Figure 2.1 Side-fired Radar detector.
Figure 2.2 Radar signal power over road surface.
Microwave radar was developed for detecting objects. The word radar was derived from the function that it performs: Radio Detection and Ranging. The term microwave refers to the wavelength of the transmitted energy of 1GHz to 30 GHz. Microwave sensors designed for traffic data collection are limited to intervals near 10.525 or 24.0 GHz. Sensors with 10.525GHz have lower range resolution , bigger size and lower cost than sensors with 24Ghz.
Microwave sensors are generally mounted as side-fire configuration (as Figure 2.1). Side-fire mode is mounted on a roadside pole with its footprint aimed at right angle to the traffic lanes. Side-fire mode can monitor up to 10 lanes for each sensor.
The sensor receives the reflected signals from all surfaces within its beam – pavement, barriers, vehicles and trees. It maintains a background signal level from fixed objects in each range slices. Vehicles are detected when their reflected signal exceeds the background level of their range slice by a certain amount called threshold (see Figure 2.2).
The main types of microwave radar sensors are used in roadside are Frequency Modulated Continuous Wave (FMCW) radar [1, 2] in which the transmitted frequency is constantly changing with respect to time, as illustrated in Figure 2.3. The FMCW radar operates as a presence detector and can detect motionless vehicles.
The carrier frequency increases linearly with time. The ramp slope is given byΔf/Δt.
The echo is received after the round trip time Tr = 2R/c where R is the distance to the target. The echo is mixed with a portion of the transmitted signal to produce an output beat frequency,
(2.1) where is range resolution.
A moving vehicle will superimpose a Doppler frequency shift on the beat frequency fd. One portion of the beat frequency will be increased and the other portion will be decreased. For a target approaching the radar, the received signal frequency is increased (shifted up in the diagram) decreasing the up-sweep beat frequency and increasing the down-sweep beat frequency (see Figure 2.4)
fb(up) = fb - fd, (2.2) fb(dn) = fb + fd.
If we look at the Doppler frequency when a vehicle passes through the radar antenna beam, the Doppler shift of a reflected signal is proportional to the velocity of the vehicle and to the angle at which the signal is reflected. This relationship is described by the equation:
For small angle Sinθ=θ, hence
(2.3) Therefore, the Doppler shift changes linearly and pass through zero as the vehicle pass through the sensor‟s field of view [3](As Figure 2.5). The slope of this linear change is a function of the velocity of the target and the distance of the target‟s path from the sensor. The Doppler shift of reflected angle is measured multiple times as the vehicle passes through the field of view of side fire sensor. A linear fit is applied to the Doppler shift measurements and results in a slope m. The slop m is converted to a speed by
. (2.4) Another vehicle speed estimating method is to use the virtual loop concept [4, 5, 6], which a detection zone of a radar is realized as an inductive loop on the ground.
Figure 2.3 FMCW Radar concept.
Figure 2.4 Doppler frequency for a moving vehicle in FMCW Radar.
Radar Sensor θ
d
fd
t V
t2
t2
t1
t1
t3
t3
fd
Figure 2.5 Time-frequency distribution of a moving vehicle in FMCW Radar.
The speed of vehicle is calculated as
, (2.5) where L is the length of detection zone, Lv is the average effective length of vehicles and Δt is the detector on time. The virtual loop speed can be a good result for average speed. But it is not accurate in general.
Radar and inductive loop detectors have historically performed vehicle classification by providing estimates of vehicle length based on vehicle speed ,v , and the detector on time. The equation for vehicle length, Lv, is given by
Lv=v*on time-effect length of detection zone.
H. Roe and G. S. Hobson (1992) [7] have described a forward-looking FMCW Radar which can separate traffic into five classes. This single lane detector uses the profile of vehicle to do vehicle classification. The profile is formed by the vehicle height and length. The vehicle speed is calculated from Doppler effect. Park et al. (2003) [8] have developed a FMCW side-looking vehicle detection radar. The velocity is estimated by using the appearance duration of the reflected signal and the length of detection zone and Doppler shift. The classification of a vehicle, as large, medium or small size, is possible by processing received power and spectrum pattern
Numerous statistic learning methods have been developed and tested for data cluster or pattern recognition, and these classifiers are categorized into two types:
supervised and unsupervised. In supervised learning, the aim is to learn a mapping from the input to an output whose correct vehicle classes are provided by a supervisor. In unsupervised learning, there is no such supervisor and we only have input of data.
K-mean cluster is a famous unsupervised classifier that has been used for numerous applications. Furthermore, support vector machine (SVM)[9, 10] and linear discriminated analysis (LDA) [11, 12] are two supervised classifiers. LDA was originally developed in 1936 by R.A. Fisher [13]. SVMs have been used for isolated handwritten digit recognition, object recognition, speaker identification and face detection in images.
K-means is one of the best known data clustering methods. The goal of k-means is to find k points of a dataset that best represent the dataset in a certain mathematical sense. These k points are also known as cluster centers. After obtaining these cluster centers, they can be used for data classification.
LDA is a supervisory classifier. LDA obtains a linear transformation ("discriminant function") of the two predictors, X and Y, which yields a new set of transformed values
that provides more accurate discrimination than either predictor alone. A transformation function is found that maximizes the ratio of between-class to within-class variance.
The transformation seeks to rotate the axes so as to maximize the differences between the groups when the categories are project on the new axes. In the ideal case, a projection can be found that completely separates the categories. However, in most cases no transformation exists that provides full separation, so the objective is to obtain the transformation that minimizes the overlap among the transformed distributions. The LDA can be derived as a plug-in Bayes classifier. LDA projects the nine feature dimension space considered in this study into a three dimension linear discriminant (LD) space. The plug-in classifier finds the average group centers for each vehicle category and saves it. When predicting a test sample vehicle, the classifier measures the Mahalanobis distance between the group center and the LD project point of the vehicle features. The plug-in classifier then estimates the posterior probability of each group using Mahalanobis distance, the prior probability which is the group probability of training set, and the covariance matrix. The testing vehicle belongs to the group with the highest posterior.
SVM is also a supervisory classifier. SVMs attempt to identify a set of support vectors, two support hyperplanes, and an optimal hyperplane for separating two groups.
SVM is a binary classifier. Two strategies can be developed to support multiple classifications: one-against-one and one-against-rest. The one-against-rest strategy constructs k SVMs to separate k groups. The m-th SVM separates the m-th group from the others. For k groups, the one-against-one strategy constructs k(k-1)/2 SVMs to separate each pair of groups.