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This study aims to address the problem of the divergence of traditional inertial navigation system (INS)/celestial navigation system (CNS)-integrated navigation for ballistic missiles. The authors introduce Doppler navigation system (DNS) and X-ray pulsar navigation (XNAV) to the traditional INS/CNS-integrated navigation system and then propose an INS/CNS/DNS/XNAV deep integrated navigation system.

DNS and XNAV can provide velocity and position information, respectively. In addition to providing velocity information directly, DNS suppresses the impact of the Doppler effect on pulsar time of arrival (TOA). A pulsar TOA with drift bias is observed during the short navigation process. To solve this problem, the pulsar TOA drift bias model is established. And the parameters of the navigation filter are optimised based on this model.

The experimental results show that the INS/CNS/DNS/XNAV deep integrated navigation can suppress the drift of the accelerometer to a certain extent to improve the precision of position and velocity determination. In addition, this integrated navigation method can reduce the required accuracy of inertial navigation, thereby reducing the cost of missile manufacturing and realising low-cost and high-precision navigation.

The velocity information provided by the DNS can suppress the pulsar TOA drift, thereby improving the positioning accuracy of the XNAV. This reflects the “deep” integration of these two navigation methods.

There are shortcomings of modern methods of ensuring the stability of Kalman filtration in unmanned vehicles’ (UVs) navigation systems under the condition of a priori uncertainty of the dispersion matrix of measurement interference. First, it is the absence of strict criteria for the selection of adaptation coefficients in the calculation of the a posteriori covariance matrix. Secondly, it is the impossibility of adaptive estimation in real time from the condition of minimum covariance of the updating sequence due to the necessity of its preliminary calculation.

This paper considers a new approach to the construction of the Kalman filter adaptation algorithm. The algorithm implements the possibility of obtaining an accurate adaptive estimation of navigation parameters for integrated UVs inertial-satellite navigation systems, using the correction of non-periodic and unstable inertial estimates by high-precision satellite measurements. The problem of adaptive estimation of the noise dispersion matrix of the meter in the Kalman filter can be solved analytically using matrix methods of linear algebra. A numerical example illustrates the effectiveness of the procedure for estimating the state vector of the UVs’ navigation systems.

Adaptive estimation errors are sharply reduced in comparison with the traditional scheme to the range from 2 to 7 m in latitude and from 1.5 to 4 m in longitude.

The simplicity and accuracy of the proposed algorithm provide the possibility of its effective application to the widest class of UVs’ navigation systems.