加速运动目标检测及跟踪技术研究
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摘要
提高雷达对机动目标的探测和跟踪能力是当前雷达技术领域所面临的前沿课题和紧迫任务。论文以弹道导弹防御为主要背景,利用时频分析方法进行加速运动目标的检测及加速度参数的估计,并把估计得到的加速度测量作为新增观测量引入到目标跟踪中,其研究成果主要体现在:
1)从理论上分析了FRFT对LFM信号的检测性能、参数估计精度和分辨性能。推导了时限线性调频(LFM)信号的分数阶Fourier变换(FRFT),根据其幅度特性确定了峰值所在分数阶Fourier域的位置及其对应的信号参数。由此说明,FRFT适合处理含有未知参数的LFM信号。从输出信噪比(SNR)的角度,分析了FRFT在处理高斯白噪声背景下含有未知参数LFM信号的检测性能。结果表明,在高SNR条件下,FRFT处理含有未知参数LFM信号的输出SNR仅比理想情况(即信号参数已知)下的匹配滤波低3dB。从参数估计精度的角度,采用一阶扰动方法推导得到了基于连续FRFT的LFM信号参数的估计误差均方差。从分辨力的角度,推导得到了基于FRFT的频率分辨力、调频率分辨力及频率—调频率联合分辨力。结果表明,FRFT处理含有未知参数LFM信号在参数估计精度和分辨力方面均达到了最优。因此,基于FRFT的方法对处理含有未知参数LFM信号是有效的。
2)分析了基于Wigner-Hough变换对加速运动目标的检测性能。研究了多种离散FRFT的实现算法,分析了其中应用最广泛的两种离散FRFT的输出峰值幅度与加速度、脉冲个数的关系,结果表明:尽管分数阶傅立叶变换的离散化形式很多,但当前还没有具有连续FRFT所具有性质的离散化形式。由于Wigner-Hough变换与FRFT的模平方存在恒等关系,因此在研究加速运动目标检测和参数估计问题时可采用Wigner-Hough变换。从理论上分析了单门限和双门限情况下基于Wigner-Hough变换的LFM信号的检测性能,推导得到了虚警概率和检测概率的数学表达式,为雷达设置合理的检测门限提供了理论依据。最后仿真比较了非起伏目标基于傅立叶变换和基于Wigner-Hough变换的检测性能,及不同起伏类型目标基于Wigner-Hough变换的检测性能,为估算雷达探测起伏目标的作用距离提供参考。
3)深入研究了基于Wigner-Hough变换的加速运动目标的参数估计算法。研究并给出了基于Wigner-Hough变换的加速度参数估计算法的实现流程,分析了接收信号时长对加速度最小可分辨单元的影响,加速度最小可分辨单元跟信号时长的平方成反比。同时,在一定范围内,通过增大Wigner分布的频率单元长度和Hough变换的距离采样数也可以提高加速度最小可分辨单元。然后进行了仿真验证,仿真结果证实了该算法的有效性。
4)把估计得到的加速度测量作为新增观测量引入到目标跟踪中,研究了恒增益跟踪滤波器设计及跟踪性能分析。利用离散Riccati方程的非递归代数解,推导得到了利用距离、速度、加速度测量的Kalman跟踪滤波器的稳态解的解析表达式,并提出了一种新的利用目标状态的不确定性对稳态协方差矩阵元素进行归一化的方法。利用引入加速度测量时Kalman跟踪滤波器的稳态解,研究了恒增益跟踪滤波器设计问题,给出了测量精度趋于无限高时的极限滤波性能。把在杂波环境中目标跟踪问题简化为测量源不确定性问题,分析了在目标跟踪中引入速度测量和进一步引入加速度测量对提高跟踪性能的影响。分析结果表明,无论是在杂波环境中还是在非杂波环境中,只要在目标跟踪中引入加速度测量,均可有效提高目标跟踪精度,并使跟踪滤波器以更快的速度收敛达到稳态。
本文的研究成果对于提高弹道导弹防御雷达对再入机动弹头的探测和跟踪能力具有重要意义,并可为弹道导弹突防技术研究及突防效果评估提供有益的参考和借鉴。
Improved detection and tracking performance of maneuvering targets in the modern radar system is a forefront and urgent task within the radar domain. Under the background of missile defense, time-frquency representations is applied to accelerating target dedetcion, and acceleration is measured directly from echo signals, then the acceleration measurements is introduced in target tracking.
1) Detection performance, estimation accuracy, and resolution is analyzed when LFM signals is processed by the fractional Fourier transform(FRFT). The FRFT of a finite duration LFM signal is derived, and the coordinates of its amplifude peak in fractional Fourier domain are determined, then the relation between the coordinates and the unknown parameters of a LFM signal are given. so the FRFT is appropriate to process LFM signals of unknown parameters. From the point of view of output Signal-to-Noise Ratio(SNR), detection preformance of an unknown parameter LFM signal based on FRFT is analyzed, and in the condition of high SNR only lower 3dB to the output SNR of matched filter of ideal situation (i.e. parameters of LFM signal are known). From the point of view of parameter measurement accuracy, the expressions for root mean square of estimation error of LFM signal parameters are derived by a first order perturbation analysis approach. Results show that the method is optimal in the sense of estimation accuracy. From the point of view of resolution, the frequency resolution, the frequency rate resolution and the united frequency and frewuency rate resolution. Results show that the method is optimal in the sense of resolution. So the FRFT is effective to process LFM signals of unknown parameters.
2) Detection performance of an accelerating target based on Wigner-Hough transform is analyzed. The relations between the output amplitude of the two most widely applied dicrete forms of FRFT and acceleration, pulse number are analyzed, results show that there is not an ideal discrete form which possesses properties of continuous FRFT though the discrete forms exit a lot. Because the identical relation between of the square of magnitude of FRFT and Wigner-Hough transform, Wigner-Hough transform is adopted to accelerating targets detection and parameter measurement. For single threshold and double detection thresholds cases, detection performance of LFM signals based on Wigner-Hough transform is analyzed in theory, and expressions for PF and PD, as a function of the number of accessible Hough space accumulator cells and detection threshold, is derived, which provide a basis for setting radar detection threshholds. Finally comparison of detection performance of based on Fourier transform and based on Wigner-Hough transform is made, and comparison of detection performance of different Swerling fluctuating targets is also made, which provide a reference to estimate the radar operating range for a fluctuating target.
3) The algorithm of parameters estimation of an accelerating target based on Wigner-Hough transform is proposed. The algorithm of estimating radical acceleration based on Wigner-Hough transform is studied, and estimation flow is provided. The impact of observation interval on radial acceleration resolution is analyzed. Simulation is carried out and results verify its efficiency.
4) The tracking filter design and tracking performance evaluation is studied when acceleration measurements are incorporated into the tracking filter. According to the non-recursive solution for the discrete Riccati equation, a closed-form steady-state solution is derived for a three-state Kalman filter which estimates the range, range rate and range acceleration when range, range rate and range acceleration are measured, and a new normalization of the steady-state covariance is introduced. Constant gain filter design is studied according to the steady-state solution, and ultimate performance is given by numerical analysis when measurements accuricies tend to infinitely high. Tracking a target in clutter is taken to a situation with measurement origin uncertainty, and the tracking performance is analyzed when velocity measuremrents, and furthermore acceleration measurements are incorporated into the tracking filter. Results show that whether in clutter or not, lower steady state tracking errors and earlier attainment of steady state accuricies are the direct consequence when acceleration measurements are incorporated into the tracking filter.
The results of this thesis are beneficial not only to improve detection and tracking performance of the missile defense radar for maneuvering reentry warhead, but also to study penetration technologies and penetration effectiveness evaluation.
1)从理论上分析了FRFT对LFM信号的检测性能、参数估计精度和分辨性能。推导了时限线性调频(LFM)信号的分数阶Fourier变换(FRFT),根据其幅度特性确定了峰值所在分数阶Fourier域的位置及其对应的信号参数。由此说明,FRFT适合处理含有未知参数的LFM信号。从输出信噪比(SNR)的角度,分析了FRFT在处理高斯白噪声背景下含有未知参数LFM信号的检测性能。结果表明,在高SNR条件下,FRFT处理含有未知参数LFM信号的输出SNR仅比理想情况(即信号参数已知)下的匹配滤波低3dB。从参数估计精度的角度,采用一阶扰动方法推导得到了基于连续FRFT的LFM信号参数的估计误差均方差。从分辨力的角度,推导得到了基于FRFT的频率分辨力、调频率分辨力及频率—调频率联合分辨力。结果表明,FRFT处理含有未知参数LFM信号在参数估计精度和分辨力方面均达到了最优。因此,基于FRFT的方法对处理含有未知参数LFM信号是有效的。
2)分析了基于Wigner-Hough变换对加速运动目标的检测性能。研究了多种离散FRFT的实现算法,分析了其中应用最广泛的两种离散FRFT的输出峰值幅度与加速度、脉冲个数的关系,结果表明:尽管分数阶傅立叶变换的离散化形式很多,但当前还没有具有连续FRFT所具有性质的离散化形式。由于Wigner-Hough变换与FRFT的模平方存在恒等关系,因此在研究加速运动目标检测和参数估计问题时可采用Wigner-Hough变换。从理论上分析了单门限和双门限情况下基于Wigner-Hough变换的LFM信号的检测性能,推导得到了虚警概率和检测概率的数学表达式,为雷达设置合理的检测门限提供了理论依据。最后仿真比较了非起伏目标基于傅立叶变换和基于Wigner-Hough变换的检测性能,及不同起伏类型目标基于Wigner-Hough变换的检测性能,为估算雷达探测起伏目标的作用距离提供参考。
3)深入研究了基于Wigner-Hough变换的加速运动目标的参数估计算法。研究并给出了基于Wigner-Hough变换的加速度参数估计算法的实现流程,分析了接收信号时长对加速度最小可分辨单元的影响,加速度最小可分辨单元跟信号时长的平方成反比。同时,在一定范围内,通过增大Wigner分布的频率单元长度和Hough变换的距离采样数也可以提高加速度最小可分辨单元。然后进行了仿真验证,仿真结果证实了该算法的有效性。
4)把估计得到的加速度测量作为新增观测量引入到目标跟踪中,研究了恒增益跟踪滤波器设计及跟踪性能分析。利用离散Riccati方程的非递归代数解,推导得到了利用距离、速度、加速度测量的Kalman跟踪滤波器的稳态解的解析表达式,并提出了一种新的利用目标状态的不确定性对稳态协方差矩阵元素进行归一化的方法。利用引入加速度测量时Kalman跟踪滤波器的稳态解,研究了恒增益跟踪滤波器设计问题,给出了测量精度趋于无限高时的极限滤波性能。把在杂波环境中目标跟踪问题简化为测量源不确定性问题,分析了在目标跟踪中引入速度测量和进一步引入加速度测量对提高跟踪性能的影响。分析结果表明,无论是在杂波环境中还是在非杂波环境中,只要在目标跟踪中引入加速度测量,均可有效提高目标跟踪精度,并使跟踪滤波器以更快的速度收敛达到稳态。
本文的研究成果对于提高弹道导弹防御雷达对再入机动弹头的探测和跟踪能力具有重要意义,并可为弹道导弹突防技术研究及突防效果评估提供有益的参考和借鉴。
Improved detection and tracking performance of maneuvering targets in the modern radar system is a forefront and urgent task within the radar domain. Under the background of missile defense, time-frquency representations is applied to accelerating target dedetcion, and acceleration is measured directly from echo signals, then the acceleration measurements is introduced in target tracking.
1) Detection performance, estimation accuracy, and resolution is analyzed when LFM signals is processed by the fractional Fourier transform(FRFT). The FRFT of a finite duration LFM signal is derived, and the coordinates of its amplifude peak in fractional Fourier domain are determined, then the relation between the coordinates and the unknown parameters of a LFM signal are given. so the FRFT is appropriate to process LFM signals of unknown parameters. From the point of view of output Signal-to-Noise Ratio(SNR), detection preformance of an unknown parameter LFM signal based on FRFT is analyzed, and in the condition of high SNR only lower 3dB to the output SNR of matched filter of ideal situation (i.e. parameters of LFM signal are known). From the point of view of parameter measurement accuracy, the expressions for root mean square of estimation error of LFM signal parameters are derived by a first order perturbation analysis approach. Results show that the method is optimal in the sense of estimation accuracy. From the point of view of resolution, the frequency resolution, the frequency rate resolution and the united frequency and frewuency rate resolution. Results show that the method is optimal in the sense of resolution. So the FRFT is effective to process LFM signals of unknown parameters.
2) Detection performance of an accelerating target based on Wigner-Hough transform is analyzed. The relations between the output amplitude of the two most widely applied dicrete forms of FRFT and acceleration, pulse number are analyzed, results show that there is not an ideal discrete form which possesses properties of continuous FRFT though the discrete forms exit a lot. Because the identical relation between of the square of magnitude of FRFT and Wigner-Hough transform, Wigner-Hough transform is adopted to accelerating targets detection and parameter measurement. For single threshold and double detection thresholds cases, detection performance of LFM signals based on Wigner-Hough transform is analyzed in theory, and expressions for PF and PD, as a function of the number of accessible Hough space accumulator cells and detection threshold, is derived, which provide a basis for setting radar detection threshholds. Finally comparison of detection performance of based on Fourier transform and based on Wigner-Hough transform is made, and comparison of detection performance of different Swerling fluctuating targets is also made, which provide a reference to estimate the radar operating range for a fluctuating target.
3) The algorithm of parameters estimation of an accelerating target based on Wigner-Hough transform is proposed. The algorithm of estimating radical acceleration based on Wigner-Hough transform is studied, and estimation flow is provided. The impact of observation interval on radial acceleration resolution is analyzed. Simulation is carried out and results verify its efficiency.
4) The tracking filter design and tracking performance evaluation is studied when acceleration measurements are incorporated into the tracking filter. According to the non-recursive solution for the discrete Riccati equation, a closed-form steady-state solution is derived for a three-state Kalman filter which estimates the range, range rate and range acceleration when range, range rate and range acceleration are measured, and a new normalization of the steady-state covariance is introduced. Constant gain filter design is studied according to the steady-state solution, and ultimate performance is given by numerical analysis when measurements accuricies tend to infinitely high. Tracking a target in clutter is taken to a situation with measurement origin uncertainty, and the tracking performance is analyzed when velocity measuremrents, and furthermore acceleration measurements are incorporated into the tracking filter. Results show that whether in clutter or not, lower steady state tracking errors and earlier attainment of steady state accuricies are the direct consequence when acceleration measurements are incorporated into the tracking filter.
The results of this thesis are beneficial not only to improve detection and tracking performance of the missile defense radar for maneuvering reentry warhead, but also to study penetration technologies and penetration effectiveness evaluation.
引文
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