噪声背景下chirp信号参数估计理论与方法研究
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摘要
本文围绕噪声背景下chirp信号的频率、时延以及波达方向参数估计问题展开研究。提出了基于时变互高阶累积量的参数估计方法,在混合噪声背景下分别对多分量chirp信号的频率参数以及chirp信号的多径时延参数进行了有效估计。提出了模糊函数特征向量DOA估计法,实现了高精度的宽带多源chirp信号波达方向估计,将该方法与总体最小二乘法相结合,可以在一般阵列误差情况下估计chirp信号的一维及二维到达角。提出了基于互相关的宽带chirp信号DOA估计方法,在理想与非理想阵列中都能有效地抑制非高斯有色噪声,实现高效的chirp信号一维及二维到达角估计。理论分析和仿真实验表明,本文提出的各种chirp信号参数估计方法,普遍具有噪声抑制能力强、估计精度高、计算量小等优点。
Chirp signal (Liner frequency modulated signal or LFM signal) is a typical nonstationary signal. It is widely used in many systems, e.g., radar, sonar, communication, geology exploration and medical imaging. The research on chirp signal is of significance both in signal processing theory and in its practical applications.
Scholars have developed many theories and methods of chirp signals in recent years. However, most of existing chirp parameter estimation approaches are restricted by white Gaussian noise assumption, high computational cost and ideal signal models. To improve these methods, time-varying cross-higher-order cumulant theory, ambiguity function eigenvector algorithm and cross correlation DOA estimation technique are proposed in this paper. Three primary research aspects are studied which includes: frequency parameter estimation of multi-component chirp signals, multi-path time delay estimation of chirp signals, wideband DOA estimation of chirp signals. The main work can be generalized as:
1. Multi-component chirp frequency parameters estimation based on time- varying cross-higher-order cumulant.
Most of existing chirp frequency parameter estimation methods are based on white Gaussian noise assumption. This assumption is in favor of theory analysis and processing, but noise is often more complicated in practice. So these approaches are no longer suitable.
In this paper a kind of time-varying cross-higher-order cumulant techniques are proposed. They can do nonstationary chirp signals processing and have advantages of higher-order cumulant and cross spectral. The time-varying cross-higher-order cumulant can suppress correlated Gaussian noise and all kinds of uncorrelated noise. Because the special time-varying cross-higher-order cumulant of chirp signals derived by the analysis of chirp structure is time independent, complicated nonstationary algorithms are avoided. In stationary domain, higher-order cumulant belongs to tools with large computational burden, but for nonstationary chirp signal processing the computational cost of time-varying cross-higher-order cumulant is lower than which of maximum likelihood or time-frequency analysis methods. In this paper three subspace decomposition methods are presented which are MUSIC, SVD-MN and TLS-ESPRIT. Emulation results show that the three algorithms can realize high accurate and high reliable frequency parameter estimation of multi-component chirp signals in mixed noise environments.
2. Multi-path chirp time delay estimation based on time-varying cross- higher-order cumulant.
Time delay estimation of chirp signals is generally used in radar, sonar and geology exploration, etc. In general, echoes received by sensors are results of multi-path transmission, so study on chirp multi-path time delay estimation is very practical. In this paper two chirp multi-path time delay estimation problems are discussed:
(1) Multi-path time delay estimation of chirp signals. A time-varying cross-higher-order cumulant being defined, multi-path time delay estimation of nonstationary chirp signal is converted into frequency estimation of stationary multi-component signal. Then MUSIC, SVD-MN and TLS-ESPRIT methods based on this time-varying cross-higher-order cumulant are proposed. To reduce the aliasing ambiguities in multi-path time delay estimation, an unambiguous technique based on multi-frequency sampling theory is presented. Emulation results verify these multi-path time delay estimation approaches have advantages of high accuracy, high robustness and strong noise suppression ability.
(2) Joint multi-path time delay and Doppler stretch estimation of wideband chirp signals. Joint time delay and Doppler estimation problem can be viewed as an extent of time delay estimation. Chirp signal is a wideband signal, so joint multi-path time delay and Doppler stretch estimation should be used when relative motion of objects cannot be ignored. In this paper a time-varying higher-order cumulant is presented to estimate Doppler stretch factor. Then, the factor is used to reconstruct a reference signal, and multi-path time delay is estimated through time-varying cross-higher-order cumulant algorithms. These joint estimation algorithms can suppress Gaussian colored noise and their computational loads are smaller than most nonstationary joint estimation approaches.
3. Wideband multi-source chirp DOA estimation based on ambiguity function. DOA estimation of chirp signals is widely used in engineering. It has become a study focus in modern signal processing domain recently. In this paper wideband multi-source chirp DOA estimation based on ambiguity function in ideal and non-ideal sensor array is studied.
(1) Chirp DOA estimation based on ambiguity function in ideal sensor array. Ambiguity function transform on wideband multi-source chirp signals is analyzed and an eigenvector method based on ambiguity function is proposed to estimate chirp DOA. This algorithm works well even when the number of sources is greater than the number of sensors. The signal frequency can be higher than the array design frequency. Time delay property of ambiguity function is used to separate ambiguity function and its time delay item without adding short time window, so the precision of ambiguity function DOA method is higher than spatial PWVD DOA method.
(2) Chirp DOA estimation based on ambiguity function in non-ideal sensor array. Errors in sensor array occur commonly in practice. Many algorithms suitable for ideal array cannot satisfy non-ideal array signal processing. Through analysis of the eigenvector method based on ambiguity function in non-ideal sensor array, an ambiguity function array calibration method is presented. It has robustness on phase and gain errors. Combining with total least squares algorithm, it can restrain errors in the element locations. In this paper the array calibration method based on ambiguity function is applied in non-ideal uniform linear array and L shape array to realize 1-D and 2-D angle estimation.
4. Wideband chirp DOA estimation based on cross correlation.
The eigenvector method based on ambiguity function for chirp DOA estimation can work well both in ideal and in non-ideal sensor array, but its computational cost is high. So a cross correlation chirp DOA estimation method is presented and its application in ideal and non-ideal sensor array is discussed.
(1) Chirp DOA estimation based on cross correlation in ideal sensor array. After calculating the conjugate product of each sensor and the referenced sensor, a cross correlation approach is proposed to estimate wideband chirp DOA estimation. Then, estimation results of multiple sensors are synthesized by least squares method to decrease errors. The cross correlation DOA estimation approach is simple, effective and can suppress uncorrelated non-Gaussian colored noise.
(2) Chirp DOA estimation based on cross correlation in non-ideal sensor array. Array calibration methods combined cross correlation with total least squares is proposed. They can calibrate phase, gain and location errors in the array elements. Performance analysis shows that the cross correlation calibration method can estimate 1-D and 2-D angle in non-ideal uniform linear array and L shape array.
Summarily, chirp signal parameter estimation approaches proposed in this paper have many prominent virtues such as strong noise suppression ability, high estimation accuracy and low computational cost. Both theoretical analysis and simulation results demonstrate the effectiveness of the new methods.
Chirp signal (Liner frequency modulated signal or LFM signal) is a typical nonstationary signal. It is widely used in many systems, e.g., radar, sonar, communication, geology exploration and medical imaging. The research on chirp signal is of significance both in signal processing theory and in its practical applications.
Scholars have developed many theories and methods of chirp signals in recent years. However, most of existing chirp parameter estimation approaches are restricted by white Gaussian noise assumption, high computational cost and ideal signal models. To improve these methods, time-varying cross-higher-order cumulant theory, ambiguity function eigenvector algorithm and cross correlation DOA estimation technique are proposed in this paper. Three primary research aspects are studied which includes: frequency parameter estimation of multi-component chirp signals, multi-path time delay estimation of chirp signals, wideband DOA estimation of chirp signals. The main work can be generalized as:
1. Multi-component chirp frequency parameters estimation based on time- varying cross-higher-order cumulant.
Most of existing chirp frequency parameter estimation methods are based on white Gaussian noise assumption. This assumption is in favor of theory analysis and processing, but noise is often more complicated in practice. So these approaches are no longer suitable.
In this paper a kind of time-varying cross-higher-order cumulant techniques are proposed. They can do nonstationary chirp signals processing and have advantages of higher-order cumulant and cross spectral. The time-varying cross-higher-order cumulant can suppress correlated Gaussian noise and all kinds of uncorrelated noise. Because the special time-varying cross-higher-order cumulant of chirp signals derived by the analysis of chirp structure is time independent, complicated nonstationary algorithms are avoided. In stationary domain, higher-order cumulant belongs to tools with large computational burden, but for nonstationary chirp signal processing the computational cost of time-varying cross-higher-order cumulant is lower than which of maximum likelihood or time-frequency analysis methods. In this paper three subspace decomposition methods are presented which are MUSIC, SVD-MN and TLS-ESPRIT. Emulation results show that the three algorithms can realize high accurate and high reliable frequency parameter estimation of multi-component chirp signals in mixed noise environments.
2. Multi-path chirp time delay estimation based on time-varying cross- higher-order cumulant.
Time delay estimation of chirp signals is generally used in radar, sonar and geology exploration, etc. In general, echoes received by sensors are results of multi-path transmission, so study on chirp multi-path time delay estimation is very practical. In this paper two chirp multi-path time delay estimation problems are discussed:
(1) Multi-path time delay estimation of chirp signals. A time-varying cross-higher-order cumulant being defined, multi-path time delay estimation of nonstationary chirp signal is converted into frequency estimation of stationary multi-component signal. Then MUSIC, SVD-MN and TLS-ESPRIT methods based on this time-varying cross-higher-order cumulant are proposed. To reduce the aliasing ambiguities in multi-path time delay estimation, an unambiguous technique based on multi-frequency sampling theory is presented. Emulation results verify these multi-path time delay estimation approaches have advantages of high accuracy, high robustness and strong noise suppression ability.
(2) Joint multi-path time delay and Doppler stretch estimation of wideband chirp signals. Joint time delay and Doppler estimation problem can be viewed as an extent of time delay estimation. Chirp signal is a wideband signal, so joint multi-path time delay and Doppler stretch estimation should be used when relative motion of objects cannot be ignored. In this paper a time-varying higher-order cumulant is presented to estimate Doppler stretch factor. Then, the factor is used to reconstruct a reference signal, and multi-path time delay is estimated through time-varying cross-higher-order cumulant algorithms. These joint estimation algorithms can suppress Gaussian colored noise and their computational loads are smaller than most nonstationary joint estimation approaches.
3. Wideband multi-source chirp DOA estimation based on ambiguity function. DOA estimation of chirp signals is widely used in engineering. It has become a study focus in modern signal processing domain recently. In this paper wideband multi-source chirp DOA estimation based on ambiguity function in ideal and non-ideal sensor array is studied.
(1) Chirp DOA estimation based on ambiguity function in ideal sensor array. Ambiguity function transform on wideband multi-source chirp signals is analyzed and an eigenvector method based on ambiguity function is proposed to estimate chirp DOA. This algorithm works well even when the number of sources is greater than the number of sensors. The signal frequency can be higher than the array design frequency. Time delay property of ambiguity function is used to separate ambiguity function and its time delay item without adding short time window, so the precision of ambiguity function DOA method is higher than spatial PWVD DOA method.
(2) Chirp DOA estimation based on ambiguity function in non-ideal sensor array. Errors in sensor array occur commonly in practice. Many algorithms suitable for ideal array cannot satisfy non-ideal array signal processing. Through analysis of the eigenvector method based on ambiguity function in non-ideal sensor array, an ambiguity function array calibration method is presented. It has robustness on phase and gain errors. Combining with total least squares algorithm, it can restrain errors in the element locations. In this paper the array calibration method based on ambiguity function is applied in non-ideal uniform linear array and L shape array to realize 1-D and 2-D angle estimation.
4. Wideband chirp DOA estimation based on cross correlation.
The eigenvector method based on ambiguity function for chirp DOA estimation can work well both in ideal and in non-ideal sensor array, but its computational cost is high. So a cross correlation chirp DOA estimation method is presented and its application in ideal and non-ideal sensor array is discussed.
(1) Chirp DOA estimation based on cross correlation in ideal sensor array. After calculating the conjugate product of each sensor and the referenced sensor, a cross correlation approach is proposed to estimate wideband chirp DOA estimation. Then, estimation results of multiple sensors are synthesized by least squares method to decrease errors. The cross correlation DOA estimation approach is simple, effective and can suppress uncorrelated non-Gaussian colored noise.
(2) Chirp DOA estimation based on cross correlation in non-ideal sensor array. Array calibration methods combined cross correlation with total least squares is proposed. They can calibrate phase, gain and location errors in the array elements. Performance analysis shows that the cross correlation calibration method can estimate 1-D and 2-D angle in non-ideal uniform linear array and L shape array.
Summarily, chirp signal parameter estimation approaches proposed in this paper have many prominent virtues such as strong noise suppression ability, high estimation accuracy and low computational cost. Both theoretical analysis and simulation results demonstrate the effectiveness of the new methods.
引文
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