# Uncertainty Analysis and Improvement of Propellant Gauging System Applied in Space
## 1 Introduction  
The measurement accuracy of residual propellant during the end-of-life state shows great value for spacecraft [1; 2; 3]. Based on the measured results, a detailed transferring strategy for the grave orbit can be formulated [4]. Usually, the cost of one commercial communication satellite reaches several billion dollars. It is a valuable cost-saving method to improve the measuring accuracy of the residual propellant at the end-of-life state. In this way, the satellite can be used until the very end of its service life. Researchers focusing on the ultrahigh precision method for propellant gauging have been studying this for decades [1; 5]. Since the 1960s, major countries, including the United States of America and Europe, have investigated the residual propellant mass gauge (MG) [1]. There are several main MG methods. The bookkeeping (BK) method is based on the accumulation of the engine's work time in space. The measurement uncertainty of the used propellant increases as time lapses. The BK method is primarily used in the short time measurement when the engine is working. The Pressure-Volume-Temperature method (PVT) [6; 7; 8; 9] is often chosen as a long-duration measurement method as it is an absolute error method. The uncertainty of PVT is decided by the uncertainty of the precision of the gas law to real gas as well as the precision of the temperature and pressure sensors applied in the measurement. The PVT method is based on the gas law of pressure, temperature, and volume for a certain amount of gas. Usually, the gas law is applied with real gas modification. The Compression Mass Gauge (CMG) is a modified PVT method, which uses a bellow to change the total gas volume with the tank volume [5; 10; 11; 12]. For instance, the changed volume is 0.01% of the tank volume. The CMG method is a promising way to obtain ultrahigh precision as well as a relatively heavy weight. The use of the CMG method also requires ultrahigh precision of the real gas law. [PERSON] [12; 13; 14; 15] conducted a series of ground tests using the CMG method. From their theoretical analysis, the measuring uncertainty of CMG can be within 1%, which maintains the application requirement. [PERSON] [16; 17] accomplished the residual propellant mass gauge with a modified propellant gauge system in an FY-4 satellite fromthe HS601. The measuring uncertainty was approximately 1.65%. The Propellant Gauge System (PGS) method is another improved PVT method, which uses a certain amount of gas to inject into the tank. From the pressure and temperature before and after the gas injection, the amount of gas in the tank can be calculated. The PGS method is usually applied in a large satellite that contains a rather large tank. In order to improve its use, the right theoretical model, such as isothermal or adiabatic process assumption, is firstly discussed. The obvious shortcoming of the PGS method is the limit of the injected gas amount. The Optical Mass Gauge (OMG) [2; 18; 19; 20] method is based on the energy loss law during the process where the light is passed from liquid to gas. It uses the Beer-Lambert Law. The OMG method is promising for use in large tanks. However, the inner surface of the tank is required to be smooth, and the optical fiber is settled in certain locations. [PERSON] [18] manufactured a theoretical machine of the OMG method by building an optical measuring setup. The uncertainty of liquid Oxygen on the ground is approximately 3%. The Thermal Mass Gauge (TMG) method [21; 22; 23] is applied according to the thermal response to a given thermal signal. When it comes to the end of a satellite, there remains little propellant. The thermal response can be distinguished easily as the temperature varies to a certain amount of given heat. The uncertainty of TMG is unacceptable at the early age of a satellite as there is too much propellant. In recent years, TMG has been growing to become a new research hot point [22; 23; 24], and it shows high measuring precision at a rather low propellant fulfillment.