## 1 Introduction
To improve the navigation availability and attain a better anti-jamming ability, reference [8] (from the perspective of a signal design system) proposed a frequency-hopping binary offset carrier (BOC) modulation scheme with a strong anti-interference ability, in order to improve the anti-jamming capability of LEO constellation navigation at the signal-design level. For exploration of the application of a single satellite in navigation and positioning, references [9; 10; 11] located the radiation source by measuring the phase difference or frequency of the incoming wave. Additionally, references [12; 13] proposed a positioning method based on a single-satellite Doppler integral, which has a high positioning accuracy for static targets, but the positioning accuracy decreases rapidly for dynamic targets. To overcome this problem, reference [12; 13; 14] proposed a scheme based on integrated navigation. Moreover, reference [15] proposed a single-satellite positioning method based on the inertial navigation system (INS) and Doppler pseudorange difference. To solve the problem of parameter estimation and target location being divided into two independent stages in traditional single-satellite positioning, a single-satellite passive location method using spatial sparsity is proposed in [16]. To cope with the demand for location services under challenging environmental conditions, different scholars have provided different solutions in different positioning situations. Reference [17] developed an INS that can be used by a navigation vehicle to assist INS through Doppler measurements and tightly coupled LEO satellite signals when GNSSsignals are not available. Furthermore, reference [18] pointed out that under the condition of global coverage, users may have 1-3 visible satellites in different times and places and proposed that under different conditions, only Doppler observations should be used for positioning solutions. Reference [19] proposed a Doppler positioning algorithm based on a LEO satellite system in a complex environment when the GPS signal is accidentally blocked. To improve the dynamic positioning accuracy of single-satellite positioning in emergencies, reference [20] proposed an INS-aided single-satellite positioning algorithm in the case of GNSS system rejection. This INS-aided single-satellite positioning algorithm can provide certain space-based positioning services for dynamic targets. The new single-satellite integrated navigation and positioning algorithm based on broadband LEO constellation communication links offers a low-cost approach, a strong engineering practicability, and an anti-jamming scheme. The accuracy of navigation and positioning is better than the accuracy of navigation and positioning of the traditional algorithm of single-satellite and MEO constellation algorithms, and effectively overcomes the problem of INS divergence. The new single-satellite integrated navigation and positioning algorithm can provide a cm-level navigation scheme for relevant personnel engaged in outdoor tourism, exploration, or scientific research in challenging environments, such as lush forests, canyons, high latitude areas, and polar regions, without relying on GNSS. In Section 2, based on introducing the traditional single-satellite positioning algorithm, we give the principle of our algorithm and compare it with the traditional algorithm. Next, in Section 3, we model and analyze the errors involved in the system. In Section 4, based on the unscented Kalman filter (UKF), we model the state and observation vectors of the algorithm and give the corresponding state and observation equations. Finally, in Section 5, we simulate the algorithm and perform qualitative and quantitative analysis for different scenarios, comparing our algorithm with the traditional single-satellite navigation algorithm, and present our conclusion in the last section.