Angle Estimation of Unresolved One- or Two- Targets in Monopulse Radar

Abstract

The main objective is to estimate the unresolved one- or two- target angles in monopulse radar. The unresolved targets mean that two targets are within same resolution cell (range, beamwidth, Doppler). In this case, the estimated angle has a large error in conventional monopulse processing because the monopulse radar may receive the vector-summed reflected signals from two targets. In chapter 1, we explained the conventional monopulse processing that can be used in one target case. Amplitude Comparison Monopulse (ACM) radar uses two squinted antennas that have same phase center in certain coordinate. It can estimate a target angle using the fact that the amplitudes of the received signals from a target in two antennas are different and phases of those are same according to the target angle. On the other hand, Phase Comparison Monopulse (PCM) radar uses two parallel antennas that have different phase center in certain coordinate. It can estimate a target angle using the fact that the phases of the received signals from a target in two antennas are different and amplitudes of those are same according to the target angle. However, in two unresolved targets case, conventional monopulse processing cannot be used and we showed that in this chapter. In chapter 2, we explained the conventional two unresolved target angles estimation methods. Methods to solve this limitation of monopulse radar can be classified as statistical or deterministic. Statistical methods work only for certain types of target model, and require that the types of target should be identified before angle estimation. Deterministic methods need only one or two pulses, and therefore do not share these limitations. In the earliest study of the deterministic method, Sherman proposed a method to use monopulse radar to distinguish two unresolved targets. This method uses two pulses and their complex sum and difference signals. It can also estimate a single-target angle by using an indicator that can select the true target angle from the two results of the two-target algorithm in the single-target scenario. However, this method has two serious problems. The first is that the pulses should satisfy two conditions: the relative amplitude ratio of the two targets in the sum signal should be invariant, and the relative phase difference of two targets in the sum signal should vary between two pulses. That is, the pulse repetition interval must be long enough to satisfy Sherman’s phase condition and short enough to satisfy Sherman’s amplitude condition. Therefore, the commonly-applicable target model is non-fluctuating or slowly-fluctuating. The second problem is that the equation is very difficult to solve; Sherman attempted to do this by using a graphical method, and mathematical programs (e.g., Mathcad). To solve the second problem, Z. Lu proposed a quadratic equation. It can solve the quadratic equation using two pulses that satisfy the Sherman`s conditions, but it cannot estimate a single target angle. Y. Zheng proposed a closed-form and single-pulse solution; it solved both of Sherman’s problems, but also cannot estimate a single-target angle and cannot estimate two target angles that have the same azimuth or elevation angle. In Chapter 3, we proposed methods that can solve both of Sherman’s problems and can estimate a single- target angle. First, we propose exact algebraic solutions instead of graphical (or numerical) ones to solve Sherman’s second drawback. Although this method should also use two pulses, it can estimate a single-target angle and can estimate the angles when the two targets are positioned at the same azimuth or elevation angle. By doing this we can prove that Sherman’s method has a unique solution and it can be used in single target case. Second, we propose a method that circumvents Sherman’s first problem and maintains accuracy of angle estimation, including in the single-target scenario. This method uses only one- pulse instead of two- pulses for PCM, so the target fluctuation model is not constrained. If the proposed both of proposed methods are used together, Sherman’s two problems can entirely be solved in PCM radar. In chapter 4, we showed that the possibility of our proposed methods in real application using lab-made monopulse emulator. Finally we conclude in chapter 5.