Modeled Adaptive Filtering And Its Application Research

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.