On The Parameter Estimators In Signal Processing

Signal processing technology has been widely applied in communications, geo-physics, acoustics, medical diagnostics and so on. Detecting the number of the effec-tive signals and estimating amplitudes and frequencies of signals are two issues in array signal processing model which plays a very important role in signal processing. In this thesis we present some methods to estimate amplitudes and frequencies of signals in array signal processing model.Generally, in the two dimensional array signal processing model, the least squares estimator and maximum likelihood estimator, which are consistent and have asymptotic normal distribution, are proposed. It is well known that if we use the normal distribution to approximate to that of the least squares estimator, then several nuisance parameters need to be estimated in advance. Therefore, we adopt random weights estimator in this paper to approximate to the distribution of least-square estimator. Our proposed method can avoid the estimation of nuisance parameters, and has good performance by numerical simulation.In one dimensional signal processing model, we present robust estimates for pa-rameter amplitudes via constructing a two-step estimation procedure. For certain pre-specified consistent estimators of frequencies, we plug them into the M estimation e-quations in step one. Subsequently, we obtain M estimators for parameter amplitudes, which are consistent. Simulation studies show that the two-step estimator performs better than the traditional least squares estimator.In the rest of paper, we propose a rank method to test hypothesis of ranking perfect in multi-cycle ranked set sampling. Evidently, compared to simple random sampling method, a more efficient sampling method is ranked set sampling which can been ap-plied in many fields, such as agriculture, forestry, medicine studies and so on. Many of issues about ranked set sampling method are studied under the assumption that the ranking is perfect, however, in application the assumption is generally not satisfied. Therefore, it is important and pressing to test whether the ranking is perfect or not. In this paper, different from the traditional studies, three rank testing statistics are present-ed where we do not need the condition that ranked set sampling is balanced. Moreover, the null distributions of these statistics are developed. Our proposed methods hold un-der all kinds of situations, including single cycle and multi-cycle cases. These methods can be applied to unbalanced sampling case, which is more suitable to real application data.