**3. Classification**

Target recognition is a challenge for each radar engineer. A reliable feature extraction and classification process has to be implemented. To describe the characteristics of pedestrians and vehicles, the velocity profile and range profile signal features have been introduced. These are the basis in the feature extraction and target recognition system based on a single radar measurement (single look of 39 ms duration) as described in subsection 3.1. An extended extraction based on the spreading and contraction of the spectra by observing several measurements is considered in subsection 3.2. Finally in subsection 3.3, a tracker feedback is calculated where additional features based on the Kalman gain and innovation are extracted. In the next step, the classification process is performed, which maps the extracted features into classes. An evaluation of the classification results is shown by means of a confusion matrix for the case of a single measurement- and multiple measurements-feature extraction.

### **3.1. Classification based on a single radar measurement**

Radar sensors provide continuously available measurement results in an interval of a few milliseconds. This interval is determined by the duration of the transmission signal *T*CPI = 39 ms in which a single MFSK signal is transmitted. The echo signal is downconverted and Fourier-transformed, which allows the described features to be extracted continuously. Rather than examinating a received sequence of radar echoes, this subchapter will initially focus on a single radar measurement of *T*CPI = 39 ms.

### *3.1.1. Feature extraction*

6 Will-be-set-by-IN-TECH

The range profile and velocity profile features do not depend on the modulation signal. Solely, the range and velocity resolution must be smaller than the expected extension. For example, in the case of a continous wave modulation signal, the range profile can be read directly from the Fourier transformed radar echo signal and the velocity profile can be evaluated from the Doppler spectrum. Also, instead of these spectra or the frequency spectrum and phase difference analysis, it is possible to calculate the extension of an object in range and velocity on the basis of target lists by applying a detection algorithm. On this basis, an extended range profile with a point-shaped velocity profile can also be measured for a vehicle. For a

pedestrian, the profiles remain vice versa. Figure 5 depicts this context.

**Figure 5.** Range profile and velocity profile of a pedestrian and a vehicle.

**3. Classification**

extraction.

The longitudinally and laterally moving pedestrians are classified as **pedestrians**, longitudinally and laterally moving vehicles as **vehicles**, all other signals received from objects such as parked cars, poles, trees and traffic signs are classified as **other** objects.

Target recognition is a challenge for each radar engineer. A reliable feature extraction and classification process has to be implemented. To describe the characteristics of pedestrians and vehicles, the velocity profile and range profile signal features have been introduced. These are the basis in the feature extraction and target recognition system based on a single radar measurement (single look of 39 ms duration) as described in subsection 3.1. An extended extraction based on the spreading and contraction of the spectra by observing several measurements is considered in subsection 3.2. Finally in subsection 3.3, a tracker feedback is calculated where additional features based on the Kalman gain and innovation are extracted. In the next step, the classification process is performed, which maps the extracted features into classes. An evaluation of the classification results is shown by means of a confusion matrix for the case of a single measurement- and multiple measurements-feature Automotive radar sensors are an important source of information for security and comfort systems. The information is measured in terms of range, radial velocity and signal level. However, information about the object types do not exist. To fill this gap, features from the available information are extracted, which describe the object types and allow a decision of the related class on the basis of measured sensor data. To describe a detected object, this signal processing step calculates a number of features, which are discriminant for measurements containing different object types and match for objects from the same type. Thereby, moderately separated features achieve even in a perfect classification algorithm only moderate or even poor results ([16], [17]). An ideal feature extractor on the other hand shows good classification performance by using simple linear classifiers. This is why the feature extraction is so important. For a distinct classification, transformation-invariant features are sought. Still, there is no recipe to determine a feature set and since each sensor type describes an object specifically and each task is different, the feature set for pedestrian recognition based on an automotive radar sensor is explained shortly. Figure 6 shows the feature extraction with the specific object description in the context of the signal processing chain.

The basis for feature extraction are the velocity profile and the range profile of a detected object which has been described previously. The term of the profile describes the physical and kinematic dimensions of an object in the distance, angle and velocity. This can be measured in the case of multiple reflection points with different velocities greater than zero for any object. It can involve an extended or a point-shaped profile for the range and velocity depending on the type of expansion. On this basis, a number *n* of features can be calculated which describe the object in terms of a radar measurement. All *n* calculated real valued features *x*1, ..., *xn* are saved in a feature vector *x* and build the basis for further signal processing steps.

$$\vec{\mathbf{x}} = (\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n) \; n \in \mathbf{N}, \mathbf{x}\_i \in \mathbf{R} \tag{5}$$

Exemplarily, the calculation of the range profile *R*profile is given in Equation (6). Analogously, the velocity profile *v*profile of the spectrum can be calculated, Equation (7).

$$\mathbf{x}\_1 = R\_{\text{profile}} = R\_{\text{max}} - R\_{\text{min}} \tag{6}$$

$$\mathbf{x}\_{\mathsf{5}} = v\_{\text{profile}} = v\_{\text{max}} - v\_{\text{min}} \tag{7}$$

0 1 2 3 4 5

0 1 2 3 4 5

Pedestrian Recognition Based on 24 GHz Radar Sensors 249

(b) *v*profile, Vehicle

v profile [m/s]

0

0.2

0.4

0.6

Probability

**Figure 7.** Feature histogram of the velocity profile using single radar measurements as a basis for feature

statement about the performance of the algorithm and designed model. Figure 8 depicts this

extraction Classification

Model Training

Feature

Test

**Figure 8.** Signal flow graph of the classification process. Using a training data-set a model can be evaluated which performance is measured by a labelled test data set. This model is used for the

A classifier based on statistical learning theory is the support vector machine (SVM), introduced by Boser et al. in 1992 [24]. The SVM became very famous as studies about classification algorithms show good performance [25]. The classification process has low complexity and is very effective for high dimensional feature vectors. An SVM separates a set of training data by calculating a hyperplane *h*(*x*) with maximum margin between the two classes ±1 in a higher dimensional space in order to find the best classification function.

In this classification process, the SVM is able to map the extracted feature set into three different classes by using a majority voting algorithm. The verification of the previous training

Table 3 shows the classification results. A trained and tested SVM was applied to different data sets of the extracted features from single measurements. All measurements were taken in an urban area with an ego velocity of 50 km/h. Applying new test data results in 71.32%

These quantitative results show already a possibility to distinguish between vehicles, pedestrians and other objects. However the performance is not good enough. Therefore

is conducted with the help of test data sets recorded from real urban measurements.

true positive for a vehicle and 45.20% true positive for a pedestrian.

0.8

1

vprofile [m/s]

(a) *v*profile, Pedestrian

extraction. The common area index is calculated to 0.57.

Radar measurements

0

classification process.

0.2

0.4

0.6

Probability

process.

0.8

1

The approach in feature extraction, using stochastic features, assumes that the measured data are random variables with independent and identical distribution. From this data within a single measurement cycle the variance and the standard deviation is estimated. To support the classification process, the number of scatterers is extracted, which describes the number of detected reflection points of an object. This approach allows a classification of the object type within a single measurement. The entire feature set for *n* = 8 features is shown in Table 2 below.


**Table 2.** Feature Set of each object in a single measurement.

To determine the quality of a feature, the common area index (CAI) of two histograms is considered. While a common area index of 0 describes a complete overlapping of the feature space, a CAI of 1 describes an absolutely separable feature.

Several urban measurement scenarios of longitudinally moving vehicles and pedestrians were measured with an automotive radar sensor. From the detections of each single measurement cycle the features are extracted. Exemplarily, the velocity profile of a vehicle and a pedestrian is depicted in Figure 7 as a histogram. It shows a strong overlap of the area with a point shaped extension. This results directly from the model. A pedestrian is not extended at all times, because the arms and legs move sinusoidally. In addition, the echo signal fluctuates which causes fewer detections in a measurement. The vehicle equipped with the radar sensor moves also. The quality of the feature is calculated to CAI = 0.57.

### *3.1.2. Classification*

The assignment of a measured object to a class is performed by a subjective decision algorithm based on the extracted characteristics. This process is called classification. The features therefore have been described previously, and are extracted within a single radar measurement of *T*CPI = 39 ms. In supervised classifiers, the model of the classifier is generated in a training phase by using a training data set. The verification is performed in an evaluation phase with a test data set. The training data and test data consist of randomly selected feature vectors *x* of the radar measurements and corresponding assigned class labels. In the training and evaluation phase the classification result can be compared to the class labels and make a

8 Will-be-set-by-IN-TECH

Exemplarily, the calculation of the range profile *R*profile is given in Equation (6). Analogously,

The approach in feature extraction, using stochastic features, assumes that the measured data are random variables with independent and identical distribution. From this data within a single measurement cycle the variance and the standard deviation is estimated. To support the classification process, the number of scatterers is extracted, which describes the number of detected reflection points of an object. This approach allows a classification of the object type within a single measurement. The entire feature set for *n* = 8 features is shown in Table

*x*<sup>2</sup> *std*(*R*) Standard deviation in range

*x*<sup>6</sup> *std*(*vr*) Standard deviation in velocity

To determine the quality of a feature, the common area index (CAI) of two histograms is considered. While a common area index of 0 describes a complete overlapping of the feature

Several urban measurement scenarios of longitudinally moving vehicles and pedestrians were measured with an automotive radar sensor. From the detections of each single measurement cycle the features are extracted. Exemplarily, the velocity profile of a vehicle and a pedestrian is depicted in Figure 7 as a histogram. It shows a strong overlap of the area with a point shaped extension. This results directly from the model. A pedestrian is not extended at all times, because the arms and legs move sinusoidally. In addition, the echo signal fluctuates which causes fewer detections in a measurement. The vehicle equipped with the radar sensor

The assignment of a measured object to a class is performed by a subjective decision algorithm based on the extracted characteristics. This process is called classification. The features therefore have been described previously, and are extracted within a single radar measurement of *T*CPI = 39 ms. In supervised classifiers, the model of the classifier is generated in a training phase by using a training data set. The verification is performed in an evaluation phase with a test data set. The training data and test data consist of randomly selected feature vectors *x* of the radar measurements and corresponding assigned class labels. In the training and evaluation phase the classification result can be compared to the class labels and make a

*x*<sup>1</sup> = *R*profile = *R*max − *R*min (6)

*x*<sup>5</sup> = *v*profile = *v*max − *v*min (7)

the velocity profile *v*profile of the spectrum can be calculated, Equation (7).

Feature Annotation Description *x*<sup>1</sup> *R*profile Extension in range

*x*<sup>3</sup> *var*(*R*) Variance in range *x*<sup>4</sup> *v*<sup>r</sup> Radial Velocity *x*<sup>5</sup> *v*profile Extension in velocity

*x*<sup>7</sup> *var*(*vr*) Variance in velocity *x*<sup>8</sup> scatterer Number of scatterers

**Table 2.** Feature Set of each object in a single measurement.

space, a CAI of 1 describes an absolutely separable feature.

moves also. The quality of the feature is calculated to CAI = 0.57.

2 below.

*3.1.2. Classification*

**Figure 7.** Feature histogram of the velocity profile using single radar measurements as a basis for feature extraction. The common area index is calculated to 0.57.

statement about the performance of the algorithm and designed model. Figure 8 depicts this process.

**Figure 8.** Signal flow graph of the classification process. Using a training data-set a model can be evaluated which performance is measured by a labelled test data set. This model is used for the classification process.

A classifier based on statistical learning theory is the support vector machine (SVM), introduced by Boser et al. in 1992 [24]. The SVM became very famous as studies about classification algorithms show good performance [25]. The classification process has low complexity and is very effective for high dimensional feature vectors. An SVM separates a set of training data by calculating a hyperplane *h*(*x*) with maximum margin between the two classes ±1 in a higher dimensional space in order to find the best classification function.

In this classification process, the SVM is able to map the extracted feature set into three different classes by using a majority voting algorithm. The verification of the previous training is conducted with the help of test data sets recorded from real urban measurements.

Table 3 shows the classification results. A trained and tested SVM was applied to different data sets of the extracted features from single measurements. All measurements were taken in an urban area with an ego velocity of 50 km/h. Applying new test data results in 71.32% true positive for a vehicle and 45.20% true positive for a pedestrian.

These quantitative results show already a possibility to distinguish between vehicles, pedestrians and other objects. However the performance is not good enough. Therefore

10 Will-be-set-by-IN-TECH 250 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Pedestrian Recognition Based on 24 GHz Radar Sensors <sup>11</sup>


It can be seen that a long measurement buffer increases the probability to detect the maximum velocity profile. But even a smaller velocity profile can be detected and fulfils the

Using current and time delayed range measurements leads to incorrect range profiles, due to the movement of the objects during the elapsed buffer time. To cope this, the corresponding range measurements inside the buffer must therefore be predicted in range. Each stored measurement is predicted in range by the elapsed time Δ*T*Buffer and the velocity *v* = (*v*x, *v*y) during the measurements to compensate the movement. A new estimated range *<sup>R</sup>* <sup>=</sup> <sup>|</sup>*<sup>R</sup>*∗| can

The multiple measurement feature set is shown in Table 4. It consists of the same characteristics as the single measurement feature set, but is calculated from a basis of several

*x*<sup>10</sup> *std*(*R*,buf) Standard deviation in range

*x*<sup>14</sup> *std*(*v*r,buf) Standard deviation in velocity

measurements, each single measurement *R*, *v*<sup>r</sup> is stored in a buffer of several milliseconds. This ensures a

In the previous section the characteristic velocity profile of a vehicle and a pedestrian was depicted as a histogram. On the basis of a single radar measurement a quality of CAI = 0.57 was determined. Using multiple radar measurements the feature extraction is based on a larger number of measurement values. This leads to a higher separability of the features as shown exemplarily in Figures 9(a), 9(b). The common area index has a value of CAI = 0.88

In the single measurement it is described how range and velocity measurements build the basis for the feature vector and the classification process. In the multiple measurement, the basis is an extended feature vector based on several range and velocity measurements of an object stored inside a buffer. Instead of using 8 features from a single measurement, additional 8 features are available for the first time with a filled buffer. For a successful classification using a SVM, a new model is built, which is also trained/tested with in total 16 features and is a basis for the following classification process. As shown in the confusion matrix in Table 5 by the additional features, the correct classification and the overall performance achieved, increases by using a total number of 16 features from single and multiple measurements.

*R* = (*X*,*Y*) and *v* = (*v*x, *v*y) (10)

Pedestrian Recognition Based on 24 GHz Radar Sensors 251

requirements. In these measurements, a buffer of *T*Buffer = 150 ms is applied.

be calculated by a cartesian representation using velocity and elapsed time:

*<sup>R</sup>* <sup>+</sup> <sup>Δ</sup>*T*Buffer ·*<sup>v</sup>* with

Feature Annotation Description

*x*<sup>9</sup> *R*profile,buf Extension in range

*x*<sup>11</sup> *var*(*R*,buf) Variance in range *x*<sup>12</sup> *v*r,buf Radial Velocity *x*<sup>13</sup> *v*profile,buf Extension in velocity

*x*<sup>15</sup> *var*(*v*r,buf) Variance in velocity *x*<sup>16</sup> scatterer,buf Number of scatterers

**Table 4.** An additional feature set extracted from multiple measurements. To cover multiple

and thus increases by 31% compared to the single measurement feature extraction.

quick availability of an additional feature set for pedestrian classification.

*3.2.2. Classification*

*R*<sup>∗</sup> =

buffered velocity and predicted range measurements.

**Table 3.** Confusion matrix: classification applied to a single measurement test data set containing 8000 data samples.

multiple radar measurements are considered to extract a more significant features set for the classification process.

### **3.2. Classification based on multiple radar measurements**

From the continuously available radar measurements, a single measurement can be used to extract a feature set on the basis of range profile and velocity profile and estimated stochastic features. In this section, several range and velocity measurements are buffered and build the basis for the additional extraction process. From these buffered measurements a second **multiple measurement feature set** is extracted. This extends the classification process, which was previously based on a single measurement only.

### *3.2.1. Feature extraction*

To gain performance, the choice of the measurement buffer dimension is cruical. A long measurement buffer builds the basis for a more successful feature extraction, however results in a long classification time, as the classifier has to wait for the buffer to be filled. A short buffer, on the other hand is not always able to build the basis for separable features, as shown in the previous section where a single measurement is used. In this section, the dimension of the buffer is explained by means of "probability of maximum velocity profile" and fast availability deduced from the step frequency of a moving pedestrian.

An ideal measurement of a moving pedestrian allows to extract the step frequency from the spreading and contraction of the velocity profile [9]. This step frequency of *f*ped = 1.4 − 1.8 Hz can be used to determine a necessary buffer dimension. Every 1.4 Hz the maximum velocity profile can be observed considering a moving pedestrian, which allows to extract the maximum velocity profile and range profile. At all other times, the expansion in velocity is lower or even zero. To detect at least one expansion in velocity, the number of measurements should therefore span a period of *T*ped = <sup>1</sup> *<sup>f</sup>*ped . However, it can be assumed that all measurements are independent of each another, due to the ego motion of the radar, vibrations and fewer detections. Applying the feature extraction process using a single measurement, the probability *P* to extract an extended velocity is then given by:

$$P\_{v\_{\text{projike}}, \text{single}} = \frac{T\_{\text{CPI}}}{1/f\_{\text{ped}}} \tag{8}$$

Assuming an equal distribution, multiple measurements increase the probability to extract a velocity profile by the factor *<sup>T</sup>*Buffer *<sup>T</sup>*CPI .

$$P\_{\text{vọnále,multiple}} = \frac{T\_{\text{Buffer}}}{T\_{\text{CPI}}} \cdot \frac{T\_{\text{CPI}}}{1/f\_{\text{ped}}} \tag{9}$$

It can be seen that a long measurement buffer increases the probability to detect the maximum velocity profile. But even a smaller velocity profile can be detected and fulfils the requirements. In these measurements, a buffer of *T*Buffer = 150 ms is applied.

Using current and time delayed range measurements leads to incorrect range profiles, due to the movement of the objects during the elapsed buffer time. To cope this, the corresponding range measurements inside the buffer must therefore be predicted in range. Each stored measurement is predicted in range by the elapsed time Δ*T*Buffer and the velocity *v* = (*v*x, *v*y) during the measurements to compensate the movement. A new estimated range *<sup>R</sup>* <sup>=</sup> <sup>|</sup>*<sup>R</sup>*∗| can be calculated by a cartesian representation using velocity and elapsed time:

$$
\vec{R}^\* = \vec{R} + \Delta T\_{\text{Buffer}} \cdot \vec{v} \text{ with } \vec{R} = (\mathbf{X}, \mathbf{Y}) \text{ and } \vec{v} = (v\_{\mathbf{x}\prime} v\_{\mathbf{y}}) \tag{10}
$$

The multiple measurement feature set is shown in Table 4. It consists of the same characteristics as the single measurement feature set, but is calculated from a basis of several buffered velocity and predicted range measurements.


**Table 4.** An additional feature set extracted from multiple measurements. To cover multiple measurements, each single measurement *R*, *v*<sup>r</sup> is stored in a buffer of several milliseconds. This ensures a quick availability of an additional feature set for pedestrian classification.

In the previous section the characteristic velocity profile of a vehicle and a pedestrian was depicted as a histogram. On the basis of a single radar measurement a quality of CAI = 0.57 was determined. Using multiple radar measurements the feature extraction is based on a larger number of measurement values. This leads to a higher separability of the features as shown exemplarily in Figures 9(a), 9(b). The common area index has a value of CAI = 0.88 and thus increases by 31% compared to the single measurement feature extraction.

### *3.2.2. Classification*

10 Will-be-set-by-IN-TECH

Vehicle 71.32 5.87 22.81 Pedestrian 10.29 45.20 44.52 Other 23.56 26.65 49.78

**Table 3.** Confusion matrix: classification applied to a single measurement test data set containing 8000

multiple radar measurements are considered to extract a more significant features set for the

From the continuously available radar measurements, a single measurement can be used to extract a feature set on the basis of range profile and velocity profile and estimated stochastic features. In this section, several range and velocity measurements are buffered and build the basis for the additional extraction process. From these buffered measurements a second **multiple measurement feature set** is extracted. This extends the classification process, which

To gain performance, the choice of the measurement buffer dimension is cruical. A long measurement buffer builds the basis for a more successful feature extraction, however results in a long classification time, as the classifier has to wait for the buffer to be filled. A short buffer, on the other hand is not always able to build the basis for separable features, as shown in the previous section where a single measurement is used. In this section, the dimension of the buffer is explained by means of "probability of maximum velocity profile" and fast

An ideal measurement of a moving pedestrian allows to extract the step frequency from the spreading and contraction of the velocity profile [9]. This step frequency of *f*ped = 1.4 − 1.8 Hz can be used to determine a necessary buffer dimension. Every 1.4 Hz the maximum velocity profile can be observed considering a moving pedestrian, which allows to extract the maximum velocity profile and range profile. At all other times, the expansion in velocity is lower or even zero. To detect at least one expansion in velocity, the number of

that all measurements are independent of each another, due to the ego motion of the radar, vibrations and fewer detections. Applying the feature extraction process using a single

*Pv*profile,single <sup>=</sup> *<sup>T</sup>*CPI

Assuming an equal distribution, multiple measurements increase the probability to extract a

*T*CPI

1/ *f*ped

· *<sup>T</sup>*CPI 1/ *f*ped

measurement, the probability *P* to extract an extended velocity is then given by:

*Pv*profile,multiple <sup>=</sup> *<sup>T</sup>*Buffer

*<sup>f</sup>*ped . However, it can be assumed

(8)

(9)

**3.2. Classification based on multiple radar measurements**

availability deduced from the step frequency of a moving pedestrian.

measurements should therefore span a period of *T*ped = <sup>1</sup>

*<sup>T</sup>*CPI .

velocity profile by the factor *<sup>T</sup>*Buffer

was previously based on a single measurement only.

data samples.

classification process.

*3.2.1. Feature extraction*

Vehicle Pedestrian Other

In the single measurement it is described how range and velocity measurements build the basis for the feature vector and the classification process. In the multiple measurement, the basis is an extended feature vector based on several range and velocity measurements of an object stored inside a buffer. Instead of using 8 features from a single measurement, additional 8 features are available for the first time with a filled buffer. For a successful classification using a SVM, a new model is built, which is also trained/tested with in total 16 features and is a basis for the following classification process. As shown in the confusion matrix in Table 5 by the additional features, the correct classification and the overall performance achieved, increases by using a total number of 16 features from single and multiple measurements.

estimate a new state using a well-known prior state (e.g. position, velocity, acceleration). This

The Kalman filter is a linear, recursive filter, whose goal is to determine an optimal estimate of the state parameters. The optimal estimate is based on available measurements and the models which describe the observed objects. In the equation of the motion model and observation model, the measurement noise is assumed to be average free, white Gaussian noise with the known covariance *Qk*−<sup>1</sup> and *Rk* respectively. Under the given conditions, i.e., linear models and Gaussian statistics, the Kalman filter provides the optimal solution for the estimation of the state in the sense of minimizing the mean squared error, as described in [26]. The tracking for the object described by the motion model of the Kalman filter works fine as long as the motion models fit to the object. Pedestrians, vehicles, and static objects have different motion, which makes the tracking more difficult. Instead of creating a different motion and observation model for each object, it is proposed to determine the covariance of process noise *Qk* and the measurement noise *Rk* adaptively. The process noise considers a non-modeled behavior in the motion model, while the measurement noise consideres uncertainty in the measurement. The original Kalman filter is not adaptive, which is why deviations from the model can not be handled. The gain matrix *K*, which is calculated from the process and measurement noise, reaches a stable condition after a short measurement time. An increase in the covariance *Qk* leads to a larger value for *K*, so that the measured values are

In addition to an improved tracking effect, additional features can be extracted from the adaptive adjustment of the process noise, as pedestrian measurements in range and velocity differ from those of vehicles. Next to the process noise *Qk*,*<sup>v</sup>* of the velocity, the Kalman gain *Kv* (velocity component of the matrix *K*) is a good feature as measurements show. Anyhow, in an adaptive adjustment of the process noise, a compromise between the compensation of non-modeled movements and the filtering effect to reduce noise must be found, even though

The process noise matrix *Q* describes object-specific measurement properties that are initially set and are readjusted during operation of the tracker. For example, the readjustment of a single coefficient *Qk*,*<sup>v</sup>* in the *Q* matrix at the measurement *k* in respect to the velocity *v* is based on the actual target range *R*, the velocity *v*, the parameters *a* and *b* in an alpha-beta filter. Equation (11) shows the relation. The velocity of a pedestrian deviates between consecutive measurements, while the velocity deviation of a car within consecutive measurements is small

The predicted covariance matrix *Pk*|*k*−<sup>1</sup> in the tracking process depends on the motion model *Fk*−1, the currently measured covariance *Pk*−1|*k*−<sup>1</sup> and the process noise *Qk*−<sup>1</sup> as shown in

*Pk*|*k*−<sup>1</sup> <sup>=</sup> *Fk*−<sup>1</sup>*Pk*−1|*k*−1*F<sup>T</sup>*

<sup>|</sup>*zk*,*<sup>v</sup>* <sup>−</sup> *vk*|*k*−1<sup>|</sup>

*Rk*|*<sup>k</sup>* · *<sup>a</sup>* <sup>+</sup> *<sup>b</sup>* (11)

Pedestrian Recognition Based on 24 GHz Radar Sensors 253

*<sup>k</sup>*−<sup>1</sup>*Qk*−<sup>1</sup> (12)

or even zero. Consequently, the velocity *v* can be used to update the matrix *Q*.

*Qk*,*<sup>v</sup>* = (<sup>1</sup> − *<sup>β</sup>*)*Qk*−1,*<sup>v</sup>* + *<sup>β</sup>*

reduces false alarms and smoothes movements of the objects.

weighted more strongly, a decrease in *Qk* relies more on the estimation.

features are extracted.

Equation (12).

**Figure 9.** Feature histogram of the velocity profile using multiple radar measurements as a basis for feature extraction. The common area index is calculated to 0.88.

Additionally, classifying feature vectors from single and multiple measurements results in fewer false positives.


**Table 5.** Confusion matrix: classification applied to a single and multiple measurement test data set containing 8000 data samples.

Due to additionally multiple measurements as a basis for feature extraction, an improvement in the classification result is shown. Especially in terms of correct classification of a pedestrian and false alarms in which a pedestrian was classified as a vehicle, a significant enhancement is seen.
