# On-Board Parameter Optimization for Space-Based Infrared Air Vehicle Detection Based on ADS-B Data
## 2 Methodology
### Spectral Characteristics of Civil Aircraft with Multiple Flight Phases  
The research on the infrared spectral characteristics of air targets is the basis of space-based infrared detection. Air vehicles generate infrared radiation during takeoff, cruise and landing, which can be detected using infrared detectors. The infrared radiation of the aircraft in the atmosphere mainly includes the infrared radiation of the high-temperature exhaust gas emitted by the engine, the skin radiation caused by aerodynamic heating and the scattering of the aircraft skin to the ambient infrared radiation. As the key component of an aircraft, the engine is the equipment to conduct the flight process, and its high-temperature exhaust plume generates a greater proportion of infrared radiation. The exhaust plume emitted from the engine is a selective radiator, and its infrared radiation is significantly higher in the carbon dioxide absorption spectrum, near 4.3 \(\upmu\)m. In addition, when aircraft are flying at a high speed, the temperature rise of the fuselage due to aerodynamics also produces infrared radiation. The main parameters that limit the maximum thrust of the engine are the speed of the turbofan, the pressure at the inlet of the combustion chamber and the temperature at the inlet of the turbine. Since the turbine inlet temperature is not easy to measure, the Exhaust Gas Temperature (EGT) was introduced. A high EGT is the main cause of engine repair. Therefore, most civil airliners adopt a thrust-reduced take-off mode [28]. The thrust-reduced take-off methods can be further divided in two: Derated Take-off and Flexible Take-off Thrust. The specific implementation of the two methods is not the main focus of this paper, but the EGT result of thrust reduction can be used as the modeling input for calculating the infrared spectral characteristics of civil aircraft during take-off. That is, according to the regulations of the Federal Aviation Administration (FAA), when using Derated Take-off, the maximum thrust reduction cannot exceed 40% of full thrust; when using Flexible Take-off Thrust, the maximum thrust reduction cannot exceed 25% of the maximum take-off thrust. According to Ref. [29], a typical EGT can reach 783 \({}^{\circ}\)C (1056 K) during take-off at an external temperature of 15 \({}^{\circ}\)C, while reducing to 727 \({}^{\circ}\)C (1000 K) under 25% reduced thrust take-off mode. The infrared radiant intensity of an aircraft engine plume can be expressed by  
\[I_{plume}=\varepsilon_{plume}\frac{M\Big{(}T_{plume},\lambda\Big{)}}{\pi}A_{ plume}, \tag{1}\]  
where \(T_{plume}\) is the temperature of the exhaust plume, which can use EGT to characterize different flight phases; \(\varepsilon_{plume}\) is the emissivity of the hot plume gas; \(M\Big{(}T_{plume},\lambda\Big{)}\) is the spectral radiant emittance of the plume; \(\lambda\) is the spectral wavelength; and \(A_{plume}\) is the projected area considering the detection angle and occlusion. Civil aircraft generally fly at a cruise speed of 0.8 Ma, and the cruise altitude is usually greater than 6000 m. The best fuel economy altitude is generally around 9000 m. Aircraft skin will generate aerodynamic heating when flying in the air, and its skin stagnation point temperature \(T_{skin}\) can be expressed as  
\[T_{skin}=T_{0}\Big{[}1+k\Big{(}\frac{\gamma-1}{2}\Big{)}M^{2}\Big{]}, \tag{2}\]  
Figure 1: Flow chart of on-board parameter optimization method based on ADS-B. The inputs (in the red dashed box) are the target and background infrared signatures and ADS-B data (including flight altitude and speed); the on-board optimization includes two parts (in the green and blue dashed boxes), which are on-board spectral band optimization and on-board parameter optimization, using signal-to-noise ratio (\(SNR\)), signal-to-clutter ratio (\(SCR\)) and the joint signal-to-noise/clutter ratio (\(JSNCR\)) as the evaluation standard; the outputs (in the purple dashed box) are the optimized parameter set.