模型化自适应滤波及其应用研究
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摘要
本文为未知时变／时不变系统的冲击响应系数,研究了利用多项式预测模型来建模的方法,并将其视为卡尔曼滤波器的状态方程；以系统输入输出关系作为观测方程,那么就将最大似然、最大后验和最小均方等多种统计意义下无偏最优的卡尔曼滤波器引入来解决自适应滤波问题,从而提出了模型化自适应滤波方法。理论分析以及仿真结果都证明了该算法相对传统自适应滤波算法的性能优势。针对低信噪比下的自适应滤波问题,通过引入有偏估计的思想,即：将传统卡尔曼滤波器的无偏最小方差估计值乘以一个偏差因子,来折衷估计的偏差和方差以得到更小的均方误差,进而提出了有偏卡尔曼滤波和模型化的有偏自适应滤波方法。应用于低信噪比下的系统辨识,仿真结果显示模型化的有偏自适应滤波性能优于其对应的无偏算法。
针对雷达跟踪机动目标的波形选择应用,本文利用研究的模型化自适应滤波算法提出了一种新的雷达波形选择方法。由于机动目标的运动状态满足多项式规律变化,即多项式预测模型可以准确地描述目标的运动规律,因此模型化自适应滤波算法可以很好地跟踪目标运动状态并得到相应的估计误差及其预测。根据估计误差预测的误差椭圆,通过分数阶傅里叶变换来旋转测量误差椭圆以使其与预测误差椭圆正交,从而得到了一种新的最优选择雷达发射波形方法。仿真结果证明了该算法性能上的优势。
针对稀疏系统辨识的应用,本文结合研究的模型化自适应滤波算法和压缩采样的思想提出了一种新的稀疏系统辨识算法。该算法一方面利用多项式预测模型描述了系统的时变特性；另一方面利用l1范数的不等式约束来描述系统的稀疏性,将稀疏系统辨识问题转化为了一个带约束的卡尔曼滤波问题。利用伪观测技术求解这一带约束的卡尔曼滤波问题,即得到了稀疏系统辨识的结果。仿真结果表明,提出的算法由于同时考虑了系统的稀疏性和时变特性,其性能优于对比算法。
针对道路车流量的实时视频检测应用,本文结合研究的模型化自适应滤波算法和提出的两个特征参数,得到了一种新的道路车流量实时视频检测方法。根据分析,提出的对比度失真和亮度失真参数非常适合解决诸如阴影干扰、实时背景更新以及摄像机晃动等一直困扰着道路车流量视频检测的问题。但是特征参数曲线上的毛刺现象给车流量检测过程带来了严重的困扰。针对这一问题,采用提出的模型化自适应滤波算法来为特征参数曲线滤波。由于检测区域的大小通常为一个典型车辆大小,因此可以认为车辆是匀速经过检测区域的,即特征参数的上升和下降是符合一阶多项式规律的。模型化自适应滤波算法可以很好的抑制特征参数曲线上的毛刺现象,从而为后续的车流量检测算法带来了方便。不同道路、车流量和天气情况下的实验结果表明,本文提出的方法相比传统方法有着显著的优势。
A polynomial prediction model is researched in this paper to describe the time-variant/invariant impulse response coefficients of an unkown system. When the polynomial prediction model is viewed as the state equations of the unkown impulse response coefficients and the relationships between the inputs and outputs of the system are regarded as the measurements of the states, our adaptive filtering can be achieved in the framework of the Kalman filter which is unbiased optimal in the sense of the MAP (Maximum A Posteriori), ML (Most Likelihood) and MMSE (Minimum Mean Square Error). In this way, a modelized adaptive filtering algorithm is proposed. Not only do the analytical results of the algorithm but also the simulation results show that our algorithm outperforms the traditional known algorithms. For adaptive filtering problem in low SNR (Signal to Noise Ratio), the idea of biased estimation is introduced. If we multiply the unbiased minimum-variance estimation of the traditional Kalman filter by a bias factor, a tradeoff between estimation bias and estimation variance is provided to reduce the estimation mean-squared error of the traditional Kalman filter. By this approach, a biased Kalman filter and a modelized biased adaptive filter are proposed. For system identification in low SNR, the simulation results show that the modelized biased adaptive filter outperforms the unbiased one.
For the application of waveform selection for tracking maneuver target, the researched modelized adaptive filtering algorithm is used to propose a novel waveform selection approach. Because the motion equation of the target is polynomial function of time, the polynomial prediction model can describe the motion state of the target accurately. It means that the modelized adaptive filtering algorithm can track the position and velocity of the target accurately and predict the prior uncertainty error ellipse of the tracking system. According to the prior uncertainty error ellipse, we use the fractional Fourier transform (FrFT) to rotate the measurement error ellipse to make them orthogonal to each other. Thus we get the new approach to waveform selection for tracking maneuver target. The simulation results have shown the performance superiority of the proposed approach.
For the application of sparse system identification, the researched modelized adaptive filtering algorithm and the idea of compressive sensing are combined to propose a novel sparse system identification algorithm. On one hand, we use polynomial prediction model to describe the time-varying characteristic of the system. On the other hand, we use l1 norm inequality constraint to describe the sparsity of the system. Thus the sparse system identification problem is converted to a Kalman filtering problem with an inequality constraint which can be solved by the pseudo-observation approach. Both the system time-varying characteristic and the system sparsity are taken into consideration. The simulation results show that our algorithm outperforms the contrast algorithms.
For the application of vision-based real time vehicle flow information extraction, the researched modelized adaptive filtering algorithm and two new vision parameters are combined to propose a novel vision-based method for real-time extracting vehicle flow information on a road. The proposed vision parameters are called as contrast and luminance distortion respectively. The analytical results show that the proposed vision parameters are very suitable for solving many traditional problems in the vision-based vehicle flow information extraction, such as the shadow interferences, real-time background updating and the flickering of camera. But there are many burrs in the parameter curves which seriously disturb the vehicle flow information extraction. For this problem, we use the proposed modelized adaptive filtering algorithm to filter the parameter curves. Because the size of the detection zone is the size of a typical vehicle, we can assume that vehicles pass the detection zone at a uniform speed. It means that the variations of the parameters are first order polynomial functions of the time. Thus the modelized adaptive filtering algorithm can filter out the burrs in the parameter curves. The experimental results based on the different roads and different vehicle flows under different weather conditions show that the proposed method is better than the traditional methods.
针对雷达跟踪机动目标的波形选择应用,本文利用研究的模型化自适应滤波算法提出了一种新的雷达波形选择方法。由于机动目标的运动状态满足多项式规律变化,即多项式预测模型可以准确地描述目标的运动规律,因此模型化自适应滤波算法可以很好地跟踪目标运动状态并得到相应的估计误差及其预测。根据估计误差预测的误差椭圆,通过分数阶傅里叶变换来旋转测量误差椭圆以使其与预测误差椭圆正交,从而得到了一种新的最优选择雷达发射波形方法。仿真结果证明了该算法性能上的优势。
针对稀疏系统辨识的应用,本文结合研究的模型化自适应滤波算法和压缩采样的思想提出了一种新的稀疏系统辨识算法。该算法一方面利用多项式预测模型描述了系统的时变特性；另一方面利用l1范数的不等式约束来描述系统的稀疏性,将稀疏系统辨识问题转化为了一个带约束的卡尔曼滤波问题。利用伪观测技术求解这一带约束的卡尔曼滤波问题,即得到了稀疏系统辨识的结果。仿真结果表明,提出的算法由于同时考虑了系统的稀疏性和时变特性,其性能优于对比算法。
针对道路车流量的实时视频检测应用,本文结合研究的模型化自适应滤波算法和提出的两个特征参数,得到了一种新的道路车流量实时视频检测方法。根据分析,提出的对比度失真和亮度失真参数非常适合解决诸如阴影干扰、实时背景更新以及摄像机晃动等一直困扰着道路车流量视频检测的问题。但是特征参数曲线上的毛刺现象给车流量检测过程带来了严重的困扰。针对这一问题,采用提出的模型化自适应滤波算法来为特征参数曲线滤波。由于检测区域的大小通常为一个典型车辆大小,因此可以认为车辆是匀速经过检测区域的,即特征参数的上升和下降是符合一阶多项式规律的。模型化自适应滤波算法可以很好的抑制特征参数曲线上的毛刺现象,从而为后续的车流量检测算法带来了方便。不同道路、车流量和天气情况下的实验结果表明,本文提出的方法相比传统方法有着显著的优势。
A polynomial prediction model is researched in this paper to describe the time-variant/invariant impulse response coefficients of an unkown system. When the polynomial prediction model is viewed as the state equations of the unkown impulse response coefficients and the relationships between the inputs and outputs of the system are regarded as the measurements of the states, our adaptive filtering can be achieved in the framework of the Kalman filter which is unbiased optimal in the sense of the MAP (Maximum A Posteriori), ML (Most Likelihood) and MMSE (Minimum Mean Square Error). In this way, a modelized adaptive filtering algorithm is proposed. Not only do the analytical results of the algorithm but also the simulation results show that our algorithm outperforms the traditional known algorithms. For adaptive filtering problem in low SNR (Signal to Noise Ratio), the idea of biased estimation is introduced. If we multiply the unbiased minimum-variance estimation of the traditional Kalman filter by a bias factor, a tradeoff between estimation bias and estimation variance is provided to reduce the estimation mean-squared error of the traditional Kalman filter. By this approach, a biased Kalman filter and a modelized biased adaptive filter are proposed. For system identification in low SNR, the simulation results show that the modelized biased adaptive filter outperforms the unbiased one.
For the application of waveform selection for tracking maneuver target, the researched modelized adaptive filtering algorithm is used to propose a novel waveform selection approach. Because the motion equation of the target is polynomial function of time, the polynomial prediction model can describe the motion state of the target accurately. It means that the modelized adaptive filtering algorithm can track the position and velocity of the target accurately and predict the prior uncertainty error ellipse of the tracking system. According to the prior uncertainty error ellipse, we use the fractional Fourier transform (FrFT) to rotate the measurement error ellipse to make them orthogonal to each other. Thus we get the new approach to waveform selection for tracking maneuver target. The simulation results have shown the performance superiority of the proposed approach.
For the application of sparse system identification, the researched modelized adaptive filtering algorithm and the idea of compressive sensing are combined to propose a novel sparse system identification algorithm. On one hand, we use polynomial prediction model to describe the time-varying characteristic of the system. On the other hand, we use l1 norm inequality constraint to describe the sparsity of the system. Thus the sparse system identification problem is converted to a Kalman filtering problem with an inequality constraint which can be solved by the pseudo-observation approach. Both the system time-varying characteristic and the system sparsity are taken into consideration. The simulation results show that our algorithm outperforms the contrast algorithms.
For the application of vision-based real time vehicle flow information extraction, the researched modelized adaptive filtering algorithm and two new vision parameters are combined to propose a novel vision-based method for real-time extracting vehicle flow information on a road. The proposed vision parameters are called as contrast and luminance distortion respectively. The analytical results show that the proposed vision parameters are very suitable for solving many traditional problems in the vision-based vehicle flow information extraction, such as the shadow interferences, real-time background updating and the flickering of camera. But there are many burrs in the parameter curves which seriously disturb the vehicle flow information extraction. For this problem, we use the proposed modelized adaptive filtering algorithm to filter the parameter curves. Because the size of the detection zone is the size of a typical vehicle, we can assume that vehicles pass the detection zone at a uniform speed. It means that the variations of the parameters are first order polynomial functions of the time. Thus the modelized adaptive filtering algorithm can filter out the burrs in the parameter curves. The experimental results based on the different roads and different vehicle flows under different weather conditions show that the proposed method is better than the traditional methods.
引文
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