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Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter

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Abstract

This paper conducts performance evaluation for the ultra-tight integration of Global positioning system (GPS) and inertial navigation system (INS) by use of the fuzzy adaptive strong tracking unscented Kalman filter (FASTUKF). An ultra-tight GPS/INS integration architecture involves fusion of the in-phase and quadrature components from the correlator of the GPS receiver with the INS data. These two components are highly nonlinearly related to the navigation states. The strong tracking unscented Kalman filter (STUKF) is based on the combination of an unscented Kalman filter (UKF) and strong tracking algorithm (STA) to perform the parameter adaptation task for various dynamic characteristics. The STA is basically a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. In order to resolve the shortcoming in a traditional approach for selecting the softening factor through personal experience or computer simulation, the Fuzzy Logic Adaptive System (FLAS) is incorporated for determining the softening factor, leading to the FASTUKF. Two examples are provided for illustrating the effectiveness of the design and demonstrating effective improvement in navigation estimation accuracy and, therefore, the proposed FASTUKF algorithm can be considered as an alternative approach for designing the ultra tightly coupled GPS/INS integrated navigation system.

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Acknowledgements

This work is partially supported by the National Science Council of the Republic of China under grant numbers NSC 98-2221-E-019-021-MY3 and NSC 101-2221-E-019-027-MY3.

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Authors and Affiliations

  1. Department of Communications, Navigation and Control Engineering, National Taiwan Ocean University, 2 Peining Rd., Keelung, 202-24, Taiwan

    Dah-Jing Jwo, Chi-Fan Yang, Chih-Hsun Chuang & Ting-Yu Lee

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  1. Dah-Jing Jwo
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  2. Chi-Fan Yang
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  3. Chih-Hsun Chuang
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  4. Ting-Yu Lee
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Corresponding author

Correspondence to Dah-Jing Jwo.

Appendices

Appendix A: The derivatives in the Jacobian matrix

The derivatives in the Jacobian matrix H k are given by

and

where the following derivatives can be calculated

Taking derivatives of θ e and ω e with respect to the three components of position gives

and

respectively. Furthermore, taking derivatives of θ e and ω e with respect to the velocities gives

and

respectively.

Appendix B: Generation of the DGPS corrections

In this appendix, the typical DGPS implementation methods are reviewed [1], followed by the setup applicable for the ultra-tight GPS/INS integration. The two typical DGPS correction methods include (1) the position-space DGPS, which provides the position correction; and (2) range-space DGPS, which provides the pseudorange correction (PRC).

Since the ultra-tightly coupled architecture performs integration using the data in the correlator components I (in-phase) and Q (quadrature), derivation of the suitable DGPS corrections is necessary to fulfil the application requirements. The proposed DGPS correction method, here referred to as the correlator-space DGPS, is designed to generate the corrections for the correlator outputs. The method is summarized as follows. From Eqs. (4a), (4b), (5), and (6) in Sect. 2, E[I] and E[Q] depends on the errors of the carrier frequency and phase, and subsequently they can be described in terms of the position and velocity:

(36)
(37)

The DGPS corrections for the I and Q values can be obtained:

(38)
(39)

where E[I]GPS_base and E[Q]GPS_base are observed by the base station receiver, while E[I]cal and E[Q]cal are calculated based on the known coordinates of the (fixed reference) station. These two values can be calculated in a similar manner way as that for the INS predicted I and Q, i.e., E[I]INS and E[Q]INS, except that the former two are evaluated based on the known navigation states such that good accuracy can be achieved.

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Jwo, DJ., Yang, CF., Chuang, CH. et al. Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter. Nonlinear Dyn 73, 377–395 (2013). https://doi.org/10.1007/s11071-013-0793-z

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  • DOI: https://doi.org/10.1007/s11071-013-0793-z

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