# A Waveform and Velocity Ambiguity Resolution Method for Corner Radar
## 3 AB Wave Velocity Ambiguity Resolution Method
Then, the unambiguous velocities \(V^{\prime}_{A}\) and \(R^{\prime}_{A}\) are calculated as follows:  
\[V^{\prime}_{A}=V_{A}+k_{A}\cdot V_{maxA},R^{\prime}_{A}=R_{A}+V^{\prime}_{A} \cdot T_{A} \tag{9}\]  
Primary target matching based on \(A\):  
Using TarsetA_S as a reference, the target points are sought within TarsetB, with the matching condition defined by Equation (10). If the match is successful, the points in \(B\) are classified into TarsetB_S, and the corresponding \(k_{B}\) is recorded. In cases of failure, the points are categorized into TarsetB_F. Similarly, points in TarsetA_S that fail to find a match are grouped into TarsetA_F. The matching conditions are as follows:  
Figure 4: AB wave velocity ambiguity resolution. \[ \begin{split} V^{\prime}_{Bi}=V_{B}+k_{i}\cdot V_{maxB}\\ THR=\left|R^{\prime}_{A}-R_{B}\right|<Th_{R1}\\ THV_{i}=\left|V^{\prime}_{A}-V^{\prime}_{Bi}\right|<Th_{V1}\\ TH\theta=\left|\theta_{A}-\theta_{B}\right|<Th_{A1}\\ THS=\left|SNR_{A}-SNR_{B}\right|<Th_{S1}\\ k_{B}=argmin_{i}(a_{1}\times THR+a_{2}\times THV_{i}+a_{3}\times TH +a_{4}\times THS)\\ i=1\ldots(2m+1)\end{split}  \tag{10}\]  
where \(k_{i}\) is within the range of [\(-m\), \(m\)]. \(R_{B}\) represents the range estimated by wave B, \(V^{\prime}_{Bi}\) denotes the corresponding velocity in wave B when the ambiguous multiple is \(k_{i}\), and \(THV_{i}\) signifies the velocity difference between \(V^{\prime}_{Bi}\) and the true velocity. \(\theta_{A}\) and \(\theta_{B}\) denote the target azimuth estimated by the AB waveform. \(THR\), \(TH\theta\), and \(THS\) represent the range difference, azimuth difference, and SNR difference of AB waveform estimation, respectively. \(Th_{R1}\), \(ThV_{1}\), \(Th_{A1}\), and \(Th_{S1}\) are the range threshold, velocity threshold, azimuth threshold, and SNR threshold of the first matching. \(a_{1}\), \(a_{2}\), \(a_{3}\), and \(a_{4}\) are the weighting coefficients assigned to the corresponding parameters, which may be adjusted based on the estimation quality of azimuth and energy to bias towards other parameters. (3) A-based secondary target matching:  
Utilizing TargetA_F as the reference, search within TargetB_F. If the matching is successful, the points in TargetB_F are classified into TargetB_S, and the corresponding \(k_{B}\) is recorded. The conditions are as follows:  
\[ \begin{split} V^{\prime}_{Bi}=V_{B}+k_{i}\cdot V_{maxB}\\ V^{\prime}_{Aj}=V_{A}+k_{j}\cdot V_{maxA}\\ R^{\prime}_{Aj}=R_{A}+V^{\prime}_{Aj}\cdot T_{A}\\ THR=\left|R^{\prime}_{Aj}-R_{B}\right|<Th_{R2}\\ THV_{ij}=\left|V^{\prime}_{Aj}-V^{\prime}_{Bi}\right|<Th_{V2}\\ TH\theta=\left|\theta_{A}-\theta_{B}\right|<Th_{A2}\\ THS=\left|SNR_{A}-SNR_{B}\right|<Th_{S2}\\ k_{B}=argmin_{i}(a_{1}\times THR+a_{2}\times THV_{ij}+a_{3}\times TH +a_{4}\times THS)\\ i=1\ldots(2m+1),j=1\ldots(2m+1)\end{split}  \tag{11}\]  
where \(k_{i}\) and \(k_{j}\) range from \(-m\) to \(m\). \(THV_{ij}\) represents the velocity difference between the estimates from wave B (\(k_{i}\)) and wave A (\(k_{j}\)). (4) B-based primary target matching:  
Search within TargetA_S using TargetB_F as the reference. If the match is successful, the points in TargetB_F are classified into TargetB_S, and \(k_{B}\) is recorded according to the following conditions:  
\[ \begin{split} V^{\prime}_{Bi}=V_{B}+k_{i}\cdot V_{maxB}\\ THR=\left|R^{\prime}_{A}-R_{B}\right|<Th_{R3}\\ THV_{i}=\left|V^{\prime}_{A}-V^{\prime}_{Bi}\right|<Th_{V3}\\ TH\theta=\left|\theta_{A}-\theta_{B}\right|<Th_{A3}\\ THS=\left|SNR_{A}-SNR_{B}\right|<Th_{S3}\\ k_{B}=argmin_{i}(a_{1}\times THR+a_{2}\times THV_{i}+a_{3}\times TH +a_{4}\times THS)\\ i=1,\ldots,2m\end{split}  \tag{12}\]  
where \(THV_{i}\) represents the velocity difference between wave B (\(k_{i}\)) and the true velocity. (5) Secondary target matching based on B:Utilizing TargetB_S as the reference, search within TargetB_F. If the match is successful, the points in TargetB_F are classified into TargetB_S, and \(k_{B}\) is recorded. The conditions are as follows:  
\[