[b]1 Introduction[/b] Due to its simple structure, high reliability, small size, light weight, low cost, and ease of maintenance, strapdown inertial systems have developed rapidly in recent years and have been applied in some tactical weapons. However, its application scope is limited to some extent because its accuracy has not yet reached the level of platform systems. GPS (Global Positioning System)/inertial combination technology has achieved remarkable success in improving accuracy, reducing costs, providing all-weather, and global navigation, and its application scope is gradually expanding. However, due to GPS licensing restrictions, dynamic performance, and anti-interference capabilities, its military application scope is limited to some extent. The solution is to conduct research on the combination technology of inertial technology and multi-system navigation satellite systems to avoid the limitations of the single GPS/INS combination mode. By adopting a deep combination of GPS and inertial systems, the dynamic performance and anti-interference capabilities of navigation systems can be improved, providing high-performance navigation equipment for military equipment. In the later stages of World War II, the Germans were the first to use simple strapdown inertial instruments as the core component of the autonomous guidance system of the V-2 short-range ballistic missile. Subsequently, the United States and the Soviet Union entered the long-term arms race of the post-war Cold War. With the development and continuous improvement of various strategic and tactical missiles, space technology, aviation, navigation, and land combat vehicles, inertial technology has also achieved unprecedented development and progress. The primary focus of inertial technology development has been on platform systems and various inertial instruments based on air-float, liquid-float, and electrostatic levitation support technologies. Over a period of more than 30 years, gyroscope drift improved from approximately 10°/h to 0.000015°/h, an improvement of almost six orders of magnitude. However, gyroscopes used in actual engineering applications remained at around 0.001°/h for a long time. Achieving high-precision inertial systems has come at a very high cost; the development cost of a single floating platform system exceeded $10 million, and even after mass production, the cost of each unit reached $4 million. Only the U.S. Air Force has used this expensive product on its MX strategic missiles. Market demand is the driving force behind scientific development and technological progress. With the collapse of the Soviet-Eastern European system and the end of the Cold War between the US and the Soviet Union, the development of various strategic offensive weapons cooled down, while various defensive tactical weapons developed rapidly. This shifted the focus of inertial instruments and systems from simply pursuing high precision to prioritizing cost reduction while also considering reliability, speed, mobility, and miniaturization as key technical indicators. The rapid advancements in electronic technology, computer technology, and modern control theory have created favorable conditions for the development of strapdown inertial technology. The successful development of a new generation of low-cost, medium-precision inertial instruments, such as flexural gyroscopes, laser gyroscopes, fiber optic gyroscopes, and quartz accelerometers, has laid the material foundation for strapdown systems. Research on strapdown technology, such as algorithm programming, error modeling, error calibration and compensation, and testing techniques, has developed rapidly. New strapdown inertial system products are widely used in various tactical weapons and aircraft attitude control systems. With the continuous improvement of the accuracy of solid-state instruments and the gradual perfection of error compensation technology, strapdown systems will gradually replace platform systems. [b]2. Accuracy of Strapdown Systems[/b] Currently, the accuracy of strapdown systems has not yet reached the level achieved by platform systems, and cannot fully meet the requirements of various military and civilian applications. The reasons are as follows: a) After the drift of new strapdown inertial instruments, such as dynamically tuned gyroscopes, laser gyroscopes, and fiber optic gyroscopes, reaches 0.01°/h, and the scaling factor error of quartz accelerometers reaches 1×10⁻⁴, further improvements in instrument accuracy will encounter limitations in processing technology, materials, and optoelectronic components. Further improvements in instrument hardware accuracy will become even more difficult, and substantial additional investment may not yield proportional technical benefits, while also casting a shadow on the low-cost advantage of strapdown systems. b) The inertial instruments in strapdown systems are directly connected to the carrier. Harsh dynamic environments of aircraft, such as overload impacts, vibrations, and maneuvering, will introduce dynamic errors into the inertial instruments and strapdown systems. These errors are difficult to compensate for, which is also the main reason why strapdown systems have not yet reached the accuracy level of platform systems. c) To fully leverage the technological advantages of strapdown inertial systems, and utilize high-precision measurement information from other systems to compensate for and suppress the increasing errors of the inertial system over time, thereby improving navigation (guidance) accuracy, a combined navigation system based on the inertial system and supplemented by various other measurement information is established. The development of inertial technology indicates that the general trend in future inertial technology development is: a shift from traditional mechanical rotor gyroscopes to solid-state gyroscopes (laser, fiber optic, and hemispherical resonator gyroscopes) and further towards micromechanical vibrating gyroscopes based on semiconductor silicon; a shift from frame-type platform systems to strapdown systems; and a development from pure inertial strapdown systems to multi-system combined navigation systems based on inertial systems. [b]3 Advantages of Combined Navigation Technology[/b] Combined navigation system technology relieves the inertial system of its accuracy burden while retaining its autonomy, relatively high accuracy over short periods, and the ability to continuously provide all navigation (guidance) parameters. The US Pershing II ballistic missile employs a medium-precision flexure gyroscope platform, combined with digital scene matching terminal guidance technology, achieving a CEP (Circular Error Probable) of 39 m at a range of 1,800 km. The Tomahawk cruise missile, using the LN-35 pure inertial system, has a navigation error of 1.17 km/h, already a remarkably high level of accuracy. However, by further employing inertial and terrain matching technology, the CEP is further reduced to 100 m at a cruise range of 2,000 km. The Trident II intercontinental ballistic missile uses a combined starlight/inertial guidance system, achieving a CEP of 120 m, comparable to the accuracy achieved by the MX missile's float platform technology. However, the Trident II's development cost was only one-fifth that of the MX. While such combined guidance systems require significant manpower, resources, and funding for creating high-precision terrain maps of various operational areas and developing high-precision starlight sensors, they are still much simpler than float platform technology. Utilizing existing foreign navigation satellite resources to research the integration of navigation satellites and inertial systems is a relatively simple technical approach. GPS, short for Navstar GPS, is a second-generation satellite-based radio navigation system developed by the United States starting in the 1970s. The system includes a ground master control station, monitoring stations, and injection stations, and comprises 24 navigation satellites in space. GPS satellite deployment was completed in 1994, and it officially entered service. The former Soviet Union also established its own Global Navigation Satellite System (GLONASS), whose working principle and composition are similar to GPS. The basic idea of ​​the Global Navigation Satellite System (GNSS), which the International Civil Aviation Organization (ICAO) has determined and implemented, is to establish a multi-constellation satellite navigation system, not controlled solely by any one major power. The first generation of GNSS consisted of GPS, GLONASS, and INMARSAT, with INMARSAT being the communication and navigation satellite of the International Maritime Satellite Organization. It includes 4 geostationary satellites and 15 mid-to-high altitude (10,000 km) asynchronous satellites. This system is relatively independent of GPS and GLONASS, and can still meet global navigation needs even if the former two shut down or withdraw from service. GPS can provide users with accurate position, velocity, and timing data globally, 24/7, and its navigation data is stable and accurate. However, it cannot provide attitude information of the vehicle, and its performance is affected by environmental conditions (mountains, forests, tunnels, urban buildings, and the vehicle itself), vehicle maneuvering, and radio interference. Inertial navigation systems (INS) have the advantages of good autonomy, being unaffected by the environment, vehicle maneuvering, and radio interference. They can continuously provide all navigation parameters (position, velocity, and attitude), have a fast data update rate, a large range, and high relative accuracy over a short period. However, as the operating time increases, navigation errors accumulate, and for strapdown systems, there are additional dynamic errors. Implementing a GPS/SINS integrated navigation system based on an inertial system can complement each other's advantages and compensate for each other's shortcomings. The high-precision positioning information from the GPS receiver is used through a combined filter to calibrate and compensate for the accumulated errors of the strapdown system, improving navigation accuracy. Simultaneously, the speed and acceleration information from the strapdown system is used to assist the GPS receiver in improving its anti-interference capability and dynamic performance. Even if the GPS receiver's measurement data fails or disappears for a short period, the inertial system can still operate independently and provide high-precision navigation data. This is an optimal combination scheme, whose performance, cost, and size meet the navigation technology requirements of various vehicles. However, this combined navigation scheme also has some shortcomings in practical applications: a) GPS is controlled by the US military, which applies SA noise signals to the satellite system, causing the receiver's accuracy to decrease when using C/A codes, with positioning errors reaching 100 m. Furthermore, given the development of the international situation, the US military may impose regional blockades or shutdowns on foreign users, which is a cause for concern for foreign military users. To mitigate this risk, the combination of multi-constellation satellite navigation systems and inertial systems should be researched and developed. A multi-compatible combination mode is adopted, integrating the inertial system with the US GPS, Russia's GLONASS, and the International Maritime Satellite Organization's INMARSAT, to reduce the risk of certain major powers unilaterally controlling, blocking, or even shutting down foreign users at specific times, preventing any single country from monopolizing satellite resources, and ensuring the safe and reliable operation of users. b) To effectively solve the anti-interference and dynamic performance problems of GPS receivers, it is necessary to conduct in-depth research on some issues related to deep integration. For example, converting inertial velocity information (acceleration information) into Doppler frequency change estimates and inputting them into the receiver's carrier loop can extend the receiver's fast tracking capability and improve dynamic performance. Alternatively, adaptive bandwidth control and adaptive correlator range extension techniques can be used to improve the receiver's dynamic performance. Of course, this is not an easy task; it requires changing the internal circuitry and modifying the internal software. However, the required investment is not as large as developing inertial devices, while the benefits are considerable. The observations of the position integration (i.e., shallow integration) filter are the position and velocity information output by the GPS receiver, which has undergone primary filtering. If this information is used for a second filtering with the output information of the inertial system, followed by feedback correction, system instability is likely to occur. To reduce the correlation of filtering, the iteration frequency of the combined filter must be strictly limited. A combination mode of pseudorange and pseudorange rate of change can avoid the correlation problem of the combined filter. Because pseudorange and pseudorange rate of change are raw measurement data from the GPS receiver channel, without filtering processing, there is no correlation problem in the combined filter. These measurement data are very large, making calculation in the combined filter inconvenient. Using the residuals of pseudorange and pseudorange/pseudorange rate of change for combined filtering is much more convenient. These are not raw data, but rather quasi-raw data after compensating for deterministic errors. The residual data are small in value and change slowly, having less impact on the combined filter in terms of time delay and inaccuracy. The residuals of pseudorange and pseudorange rate of change can also be used to realize a multi-satellite measurement model for the combined filter, the so-called "All-in-view" measurement model. Using multi-satellite measurement information can achieve better navigation accuracy and improve data fluctuations caused by satellite switching. c) To broaden the application scope of the GPS/SINS combined system, new silicon micro solid-state inertial devices with lower cost and smaller size, suitable for mass production, should be researched and designed. In recent years, the development of GPS receivers has progressed rapidly, with costs decreasing significantly. Multi-channel, miniaturized multi-path navigation OEM GPS module boards have been commercialized. With the development of microelectronics, optoelectronics, and microfabrication technologies, silicon micro inertial devices have also developed rapidly. These inertial devices use silicon as the substrate material and are microfabricated using photolithography and anisotropic etching techniques from semiconductor integrated circuit production. This results in low-cost, highly reliable, vibration-resistant, shock-resistant, and extremely small size and weight inertial devices. For example, silicon micro gyroscopes include dual-frame gyroscopes, tuning fork gyroscopes, and frame vibrating wheel gyroscopes. A single gyroscope is less than 1 mm², and currently, their accuracy is not high, with a bandwidth of 60 Hz and a resolution of 0.1 °/s. It is projected that by the end of this century, gyroscope drift will reach 1 °/h. The maximum size of a silicon micro accelerometer is 1 mm, with a bias stability (after compensation) of 20 mg (-10 ℃～75 ℃) and a resolution of 2 mg (60 Hz bandwidth). Because of their small size, multiple gyroscopes and accelerometers can be fabricated on a single chip, forming an inertial measurement unit (IMU). If these are combined with a multi-channel OEM GPS receiver module to create a GPS/SINS integrated navigation system, a high-precision, highly reliable, environmentally resistant, extremely small, and low-cost navigation device can be obtained, with immeasurable commercial value and application potential. [b]References[/b] 1 Peng Yunxiang. Where is missile inertial technology headed? Modern Military, 1989(7). 2 Greiff P, et al. Vibrating whell micromechanical gyro. IEEE, 1996. Editor: He Shiping