-
9. Kluge, S., Reif, K., Brokate, M.: ‘Stochastic stability of the extended Kalman filter with intermittent observations’, IEEE Trans. Autom. Control, 2010, 55, (2), pp. 514–518 (doi: 10.1109/TAC.2009.2037467).
-
25)
-
J. Zhong ,
Y.-F. Fung
.
Case study and proofs of ant colony optimisation improved particle filter algorithm.
IET Control Theory Appl.
,
5 ,
689 -
697
-
26)
-
17. Chang, L., Hu, B., Chang, G., Li, A.: ‘Marginalised iterated unscented Kalman filter’, IET Control Theory Appl., 2012, 6, (6), pp. 847–854 (doi: 10.1049/iet-cta.2011.0457).
-
27)
-
B. Chen ,
L. Yu ,
W. Zhang
.
Robust Kalman fltering for uncertain state delay systems with random observation delays and missing measurement.
IET Control Theory Appl.
,
17 ,
1945 -
1954
-
28)
-
29. Feng, B., Ma, H.B., Fu, M.Y., Wang, S.T.: ‘A framework of finite-model Kalman filter with case study: MVDP-FMKF algorithm’, Acta Autom. Sin., 2013, 39, (8), pp. 1246–1256 (doi: 10.1016/S1874-1029(13)60048-8).
-
29)
-
3. Mohamed, A.H., Schwarz, K.P.: ‘Adaptive Kalman filtering for INS/GPS’, J. Geod., 1999, 73, (4), pp. 193–203 (doi: 10.1007/s001900050236).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.0109
Related content
content/journals/10.1049/iet-cta.2014.0109
pub_keyword,iet_inspecKeyword,pub_concept
6
6