In this paper,results of robust estimation of [1,2] are extended to state estimation with missing measurements...
LIANG Huayong1,ZHOU Tong2 1.Department of Automation,Tsinghua University,Beijing 100084,P.R.China2.Department of Automation and TNList,Tsinghua University,Beijing 100084,P.R.China
The two important features of self-organizing maps （SOM）, topological preservation and easy visualization, give it great potential for analyzing multi-dimensional time series, specifically traffic flow time series in an urban traffic network. This paper investigates the application of SOM in the representation and prediction of multi-dimensional traffic time series. Ffrst, SOMs are applied to cluster the time series and to project each multi-dimensional vector onto a two-dimensional SOM plane while preserving the topological relationships of the original data. Then, the easy visualization of the SOMs is utilized and several exploratory methods are used to investigate the physical meaning of the clusters as well as how the traffic flow vectors evolve with time. Finally, the k-nearest neighbor （kNN） algorithm is applied to the clustering result to perform short-term predictions of the traffic flow vectors. Analysis of real world traffic data shows the effec- tiveness of these methods for traffic flow predictions, for they can capture the nonlinear information of traffic flows data and predict traffic flows on multiple links simultaneously.
Two characteristics of Chinese mixed traffic invalidate the conventional queuing delay estimates for western countries. First, the driving characteristics of Chinese drivers lead to different delays even though the other conditions are the same. Second, urban traffic flow in China is often hindered by pedestrians at intersections, such that imported intelligent traffic control systems do not work appropriately. Typical delay estimates for Chinese conditions were obtained from data for over 500 vehicle queues in Beijing collected using charge coupled device （CCD） cameras. The results show that the delays mainly depend on the pro- portion and positions of heavy vehicles in the queue, as well as the start-up situations （with or without interference）. A simplified delay estimation model considers vehicle types and positions that compares well with the observed traffic delays.
Support vector machines （SVMs） have widespread use in various classification problems. Although SVMs are often used as an off-the-shelf tool, there are still some important issues which require improvement such as feature rescaling. Standardization is the most commonly used feature rescaling method. However, standardization does not always improve classification accuracy. This paper describes two feature rescaling methods： multiple kernel learning-based rescaling （MKL-SVM） and kernel-target alignment-based rescaling （KTA-SVM）. MKL-SVM makes use of the framework of multiple kernel learning （MKL） and KTA-SVM is built upon the concept of kernel alignment, which measures the similarity between kernels. The proposed meth- ods were compared with three other methods： an SVM method without rescaling, an SVM method with standardization, and SCADSVM. Test results demonstrate that different rescaling methods apply to different situations and that the proposed methods outperform the others in general.
In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.
