基于LMP检验的正弦波频率估计可靠性评估

Reliability test for frequency estimation of sinusoid based on LMP detection

针对正弦波信号频率估计结果的可靠性评估问题,提出了一种基于局部最大势(LMP,locally most powerful)检验的处理方法。先建立正弦波频率估计可靠性分析的假设检验模型,然后根据某一次特定频率估计值构造参考信号,并将其与观测信号做相关累加。通过分析不同假设下相关累加值概率分布的参数差异,利用LMP构造统计量,并给出了相应的判决门限,以实现可靠性判决。推导了LMP统计量的概率分布特性及其理论检测性能。仿真结果表明,本算法可在较低信噪比条件下实现对单次正弦波频率估计结果的可靠性判决。

A reliability test method based on locally most powerful （LMP） detection was proposed to evaluate the fre- quency estimation of sinusoid. The hypothesis test was created at first, and then a reference signal was generated depend- ing on the specific frequency estimation of the sinusoid. By analysis of the parameters differences from the probability distribution characteristics of the modulus of the cumulative sum series under the different two hypotheses, the reliability test for frequency estimate of sinusoid signal was performed by the proposed LMP-based statistic and threshold. The LMP statistic and its approximated theoretical detection performance were derived. Simulation results show that the pro- posed method can be used to verify the reliability for blind frequency estimation of sinusoid at low signal-to-noise ratio.