Research On Multi-Array Based Direct Position Determination For Radio Signals

Multi-Array localization uses signals received by several arrays from the same radio source to determine the target position. Traditional multi-array localization systems are based on two steps:first the direction of arrivals (DOA) to each array of the narrowband signal is estimated, with which the position of the target is then calculated out using triangulation algorithms. A certain amount of the target information will be lost during the parameter estimation process, thus the 2-step method meets its limit and its localization performance is hard to be further improved in low signal-to-noise ratio (SNR) situation.Multi-array direct position determination (DPD) is an important research direction raised in recent years. To estimate the target position, the array data is fused in function level or data level directly to reduce the loss of target information, so that higher localization accuracy and more stability than the 2-step way can be reached. Moreover, DPD method avoids matching the parameters and still has the ability of localizing multiple targets. In actural application, because of the large amount of data which need to be processed, wider transmission band between observing station and the process center is required.Most multi-array DPD algorithms, which are based on the assumption of accurately knowing the array response and receiving the white Gaussian noise, have good performance in theory. But in actual use, the array model errors are unavoidable, and the noise received by different arrays and different elements could be ununiform or even correlative, which cause the decline in localization accuracy. This paper starts from analyzing the effect of several model errors commonly met in actual use to the DPD algorithm, and designs several kinds of calibration DPD algorithm in different error models based on classical spectrum estimation theory. Our work aims to further improve the localization accuracy of DPD algorithms in actural use. Our research consists of 5 parts:the models of multi-array time domain data DPD algorithm and frequency domain data DPD algorithm, the design of multi-array DPD algorithm with channel gain and phase error, the design of multi-array time domain data DPD algorithm with nonuniform noise, the design of multi-array frequency domain data DPD algorithm with nonuniform noise, the design of multi-array DPD algorithm with color noise. The main research work and contributions of this paper are outlined as follows:1. The data fusion ways of the 2-step method and DPD method are summarized and compared in this section. The reasons of 2-step method’s limit and DPD’s better performance in low SNR situation are analyzed. According to the processed data form, the DPD algorithms are divided into two categories:time domain data DPD (T-DPD) and frequency domain data DPD (F-DPD). The advantages and disadvantages of the two kinds of DPD algorithms are analyzed, the localization performance is compared, and the application scopes of these algorithms are pointed out. The expiring of F-DPD in over horizon situation is pointed out specificlly.2. The F-DPD localization model with channel gain and phase errors are given out in this section. A self-adjusted multi-array DPD algorithm with array channel gain and phase error is proposed. This alternative algorithm estimates the gain-phase calibration and target position simultaneity, which improves the accuracy of the DPD algorithm with array channel gain and phase errors.3. The T-DPD localization model with unknown nonuniform noise are given out in this section, and a T-DPD algorithm with unknown nonuniform noise is proposed. The covariance matrix of the noise and the position of the targets are estimated simultaneously using covariance matrix of the array data in once/one iteration, which lower the effect of the unknown nonuniform noise. The alternative projection method is utilized to lower the algorithm complexity when multi-targets exist. In addition, the corresponding expression of Cramer-Rao lower bound (CRLB) is derived based on the localization model. The proposed method performs better than the traditional T-DPD algorithm in the presence of nonuniform noise and the noise covariance matrix is well estimates. Moreover, the proposed method can approach CRLB at high values of SNR.4. The F-DPD localization model with unknown nonuniform noise are given out in this section, and an F-DPD algorithm with unknown nonuniform noise is proposed. The power of the nonuniform noise (covariance matrix) is first estimated using the covariance matrix of the array data. Then the estimation result is used to prewhitten the covariance matrix of the array data, in order to better estimate the target position. The proposed method performs better than the traditional F-DPD algorithm in the presence of unknown nonuniform noise and the power of the noise is well estimates, when the calculation amount only slightly increases.5. The 3 algorithms mentioned all assume that the received noise is white and Gaussian, which means the noise between different arrays’ elements are uncorrelated. But in actual implementation color noise is sometimes received by the array, which declines the accuracy of the DPD algorithm. To solve the problem cause by the color noise, first the model of T-DPD localization with color noise are given out in this section, then a T-DPD algorithm based on fourth order cumulate is proposed. The corresponding expression of CRLB is derived after that. This algorithm is not sensitive to Gaussian noise model, thus high localization accuracy can be reached in spatial Gaussian color noise area.