Algorithm 3. UKF algorithm

Step (1): Let k = 1, initialize each radar transmit power $P_{q,k}^i$, target state ${\xi }_{q,k-1|k-1}$ and covariance matrix $C_{q,k-1|k-1}=J^{-1}\left({\xi }_{q,k-1|k-1}\right)$.

Step (2): The transmitting power of each radar is $P_{q,k}^i$, get the measured value $z_{q,k}$ of the target, and calculate ${\Sigma }_{q,k}$.

Step (3): Construct the 2L + 1 sigma point set ${\chi }_{q,k-1|k-1}^i$ and the weights ${\omega }_{i,k}$ corresponding to the point set according to the following formula. $\{\begin{array}{ll}{\chi }_{q,k-1|k-1}^0={\xi }_{q,k-1|k-1}\hfill & \hfill \\ {\chi }_{q,k-1|k-1}^i={\xi }_{q,k-1|k-1}+{\left(\sqrt{\left(I+\varsigma \right)C_{q,k-1|k-1}}\right)}_i\hfill & i=1,2,\dots ,I\hfill \\ {\chi }_{q,k-1|k-1}^i={\xi }_{q,k-1|k-1}-{\left(\sqrt{\left(I+\varsigma \right)C_{q,k-1|k-1}}\right)}_{i-I}\hfill & i=I+1,I+2,\dots ,2I\hfill \end{array}$ $\{\begin{array}{ll}{\omega }_{0,k}=\frac{\varsigma }{I+\varsigma }\hfill & \hfill \\ {\omega }_{i,k}=\frac{I}{2\left(I+\varsigma \right)}\hfill & i=1,2,\dots ,2I\hfill \end{array}$ Where, $\varsigma$ is a scale factor, ${\left(\sqrt{\left(I+\varsigma \right)C_{q,k-1|k-1}}\right)}_i$ represents the ith column of the square root $\sqrt{\left(I+\varsigma \right)C_{q,k-1|k-1}}$ of the matrix; I represents the dimension of the state vector.

Step (4): Map the sigma point set ${\chi }_{q,k-1|k-1}^i$ to the predicted point set ${\chi }_{q,k|k-1}^i$ through the state transition function $F_q$, and calculate the new target state ${\xi }_{q,k|k-1}$ and variance $C_{q,k|k-1}$ by weighting. ${\chi }_{q,k|k-1}^i=F_q\times {\chi }_{q,k-1|k-1}^i$ $\{\begin{array}{l}{\xi }_{q,k|k-1}={\displaystyle \sum _{i=0}^{2I}\left({\omega }_{i,k}\times {\chi }_{q,k|k-1}^i\right)}\hfill \\ C_{q,k|k-1}={\displaystyle \sum _{i=0}^{2I}{\omega }_{i,k}\left({\chi }_{q,k|k-1}^i-{\xi }_{q,k|k-1}\right){\left({\chi }_{q,k|k-1}^i-{\xi }_{q,k|k-1}\right)}^T+Q_{q,k-1}}\hfill \end{array}$

Step (5): Map the sigma prediction point set ${\chi }_{q,k|k-1}^i$ to the new point set $z_{q,k|k-1}^i$ through the measurement equation, and calculate the mean $z_{q,k|k-1}$, variance $C_{q,k}^{zz}$ and $C_{q,k}^{xz}$. $z_{q,k|k-1}^i=g\left({\chi }_{q,k|k-1}^i\right)$ $\{\begin{array}{l}{z}_{q,k|k-1}={\displaystyle \sum _{i=0}^{2I}\left({\omega }_{i,k}\times z_{q,k|k-1}^i\right)}\hfill \\ C_{q,k}^{zz}={\displaystyle \sum _{i=0}^{2I}{\omega }_{i,k}\left(z_{q,k|k-1}^i-z_{q,k|k-1}\right){\left(z_{q,k|k-1}^i-z_{q,k|k-1}\right)}^T+{\Sigma }_{q,k}}\hfill \\ C_{q,k}^{zz}={\displaystyle \sum _{i=0}^{2I}{\omega }_{i,k}\left({\chi }_{q,k|k-1}^i-{\xi }_{q,k|k-1}\right){\left({\chi }_{q,k|k-1}^i-{\xi }_{q,k|k-1}\right)}^T}\hfill \end{array}$

Step (6): Calculate the gain matrix $K_{q,k}$ and update ${\xi }_{q,k|k-1}$ and covariance $C_{q,k|k}$ matrix with the gain matrix. $\{\begin{array}{l}{K}_{q,k}=C_{q,k}^{xz}\times {\left(C_{q,k}^{zz}\right)}^{-1}\hfill \\ {\xi }_{q,k|k}={\xi }_{q,k|k-1}+K_{q,k}\left(z_{q,k}-z_{q,k|k-1}\right)\hfill \\ C_{q,k|k}=C_{q,k|k-1}-K_{q,k}\times C_{q,k}^{zz}\times {\left(K_{q,k}\right)}^T\hfill \end{array}$

Step (7): According to the intelligent hybrid algorithm proposed above, predict the radar transmission power $p_{k+1,opt}^i$ at the kth moment, let $k=k+1$ and then jump to step (2)