Angle Expansion Estimation and Correction Based on the Lindeberg–Feller Central Limit Theorem Under Multi-Pulse Integration

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript focuses on the angle measurement problem in high-resolution phased array radar systems, which is a very important field in radar detection and target tracking. The research background of the paper is clear, and it has high practical value and theoretical significance for addressing problems in practical applications. The paper proposes an angle extension model based on Gaussian distribution and uses the least squares method to fit the quadratic curve to estimate unknown parameters. This method can provide accurate angle measurement for radar systems. The manuscript verified the accuracy of the proposed model through simulation experiments, using different target motion situations and different target amplitude probability distributions. This extensive validation helps to demonstrate the universality and robustness of the model. However, the simulation experiments mentioned in the manuscript mainly focus on the parameters of Ku band high-resolution phased array radar systems and may not involve other frequencies or types of radar systems. Therefore, the universality of the experimental results needs further verification. And although the paper mentions that in order to eliminate noise interference and prove that single pulse angle measurement still follows Gaussian distribution after multi pulse integration under target motion and fluctuation, noise is inevitable in practical applications, and the paper does not consider the impact of noise on measurement results. It is suggested to add explanation. In addition, if there are errors in the expression of details in the manuscript, such as inconsistent text formatting and layout errors, it is recommended to carefully review and revise them.

Shortcomings and suggestions:

1. The simulation experiments mentioned in the paper mainly focus on the parameters of Ku band high-resolution phased array radar systems, and do not involve other frequencies or types of radar systems. It is recommended to add comparisons.

2. The simulated target amplitude in the experiment only follows four classical probability distributions, and in practical applications, the amplitude distribution of the target may be more complex, which may limit the applicability of the model.

3. Although the paper mentions that parameter estimation can reduce errors, it does not discuss in detail the accuracy and stability of parameter estimation under different signal-to-noise ratio (SNR) conditions. It is recommended to add it.

4. The paper compared the proposed algorithm with RTK data, but did not provide a comparative analysis with other existing algorithms or technologies, which limits the ability to comprehensively evaluate the performance of the algorithm.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Monopulse radar has been widely used in both military and civilian radar fields. For angle measurement under low signal-to-noise ratio, this paper proposes an angle correction algorithm based on multi-pulse integration and long-term estimation. The angle measurement performance of the proposed method is evaluated using real measurement data. The paper is well organized and written in great detail. There are some issues need to be considered.

 

1. The 3D antenna coordinate system shown in Fig. 2(b) is not intuitive. The azimuth and elevation angles in the coordinate system should be clearly defined.

 

2. When deriving the angle expansion model under amplitude fluctuation, it assumes that the amplitudes of the individual pulses satisfy the condition of being independent and identically distributed. However, the amplitude fluctuation of the target usually follows the Swerling fluctuation model, thus the amplitudes of the pulses may be relevant within a CPI, for example, the Swerling Ⅰ and Swerling Ⅲ model. Therefore, the assumption of independence does not necessarily hold. Does the derived angle expansion model still hold?

 

3. In Section 5, what is the basis for selecting the four fluctuation scenarios, i.e., the four classical distributions: Gamma, Rayleigh, Gaussian, and Weibull distributions?

 

4. In the variation in RMSE of angle error with SNR shown in Fig. 5, for the traditional monopulse angle measurement algorithm, why are the RMSE of angle errors different for the two motion scenarios, i.e. the uniform linear motion and uniformly accelerated linear motion? Theoretically, the angle error of monopulse angle measurement is independent of the motion of the target.

 

5. It is recommended to modify Fig.7 in Section 6. As range is a variable of time, time should be the horizontal ordinate while range be Y-axis.

Author Response

Since the reply is quite long, please see the attachment for details.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The previous concerns have been addressed in the revised manuscript. New simulation results are added which make the paper clearer. The quality of the paper has been improved.