Hostname: page-component-5c6d5d7d68-tdptf Total loading time: 0 Render date: 2024-08-16T11:22:42.638Z Has data issue: false hasContentIssue false

Sensability and Excitability Metrics Applied to Navigation Systems Assessment

Published online by Cambridge University Press:  04 June 2019

Martín España*
Affiliation:
(National Commission of Space Activities of Argentina (CONAE), Paseo Colon 751, 1063 Ciudad de Buenos Aires, Argentina)
Juan Carrizo
Affiliation:
(Department of Electronics, Faculty of Engineering, University of Buenos Aires, Paseo Colon 850, 1063 Ciudad de Buenos Aires, Argentina)
Juan I. Giribet
Affiliation:
(Department of Electronics, Faculty of Engineering, University of Buenos Aires, Paseo Colon 850, 1063 Ciudad de Buenos Aires, Argentina)

Abstract

To evaluate the aptness of a navigation system in a particular application, the designer needs to assess its performance over typical trajectories travelled by the vehicle itself. Moreover, he or she may be required to judge which components of the kinematics state may be better estimated (and which will not). The main contributions of this work are two novel and complementary performance measures that, in concert, allow for the assessment of a navigation system within the actual context of its application over specific trajectories. For a given on board instrumental configuration, the “excitability metric” permits the isolation of the contribution of the information conveyed by the vehicle's motion itself, while, the “sensability metric” measures the resultant overall quality of the kinematics state estimation. The same tools could help the designer planning appropriate vehicles manoeuvres in order to obtain a required precision for each estimated component. While emphasis is given on the mathematical justification of those metrics, their use is also illustrated with real flight data recorded from a sounding rocket.

Type
Research Article
Copyright
Copyright © The Royal Institute of Navigation 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, B. D. O. and Moore, J. B. (1979). Optimal Filtering. Englew Cliffs, NJ: Prentice-Hall.Google Scholar
Bageshwar, V. L., Gebre-Egziabher, D., Garrard, W. L. and Georgiou, T. T. (2009). Stochastic Observability Test for Discrete-Time Kalman Filters. Journal of Guidance, Control and Dynamics, 32(4), pp. 13561370.Google Scholar
Baram, Y. and Kailath, T. (1988). Estimability and regulability of linear systems. IEEE Transaction on Automatic Control, 33(12), pp. 11161121.Google Scholar
Bryson, A. E. Jr. (1978). Kalman filter divergence and aircraft motion estimators. AIAA Journal of Guidance, Control, and Dynamics, 1(1), pp. 7179.Google Scholar
España, M. (2017). Navegación Integrada con Aplicaciones, (Integrated Navigation with Applications), CONAE, 2017 https://www.argentina.gob.ar/sistemas-de-navegacion-integrada-con-aplicaciones.Google Scholar
Farrell, J. A. (2008). Aided Navigation: GPS With High Rate Sensors., McGraw-Hill, New York, NY, USA.Google Scholar
Giribet, J. I., España, M. and Miranda, C. (2007). Synthetic data for validation of navigation systems. Acta Astronautica, 60(2), pp. 8895.Google Scholar
Giribet, J. I., Mas, I. and Moreno, P. (2018). Vision-Based Integrated Navigation System and Optimal Allocation in Formation Flying. Proceedings of International Conference on Unmanned Aerial Systems, Dallas, USA. pp. 52–61.Google Scholar
Ham, F. M. and Brown, R. G. (1983). Observability, Eigenvalues and Kalman Filtering. IEEE Transaction on Aerospace and Electronic Systems, 19(2), pp. 269273.Google Scholar
Hoo, S., Lee, M. H., Chun, H., Kwon, S. and Speyer, J. L. (2005). Observability of Error States in GPS/INS Integration. IEEE Transactions on Vehicular Technology, 54(2), pp. 731743.Google Scholar
Jazwinski, A. H. (1970). Stochastic processes and filtering theory, Acadademic Press, New York.Google Scholar
Krener, A. J. and Kayo, I., Measures of Unobservability, 48th IEEE CDC, Shanghai, China, Dec. 1618, 2009.Google Scholar
Mohler, R.R. and Hwang, C.S. (1988). Nonlinear Data Observability and Information. Journal. of the Franklin Institute, 325(4), 443464.Google Scholar
Moore, B.C. (1981). Principal Components Analysis in Linear Systems: Controllability, Observability and Model Reduction. IEEE Transactions on Automatic Control, 26(1), pp. 1732.Google Scholar
Rhee, I., Abdel-Hafez, M. F. and Speyer, J. L. (2004). Observability of an Integrated GPS/INS During Maneuvers. IEEE Transactions on Aerospace and Electronic Systems, 40(2), pp. 526535.Google Scholar
Shen, K., Xia, Y., Wang, M., Neusypin, K. A. and Proletarsky, A. V. (2018). Quantifying Observability and Analysis in Integrated Navigation. Journal of the Institute of Navigation, 65(2), pp. 169181.Google Scholar
Salychev, O.S. (1998). Inertial systems in navigation and geophysics. Moscow: Bauman MSTU Press.Google Scholar
Starks, H. and Woods, J. W. (1994). Probability, Random Processes and Estimation Theory for Engineers. Prentice Hall, New Jersey.Google Scholar
Tang, Y., Wu, Y., Wu, M., Wu, W., Hu, X., Shen, L. (2009). INS/GPS Integration: Global Observability Analysis. IEEE Transaction on Vehicular Technology, 58(3), pp. 11291142.Google Scholar
Willems, J. and Mitter, S. K. (1971). Controllability, Observability, Pole Allocation and State Reconstruction. IEEE Transaction on Automatic Control, 16(6), pp. 582595.Google Scholar