双基雷达成像算法研究
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摘要
双基成像雷达指收发分置的雷达成像系统。与传统的单基成像雷达系统相比，具有成本低、机动灵活、隐蔽性强等优点，是雷达成像技术的一大扩展，近年来得到了广泛的关注。本论文主要对下面两方面内容进行了研究：其一是双基合成孔径雷达(SAR，SyntheticAperture Radar)成像算法；其二是基于窄带连续波的双基雷达成像算法。论文的内容可以概括为下面四个部分：
1.提出了三种双基SAR二维频谱算法。首先提出一种简化的四次精确传递函数(EETF4，Fourth-order Extended Exact Transfer Function)二维频谱算法，该算法首先将斜距历程四阶泰勒展开，通过求解其驻相点方程来得到较为精确的二维频谱。其次，为了得到更高精度的二维频谱，提出一种基于最佳平方逼近的二维频谱算法。在简化的EETF4二维频谱算法的基础上，利用最佳平方逼近方法使其斜距历程展开式在成像过程中误差积累最小，从而提升二维频谱精度。然后，提出一种微增量二维频谱算法，该算法在低阶驻相点已知的基础上，通过求解低阶驻相点与高阶驻相点之间的微增量来间接得到高阶驻相点的近似解，进而得到二维频谱。实际上，三阶驻相点是已知的，可以将其作为起点而得到更高阶的驻相点。微增量最大的特点是具有可扩展性，能够通过提高所求驻相点的阶数来提高二维频谱的精度。
2.在上述二维频谱算法的基础上，对双基SAR成像处理算法进行了研究。由于上述算法得到的二维频谱结果较为复杂，难以分解。而OMEGA-K算法仅需要二维频谱的相位存在一个与其他部分分离的距离变量，无需将整个频谱作细致分解，所以在成像处理中采用了OMEGA-K算法。OMEGA-K算法的关键步骤是利用距离频率映射函数进行stolt插值，为得到距离频率映射函数在处理过程中采用了角度不变假设。为了保证算法聚焦效果，对不变区域的大小进行了分析。
3.提出一种基于MSR二维频谱的改进的双基OMEGA-K算法。为了提升聚焦质量，在上述OMEGA-K算法的基础上，引入了斜距历程高阶项对消操作。通过此操作，降低斜距历程的残余高阶项对成像结果的影响。与传统OMEGA-K算法中二维频谱“单向”匹配回波信号相比，改进的OMEGA-K算法中二维频谱和回波信号“双向”的互相匹配。仿真实验表明，上述处理实现简单，运算量小，能够显著提升聚焦效果。在斜距历程同为二阶泰勒展开的情况下，改进的OMEGA-K算法的聚焦效果要优于常规OMEGA-K算法，而与基于三阶泰勒展开的常规OMEGA-K算法非常接近。
4.以已有的基于窄带连续波的双基雷达频域成像算法为基础，在新的成像模型下，提出一种改进的频域算法和一种时域算法。由于回波信号在频域内仅在一个圆周上分布，因此改进的频域算法在极坐标格式下进行成像处理，而时域算法则在直角坐标系下进行成像处理。两种算法都是基于平动补偿后的转台模型进行的，虽然在不同的域内进行处理，并采用了不同的坐标系格式，但因为采用了相同的成像模型和信号形式，二者的单位冲激响应的实质相同，分辨率和峰值旁瓣比(PSLR，Peak SideLobe Ratio)也相同。本文对两种算法的单位冲激响应进行了仔细分析，得到了算法聚焦能力的量度。
Bistatic imaging radar, which can be depicted as the imaging radar system with thedifferent locations for transmitter and receiver, takes many advantages over thetraditional monostatic imaging radar system, such as low cost, flexibility, reducedvulnerability, etc.. The radar system is the significant development in the radar imagingfield, and has drawn widespread attention. This thesis considers two issues including thebistatic Synthetic Aperture Radar (SAR) imaging algorithm and bistatic radar imagingalgorithm based on the narrow band continuous wave. The main contributions of thethesis are summarized as the following four parts:
1. There two-dimensional(2-D) spectrum algorithms for bistatic SAR are proposed.Firstly, the simplified Fourth-order Extended Exact Transfer Function (EETF4)2-Dspectrum algorithm is considered. The algorithm, first of all, handles the slant rangehistory by using the fourth-order Taylor expansion, then obtains the more precise2-Dspectrum by solving the stationary points equation. Moreover, in order to obtain thefurther precise2-D spectrum, the optimal-square-approach-based2-D spectrumalgorithm is raised. Based on the simplified EETF42-D spectrum algorithm, thisalgorithm minimizes the error accumulation of the slant history expansion in theimaging process to improve the accuracy of the2-D spectrum by exploiting the optimalsquare approach. Furthermore, Micro-increment2-D spectrum algorithm is given. Onthe basis of the known low-order stationary phase point, this method indirectly gets theapproximate solution of the high-order stationary phase point by considering themicro-increment between the low-order and high-order stationary phase point, and thenthe2-D spectrum can be obtained. In fact, the three-order stationary phase point isknown, and it can be selected as the starting point to acquire the higher-order stationaryphase point. It is noted that the biggest characteristic of the micro-increment isexpandability, and so it can improve the accuracy of the2-D spectrum by raising theorder of stationary phase point to be solved.
2. Based on the2-D spectrum algorithms mentioned above, the bistatic SAR dataprocessing algorithm is investigated. Due to that the result obtained by exploiting thealgorithms mentioned above is rather complicated and hard to be decomposed, while theOMEGA-K algorithm only needs the range variable which is separated between thephase in2-D spectrum and the other parts rather than makes the careful decomposition in the whole spectrum, and the OMEGA-K algorithm is exploited in the imagingprocess. The key process in the OMEGA-K algorithm is the stolt interpolation by usingthe range frequency mapping function, and employs the angle invariance hypothesis inthe process to acquire the range frequency mapping function. In order to guarantee thefocusing quality of the algorithm, the size of the invariance region is analyzed.
3. The modified bistatic OMEGA-K algorithm based on MSR2-D spectrum isgiven. Based on the mentioned-above OMEGA-K algorithm, the higher-ordercancellation operation of slant range history is introduced to improve the focusingquality. By using this operation, the effect of the residual higher-order term of the slantrange history on the imaging result can be reduced. Compared to the2-D spectrummatches the echoes in one way in the traditional OMEGA-K algorithm, they match intwo way in the modified OMEGA-K algorithm. The simulation shows that the methodabove implements simply, has low computational complexity, and improves thefocusing effect significantly. In the case of illustrating the slant range history as thesecond-order Taylor expansion, the focusing effect of the modified OMEGA-Kalgorithm overmatches the ordinary methods, while approximates that of the ordinaryOMEGA-K algorithm based on the third-order Taylor expansion very closely.
4. Based on the present bistatic radar frequency domain imaging algorithm in thecase of narrow band continuous wave, focusing on the new imaging model, a modifiedfrequency domain algorithm and a time domain algorithm are proposed, which arebased on the after-motion-compensation turntable model. Due to the echoes onlydistributes in one circle in the frequency domain, and then the modified frequency-domain algorithm handles the imaging process in the polar coordinate format, while thetime-domain considers it in the rectangular system. Although they are processed in thedifferent domain and coordinate system, the unit impulse response is identicalessentially, and the same in the resolution and the peak sidelobe ratio (PSLR) because ofexploiting the same imaging model and the signal form. The measurements of the effectcapacity of the two algorithms are obtained by analyzing the unit impulse response ofthe two algorithms carefully.
1.提出了三种双基SAR二维频谱算法。首先提出一种简化的四次精确传递函数(EETF4，Fourth-order Extended Exact Transfer Function)二维频谱算法，该算法首先将斜距历程四阶泰勒展开，通过求解其驻相点方程来得到较为精确的二维频谱。其次，为了得到更高精度的二维频谱，提出一种基于最佳平方逼近的二维频谱算法。在简化的EETF4二维频谱算法的基础上，利用最佳平方逼近方法使其斜距历程展开式在成像过程中误差积累最小，从而提升二维频谱精度。然后，提出一种微增量二维频谱算法，该算法在低阶驻相点已知的基础上，通过求解低阶驻相点与高阶驻相点之间的微增量来间接得到高阶驻相点的近似解，进而得到二维频谱。实际上，三阶驻相点是已知的，可以将其作为起点而得到更高阶的驻相点。微增量最大的特点是具有可扩展性，能够通过提高所求驻相点的阶数来提高二维频谱的精度。
2.在上述二维频谱算法的基础上，对双基SAR成像处理算法进行了研究。由于上述算法得到的二维频谱结果较为复杂，难以分解。而OMEGA-K算法仅需要二维频谱的相位存在一个与其他部分分离的距离变量，无需将整个频谱作细致分解，所以在成像处理中采用了OMEGA-K算法。OMEGA-K算法的关键步骤是利用距离频率映射函数进行stolt插值，为得到距离频率映射函数在处理过程中采用了角度不变假设。为了保证算法聚焦效果，对不变区域的大小进行了分析。
3.提出一种基于MSR二维频谱的改进的双基OMEGA-K算法。为了提升聚焦质量，在上述OMEGA-K算法的基础上，引入了斜距历程高阶项对消操作。通过此操作，降低斜距历程的残余高阶项对成像结果的影响。与传统OMEGA-K算法中二维频谱“单向”匹配回波信号相比，改进的OMEGA-K算法中二维频谱和回波信号“双向”的互相匹配。仿真实验表明，上述处理实现简单，运算量小，能够显著提升聚焦效果。在斜距历程同为二阶泰勒展开的情况下，改进的OMEGA-K算法的聚焦效果要优于常规OMEGA-K算法，而与基于三阶泰勒展开的常规OMEGA-K算法非常接近。
4.以已有的基于窄带连续波的双基雷达频域成像算法为基础，在新的成像模型下，提出一种改进的频域算法和一种时域算法。由于回波信号在频域内仅在一个圆周上分布，因此改进的频域算法在极坐标格式下进行成像处理，而时域算法则在直角坐标系下进行成像处理。两种算法都是基于平动补偿后的转台模型进行的，虽然在不同的域内进行处理，并采用了不同的坐标系格式，但因为采用了相同的成像模型和信号形式，二者的单位冲激响应的实质相同，分辨率和峰值旁瓣比(PSLR，Peak SideLobe Ratio)也相同。本文对两种算法的单位冲激响应进行了仔细分析，得到了算法聚焦能力的量度。
Bistatic imaging radar, which can be depicted as the imaging radar system with thedifferent locations for transmitter and receiver, takes many advantages over thetraditional monostatic imaging radar system, such as low cost, flexibility, reducedvulnerability, etc.. The radar system is the significant development in the radar imagingfield, and has drawn widespread attention. This thesis considers two issues including thebistatic Synthetic Aperture Radar (SAR) imaging algorithm and bistatic radar imagingalgorithm based on the narrow band continuous wave. The main contributions of thethesis are summarized as the following four parts:
1. There two-dimensional(2-D) spectrum algorithms for bistatic SAR are proposed.Firstly, the simplified Fourth-order Extended Exact Transfer Function (EETF4)2-Dspectrum algorithm is considered. The algorithm, first of all, handles the slant rangehistory by using the fourth-order Taylor expansion, then obtains the more precise2-Dspectrum by solving the stationary points equation. Moreover, in order to obtain thefurther precise2-D spectrum, the optimal-square-approach-based2-D spectrumalgorithm is raised. Based on the simplified EETF42-D spectrum algorithm, thisalgorithm minimizes the error accumulation of the slant history expansion in theimaging process to improve the accuracy of the2-D spectrum by exploiting the optimalsquare approach. Furthermore, Micro-increment2-D spectrum algorithm is given. Onthe basis of the known low-order stationary phase point, this method indirectly gets theapproximate solution of the high-order stationary phase point by considering themicro-increment between the low-order and high-order stationary phase point, and thenthe2-D spectrum can be obtained. In fact, the three-order stationary phase point isknown, and it can be selected as the starting point to acquire the higher-order stationaryphase point. It is noted that the biggest characteristic of the micro-increment isexpandability, and so it can improve the accuracy of the2-D spectrum by raising theorder of stationary phase point to be solved.
2. Based on the2-D spectrum algorithms mentioned above, the bistatic SAR dataprocessing algorithm is investigated. Due to that the result obtained by exploiting thealgorithms mentioned above is rather complicated and hard to be decomposed, while theOMEGA-K algorithm only needs the range variable which is separated between thephase in2-D spectrum and the other parts rather than makes the careful decomposition in the whole spectrum, and the OMEGA-K algorithm is exploited in the imagingprocess. The key process in the OMEGA-K algorithm is the stolt interpolation by usingthe range frequency mapping function, and employs the angle invariance hypothesis inthe process to acquire the range frequency mapping function. In order to guarantee thefocusing quality of the algorithm, the size of the invariance region is analyzed.
3. The modified bistatic OMEGA-K algorithm based on MSR2-D spectrum isgiven. Based on the mentioned-above OMEGA-K algorithm, the higher-ordercancellation operation of slant range history is introduced to improve the focusingquality. By using this operation, the effect of the residual higher-order term of the slantrange history on the imaging result can be reduced. Compared to the2-D spectrummatches the echoes in one way in the traditional OMEGA-K algorithm, they match intwo way in the modified OMEGA-K algorithm. The simulation shows that the methodabove implements simply, has low computational complexity, and improves thefocusing effect significantly. In the case of illustrating the slant range history as thesecond-order Taylor expansion, the focusing effect of the modified OMEGA-Kalgorithm overmatches the ordinary methods, while approximates that of the ordinaryOMEGA-K algorithm based on the third-order Taylor expansion very closely.
4. Based on the present bistatic radar frequency domain imaging algorithm in thecase of narrow band continuous wave, focusing on the new imaging model, a modifiedfrequency domain algorithm and a time domain algorithm are proposed, which arebased on the after-motion-compensation turntable model. Due to the echoes onlydistributes in one circle in the frequency domain, and then the modified frequency-domain algorithm handles the imaging process in the polar coordinate format, while thetime-domain considers it in the rectangular system. Although they are processed in thedifferent domain and coordinate system, the unit impulse response is identicalessentially, and the same in the resolution and the peak sidelobe ratio (PSLR) because ofexploiting the same imaging model and the signal form. The measurements of the effectcapacity of the two algorithms are obtained by analyzing the unit impulse response ofthe two algorithms carefully.
引文
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