## 2 Article Structure Description and Aircraft Dynamics Modeling  
Figure 1 shows the content structure of the article. The dynamic equation of the aircraft centroid is [31]:  
\[ \begin{array}{l}m(\dot{V}_{x}+qV_{z}-rV_{y})=F_{x}\\ m(\dot{V}_{y}+rV_{x}-pV_{z})=F_{y}\\ m(\dot{V}_{z}+pV_{y}-qV_{x})=F_{z}\end{array}  \tag{1}\]  
In the formula, \(m\) is the mass of the aircraft, \(V=\left[V_{x}\ V_{y}\ V_{z}\right]\) is the component of the aircraft speed in the airframe coordinate system, \(\Omega=\left[p\ q\ r\right]\) is the component of the aircraft angular velocity in the airframe coordinate system, and \(\left[F_{x}\ F_{y}\ F_{z}\right]\) is the component of the combined external force of the aircraft in the airframe coordinate system. The upper point of the variable represents the derivative of the variable, and this setting also applies to the rest of this article. Figure 1: Structure of the article. Combined with the force analysis, the centroid dynamic equation of the aircraft is finally expressed as follows:  
\[\left\{ \begin{array}{l}m(\dot{V}_{x}+qV_{z}-rV_{y})=-G\sin\theta+(-D\cos\alpha+ L\sin\alpha)+T\cos\phi_{\mathrm{T}}\\ m(V_{y}+rV_{x}-pV_{z})=G\sin\phi\cos\theta+F_{\mathrm{A}y}+F_{\mathrm{T}y}\\ m(\dot{V}_{z}+pV_{y}-qV_{x})=G\cos\phi\cos\theta+(-D\sin\alpha-L\cos\alpha)-T \sin\phi_{\mathrm{T}}\end{array} \right. \tag{2}\]  
In the formula, \(G\) is the gravity of the aircraft, \(D\) is the aerodynamic drag, \(L\) is the aerodynamic lift, \(F_{Ay}\) is the aerodynamic lateral force, \(\phi_{T}\) is the engine installation angle, and \(F_{\mathrm{T}y}\) is the lateral component of the engine thrust in the body coordinate system:  
The aircraft inertia matrix \(I\) is:  
\[I= \begin{bmatrix}I_{xx}&-I_{xy}&-I_{xz}\\ -I_{xy}&-I_{yy}&-I_{yz}\\ -I_{xz}&-I_{yz}&I_{zz}\end{bmatrix}  \tag{3}\]  
In the inertia matrix, \(\left[I_{xx}\ I_{yy}\ I_{zz}\right]\) respectively represent the moment of inertia of the aircraft around the three axes of the body coordinate system, and \(\left[I_{xy}\ I_{xz}\dots\ I_{yz}\right]\) denotes the product of inertia. The angular momentum equation is:  
\[H= \begin{bmatrix}H_{x}\\ H_{y}\\ H_{z}\end{bmatrix} = \begin{bmatrix}pI_{xx}-rI_{xz}\\ qI_{yy}\\ rI_{zz}-pI_{xz}\end{bmatrix}  \tag{4}\]  
In the formula, \(\left[H_{x}\ H_{y}\ H_{z}\right]\) are the components of angular momentum in the body coordinate system. The motion of the aircraft around the center of mass can be expressed as:  
\[\left[\frac{\mathrm{d}H}{\mathrm{d}t}\right]=\left[ \begin{array}{c}\dot{p}I _{xx}+qr\left(I_{zz}-I_{yy}\right)-(\dot{\omega}_{z}+pq)I_{xz}\\ \dot{q}I_{yy}-pr(I_{zz}-I_{xx})+\left(p^{2}-r^{2}\right)I_{xz}\\ \dot{r}I_{zz}+pq\left(I_{yy}-I_{xx}\right)+(q\dot{r}-\dot{p})I_{xz}\end{array}  \right]=\left[ \begin{array}{c}L_{A}+L_{T}\\ M_{A}+M_{T}\\ N_{A}+N_{T}\end{array} \right] \tag{5}\]  
In the formula, \(\left[L_{a}\ M_{a}\ N_{a}\right]\) are the components of the aerodynamic torque in the body coordinate system, and \(\left[L_{T}\ M_{T}\ N_{T}\right]\) are the components of the torque generated by the thrust in the body coordinate system, respectively. Because gravity passes through the center of mass, it does not generate torque. The torque equations are expressed as follows:  
\[\left\{ \begin{array}{l}\dot{p}=(c_{1}r+c_{2}p)q+c_{3}\overline{L}+c_{4}N \\ \dot{q}=c_{5}pr-c_{6}\big{(}p^{2}-r^{2}\big{)}q+c_{7}M\\ \dot{r}=(c_{8}p+c_{2}r)q+c_{4}\overline{L}+c_{9}N\end{array} \right. \tag{6}\]  
In this formula: \(c_{1}=\frac{(I_{y}-I_{z})I_{z}-I_{xz}^{2}}{I_{x}I_{z}-I_{xz}^{2}}\), \(c_{2}=\frac{(I_{x}-I_{y}+I_{z})I_{xz}}{I_{x}I_{z}-I_{xz}^{2}}\), \(c_{3}=\frac{I_{z}}{I_{x}I_{z}-I_{xz}^{2}}\), \(c_{4}=\frac{I_{yz}}  
When performing aerodynamic identification, the aircraft needs to reach the predetermined flight state first, then the aircraft sensor obtains real-time flight data. The detrending program will detrend these data. These data are then converted from the time domain to the frequency domain using the Chirp-Z transform (CZT) method and are then recursively identified online.