基于原点矩偏导的K分布杂波参数估计

K分布的参数估计研究对于雷达杂波特性预测和估计具有重要意义。基于矩估计的K分布参数估计方法通过联立不同阶原点矩进行参数求解，这些不同阶数下的联合，在数据长度受限情况下会产生误差。因此，通过计算原点矩偏导和原点矩之间的关系，推导出了一种新的K分布杂波参数估计方法。该方法在同阶原点矩的条件下进行参数估计，避免了不同阶原点矩之间的估计误差，具有更好的估计性能。通过仿真和实测杂波数据，分析比较了该方法与其他矩估计法的参数估计有效率和估计精度，该方法具有100%的估计有效率且估计精度更高。高阶矩对数据敏感，在矩估计法中应尽量选取低阶矩，通过合理选取阶数k可以得到较为理想的估计结果和精度。 

The Clutter Parameter Estimation of K-distribution Based on Origin Moment Derivation

? ?The parameter estimation of K-distribution had great significance for the prediction and estimation of the radar clutter characteristics. Therefore， it was very important to research the parameter estimation of the clutter distribution. The probability density function expression of K-distribution contained the complex function， so the maximum likelihood parameter estimation of K-distributed clutter was difficult to solve. The moment estimation method had the advantage of simple solution. The K-distribution parameter estimation method based on moment estimation often solved the parameters by utilizing equations with different order origin moments， such as the method of second- / fourth- order moment estimation and second- / fractional- order moment estimation. The combination of these different order origin moments would produce errors in the case of limited data length. It was found that the origin moment of K-distribution contained the product of exponential function and gamma function， and the derivatives of these two functions were related to themselves. By calculating the relationship between the origin moment deviation and the origin moment， a radar clutter parameter estimation of the K-distribution method based on the origin moment deviation was proposed. This method estimated the parameters under the condition of the same order origin moment， so it could avoid the estimation error between different order origin moments， and had better estimation performance. By utilizing the simulated data and measured clutter data， the efficiency and accuracy of parameter estimation in this method were analyzed and compared with other moment estimation methods. Both of the experiments showed that this method had 100% estimation efficiency and the higher estimation accuracy. In the moment estimation method， the high-order moment is sensitive to data， and the low-order moment should be selected as far as possible. By reasonably selecting the order k， the ideal estimation results and accuracy can be obtained.