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Hazard Warning Performance in Light of Vehicle Positioning Accuracy and Map-Less Approach Path Matching.

INTRODUCTION

Since a few decades, vehicle to vehicle and vehicle to infrastructure communication has been subject of research and technology development. In order to provide as much benefit as possible to each individual driver, the penetration rate of vehicles equipped with this technology is important. That is why there are a number of cross OEM collaboration projects in order to harmonize the technology for exchanging data between vehicles.

In the beginning, dedicated short range communication (DSRC) was the prime method of choice for networking vehicles with each other, due to the limitation of early mobile networking standards. Although the technology has been readily available and tested in pilots such as the Vehicle Infrastructure Integration (VII) initiative of the US DOT, and the sim[TD] in Germany, making the business case for introducing dedicated hardware for every vehicle was delaying the introduction.

Due to this delay, the US National Highway Transportation Safety Agency (NHTSA) decided to propose a mandate for DSRC based communication technology to be equipped with every new car built in the future [1]. In other regions, such as Europe, there has been a regulatory mandate to equip vehicles with other mobile networking solutions, such as telematics control units with support for Accident Emergency Call Systems (AECS) [2].

While the existing standards for direct short range communication, as well as for mobile network communication have different qualities [3], the upcoming mobile network standardization aims to replace both for the use case of networking vehicles. The goal is to offer both low latency, ultra reliable communication, as well as the possibility to exchange large quantities of data with distant endpoints. Popovski introduces the motivation to support and the terminology to describe ultra-reliable communication in 5G in [4].

The scope of this paper does not include the discussion of the different networking technologies; instead we want to focus on the anticipated application performance in regards to vehicle position accuracy. The cross OEM initiatives to introduce vehicle to vehicle and vehicle to infrastructure communication have identified a number of use cases for introduction scenarios. These use cases center around assisting the driver by providing hazard warning information along the direction of travel.

Day 1 Use Cases

In this paper, we follow the classification of the European CAR 2 CAR communication consortium for day 1 use cases [5]. The analysis in this paper focuses around the following quasi stationary incident warnings.

* Hazardous Location Warning

* Traffic Jam Ahead Warning

* Stationary Vehicle Warning

* Road Work Warning

We assume that an On-Board Unit (OBU) has received stationary DENMs for incidents above, and needs to trigger a hazard warning via the vehicle's human machine interface (HMI). The information is presented in order to prepare drivers for the following incidents along the way of travel.

Related Work

Related work includes a wide variety of simulation environments for both vehicle movement as well as network simulation. In [6], Lochert et al. presented a simulation framework coupling vehicle movement with network simulation.

On top of pure GPS receiver sampling and filtering of data, a technique called dead reckoning has proven to be both capable of extrapolating a vehicle's position during outage, and improving the positioning quality in noisy conditions. For this, the vehicle's sensors are being used to compare the measured distance travelled using wheel ticks and acceleration sensors with the GPS receiver supplied position and heading values. Mattos [7] presented such an integrated system, showed how dead-reckoning diverges increasingly over time, and how it synchronizes back upon availability of GPS position.

In the case in which a vehicle has total knowledge and a dense map in the vehicle, sophisticated map matching can be applied. In [8], Newson and Krumm present a hidden markov model (HMM) based approach. The approach combines the observed distances travelled of the vehicle with the distance between the road network segments. They show that depending on the GPS sampling frequency and the standard deviation, the performance for an exemplary run through Seattle is flawlessly matching the vehicle to the right road in the map.

Contribution

This paper analyzes the region specific sensitivity of road networks to vehicle positioning accuracy. This is done using a simplistic approach path, or trace matching algorithm, which was developed as part of a European Union funded collaboration project called drive c2x [9]. Testing the performance of a simplistic hazard matching algorithm is done in order to test the viability to equip even lowest specification vehicles with the new technology.

Two error modes are being investigated: Scaling white noise to measure robustness of simplistic matching versus position and heading errors, and scaling systematic offset and heading divergence, which typically occur using dead reckoning.

Structure

The following section describes the dynamically linked toolchain, which allows modular assessment of different connected applications, like hazard warning in light of vehicle position accuracy. We continue describing both the experimentation setup and results. Finally, we provide a conclusion for the analysis of simplistic hazard warning for two typical urban environments in Europe and North America.

SIMULATION TOOL ARCHITECTURE

In order for the simulation tool to import and evaluate the existing methodology for hazard warning and DENM matching, it is built using an OSGi service oriented framework.

OSGi Based Modular Framework

The OSGi platform allows dynamic linkage of different modules for navigating vehicles using different underlying map sources, different applications running on these vehicles, providing a user interface and automated experimentation. The following subsections detail the different OSGi services offered in the framework.

Simulation Core Services

The simulation core service implementation holds a list of agents which understand a notion of time. It initializes agents, and increments the time until an agent has reached its detached state. Furthermore, it provides central access to a random number generator, which can be seeded appropriately to repeat the experiments which we conducted.

Navigated Vehicle Services

The navigated vehicle service implementation constructs vehicle simulation agents, which follow specific driving models and routes. This service includes the computing the real position, heading and speed of each vehicle, as well as configurable and combinable error models which distort these values.

Additionally, it exposes an interface to compute approach paths towards hazards placed in the road network.

For constructing the vehicle and hazard simulation agents, the navigated vehicle service implementation gets configured with a rectangular bound of two latitude/longitude coordinates.

Each vehicle agent may have a tree of other simulation agents attached to it. Every simulation agent in a vehicle agent's tree is synchronized with the vehicle, meaning the time base is the same and once the vehicle detaches with the simulation core services, so do the synchronized simulation agents.

Hazard Warning Services

The hazard warning service implementation is attached and synchronized with its associated vehicle agent. It can sample the real and erroneous vehicle position and subsequently match the vehicle with all approach path traces within its vicinity.

It runs the trace matching algorithm on all approach paths for both the true as well as the sampled erroneous vehicle position.

Once a positive match occurs, a warning is issued via the HMI and it is only withdrawn as soon as the match quality increases over a hysteresis threshold.

User Interface Service

The user interface service may be used for introspection of the simulation. It may provide the map with an overlay of the vehicle coordinates as shown in Figure 2.

The vehicle agents' movements, their true and erroneous position, as well as hazards and the approach path matches are put in an overlay of the street map of the area.

Telematics Communication Simulation

Each simulated application agent can connect to the communication service and hence exchange data and see only what was being sent to it. The analysis of propagation times and effects of penetration rate are not scope of this paper, and hence the telematics communication simulation service is not described in more detail.

Experimentation and Automation Service

The experimentation and automation service facilitates the parameter study presented in this paper by automatically performing configurable and repeatable simulation runs.

For each simulation run, an output file suffix and parameter set may be defined in a table listing the experiments to be run. An experiment finishes either after a maximum simulation time, or whenever every simulation agent (vehicle) has reached its final destination and does not change its state anymore over time (detached state).

The experimentation service gathers lifecycle events, such as vehicles reaching their destination and detaching, as well as the results for matching the true and erroneous position to the hazards within proximity.

OpenStreetMap Based Geometry

We use OpenStreetMap [10] data for analyzing and comparing the sensitivity of hazard warning performance in regards to road network layout.

Position Error-Model

Figure 2 depicts a trajectory exhibiting a combined position error model with both offset diverge and white noise components. Each position error model described hereafter is assumed to get a vehicle position as input, i.e. Latitude, Longitude, Heading, and Speed, adds error terms and provides a vehicle position as output.

Offset Diverge

The offset diverge Position Error Model is used to simulate divergence of dead reckoning and resynchronization. The offset diverge (OD) error model first samples a normally distribution latitude and longitude offset O with parameters

[O.sup.OD.sub.lat]~N([mu], [sigma]), and [O.sup.OD.sub.lon]~N([mu], [sigma]) (1)

The offset divergence is then targeted into normal distributed heading offset with parameters:

[O.sup.OD.sub.heading]~N(0, [sigma]) (2)

The error term in the vehicle position is assumed to drift linearly towards the sampled offset position and in direction of the disturbed heading. The drift is assumed to happen over a random number of sample counts. After the sample count number is reached, a reset back to the true position shall occur. This sample count is computed through sampling a normal distribution and rounding to the next applicable positive integer.

[O.sup.OD.sub.samplecount]~N([mu], [sigma]) (3)

We assume to have a systematic error when dead reckoning and GPS signal diverge, for instance due to driving through a tunnel, or urban canyon. Because of this, we model the sample count as a Gaussian process instead of a Poisson process.

Figure 2 depicts the offset diverge error with the parameters listed in Table 1.

White Noise

The white noise (WN) error model adds normal distributed offsets to the latitude and longitude values, centered on the latitude and longitude values given as input.

The white noise error model additionally distorts the heading to point in the direction of the distorted sample point. Distorting the heading in this way simulates the relative uncertainty of heading in case of slow movement. The slower the vehicle moves, the higher the error in heading due to the white noise displacement of the position.

Combined Position Error Model

Since the aforementioned position error models have the same domain as well as co-domain, they can be composed. The combined position error model allows composing a list of position error models.

For the experimentation described in the following sections and the position error model example in Figure 2, we composed an Offset Diverge with a White Noise Error Model, accounting for random white noise as well as systematic error terms.

[e.sub.combined] = [e.sub.WhiteNoise] [degrees] [e.sub.OffsetDiverge] (4)

Approach Path Trace Generation

The set of approach path traces for each hazard is computed using the underlying map. The computation starts with the location of the incident and recursively traverses all incident routes into it. Between two nodes on the road, a new trace point is introduced depending on the deviation of the current position to the position added to the trace for the last time. The deviation is a function of angle and distance and defined as follows:

(distance > STRAIGHT_DENM_SPACING) OR (angle > BEARING_THRESHOLD) (5)

Every time a new node is reached in the road network, the algorithm recursively branches and forks the existing approach path trace. This is depicted in Figure 3. The hazard is assumed to be sampled on the intersection in the middle. From this node in the road network on, all incident roads are being traversed and sparse approach path trace coordinates are being overlaid. The approach path coordinates are illustrated using yellow circles.

Inspecting the approach path from the south, one can observe that more coordinates are spent, when the road is on a curved segment, due to the threshold in degrees of curvature. On a straight, a new coordinate is included once the distance threshold is exceeded.

Depending on the road class, the recursive algorithm stops traversing, after covering a minimum termination length. The values for the different road classes which are common in OpenStreetMaps, are depicted in Table 2 below.

A parameter study as to how to choose the thresholds for approach path generation is out of scope of this paper. Nevertheless, we provide an analysis of observed approach path trace quality in the next section.

Approach Path Trace Quality

Because the linearization involved in building a sparse DENM trace for approximating the approach path, does not perfectly cover the underlying street geometry, the perpendicular distance of the vehicles to the traces which they were matched to, is not always negligible. Figure 4 depicts the cumulative distribution function of the perpendicular distance of the true road geometry to the approximated approach path, as observed in the Cologne and Detroit experiments. The cumulative distribution function can be seen as a measure of the curvature of the road network. The Detroit streets can better be linearized using sparse approach paths.

The detailed simulation setup can be found in the following major section on experiment setup.

Hazard Matching Algorithm

The hazard matching algorithm takes the perpendicular distance to the trace along with the difference in heading of the trace and the vehicle. For a sample to match an approach path, the perpendicular distance combined with the difference in heading must not exceed a predefined threshold.

[T.sub.match](p) = 100-5[d.sub.perpendicular - 1.5[[alpha].sub.angle] (6)

Figure 5 shows a visualized run of a simulated vehicle which spawned north of the hazard and travels southbound past it. In this example, true matches were found at almost every sample interval of 1 Hz. True matches are indicated by a pink cross. Notably, the fourth sample did not match the approach path quality threshold. From a customer experience perspective, a single FalseNegative observation within a series of observations is negligible, because the hazard warning would be persistently displayed until the distance to the hazard increases again.

If at least one trace matches the current vehicle position, a hazard warning is issued. In the case of multiple matches, a tunable prioritization mechanism would show the more critical event either due to distance, or due to its type.

EXPERIMENTATION

Setup

The experimentation setup can be split into a common part which is the basis for both experimentation areas. This common part is described under Generic, while the specific differences of the simulation runs in the Cologne and Detroit areas follow suit.

Generic

Every simulation run gets new randomly generated vehicle routes, while the location and approach paths of the hazards remain the same.

Both the hazard location, as well as the spawn and exit points of the vehicles are generated using uniform distribution over the intervals of latitude and longitude of the respective simulation runs. Each of the random values in 2d space is then mapped to the closest node in the road network and handled appropriately.

Table 2 depicts the shared simulation parameters. A step size of 1 Hz GPS sampling frequency is a typical value for today's automotive applications. The simulation is ended after a maximum of 2400 simulation steps.

In every simulation run, 100 vehicles are driving along random routes. The number of hazards is dependent on the size of the area of simulation.

Cologne Experimentation Area

The Cologne experimentation area covers the majority of the Cologne city limits. The hazard count of 200 per 347.87 k[m.sup.2] equals to a ratio of 0.57.

As can exemplary be seen in Figure 2 and Figure 5, many streets within Cologne city limits have non-rectangular layout. This is the reason, why the perpendicular distance to the linearized trace is larger in Cologne than Detroit (cf. Figure 4).

Detroit Experimentation Area

The Detroit experimentation area spans over the majority of Detroit and Dearborn city limits, from 8 Mile and Telegraph to the southeastern end of Belle Isle.

The hazard count in the Detroit experimentation area is reduced to 171 to account for a similar density of hazards per area.

Results

The results are classified using Bayes statistics. Let M denote the event of a match given perfect vehicle position, and M be the event of a match under erroneous position assumption. Additionally, let [alpha] be the simulation parameters and [rho] be the region of interest. Hence, we define that if a match occurred under erroneous position given it was a match under perfect vehicle position, as a True Positive event.

[P.sub.[alpha],[rho]]([tilde.M]|M) [equivalent to] [TruePositive]

Similarly, no match on erroneous position given a match based on perfect position is attributed as a False Negative event.

[P.sub.[alpha],[rho]]([??]|M) = [FalsePositive]

Last but not least, the False Positive event is given, once a match under erroneous position was triggered while there was no such match given the perfect position.

[P.sub.[alpha],[rho]]([tilde.M]|[bar.M]) = [FalsePositive]

In the following subsections, we analyze the impact of scaling the error model over a number of simulation runs.

For the comparison, we utilize two position error models and scale them individually.

Position Error Model White Noise

Increasing the white noise on the observed vehicle position leads to individual vehicles detecting a hazard increasingly late. This results in late, or even wrong, i.e. False Positive warnings to the driver. Due to the white noise error model, not only the position, but also the estimate of the heading is increasingly affected.

Using this position error model, the heading is not filtered, but recalculated by computing the bearing from the last sampled to the newly sampled erroneous vehicle position point. Using this mechanism, the heading is very unstable and the error can significantly disturb the observable performance.

Figure 6 depicts the observed statistics of warnings later, i.e. after additionally traveling distance to the hazard than when compared to ground truth positioning.

In order to give better insight into what causes the increasing distance of being warned late, the following plots were extracted for the relatively high standard deviation of 18.5 m:

Figure 7 depicts the single proportions of the observations over absolute heading error. It can be seen that, due to the threshold on heading and perpendicular distance combined, there are virtually no TruePositive observations with heading error larger than 20[degrees]. We plotted the difference of the heading based on the ground truth position. There may be few true positive observations with heading error larger than 20[degrees], because the ground truth heading does not necessarily perfectly match the approach path linearization angle, while the vehicle uses that to test for the match quality threshold of 20[degrees]. Both Figure 7 and Figure 8 show, that the majority of FalsePositive warnings are close to heading errors of 180[degrees], which lead to match to hazard approach paths which are orthogonal or in the other direction of travel. In order to minimize false positives, the quality of the heading is key, which should be filtered and not estimated based on a history of only 2 positions as is the case for this analysis.

The relative proportion of true positive to false positive to false negative observations is illustrated in Figure 9. Since this is counting observations on every step size interval of 1 Hz, it basically shows that many of those observations did not qualify for triggering a hazard warning. It does not depict the customer perceivable quality, because it may be that the hazard warning was triggered early enough by one of the TruePositive observations, and subsequent FalseNegatives do not deteriorate the experience.

Table 5 lists the absolute observation count from the simulation runs which were used to plot the figures in this section.

Since a white noise position error with large standard deviation and independent error terms over time is highly unlikely due to dead reckoning and filtering techniques in modern GPS receivers, we take a look at the offset diverge position error model in the next section.

Position Error Model Offset Diverge

Similar to the white noise error model discussion, we begin the section on the offset diverge error using the observed distances of late warnings as they are illustrated in Figure 10. It can be seen that the distance is much more within bounds compared to the analysis on white noise error.

The variable box thickness indicates that there are more samples for FalseNegative observations, the higher the offset diverge standard deviation is. We exemplarily give the detailed plots for classification over absolute heading error and true speed, as well as classifications over true speed for the maximum offset standard deviation:

[O.sup.OD.sub.lat]~[O.sup.OD.sub.lon]~N(0.0 m, 20.0 m) [O.sup.OD.sub.heading]~N[0,5[degrees]] [O.sup.OD.sub.samplecount]~N[30,5]

Using these parameters, the heading error should hence be less than 2[sigma] = 10[degrees] for 95.54 % of all observations. Figure 11 shows the proportions of observed heading error and type of event for Cologne. Figure 12 shows the same for the Detroit experimentation area. In both examples, the vast majority of observations are true positive, with even fewer error cases in Detroit than in Cologne, which may be due to the differences in linearization error of the approach path depicted in Figure 4.

Figure 13 depicts the cumulative distribution of the absolute heading error by type of observation. It can be seen, that using the systematic error approach in the offset diverge model, the heading error is eliminated as the prime indicator for false negative and false positive observations.

Figure 14 and Figure 15 apportion the observations to true speed for both the Cologne and the Detroit experimentation areas. Looking at the results generated from the Cologne simulation run, one can see that the higher the true speed, the lesser False Positive and False Negative observations are seen. This may be that the roads which exhibit these speed limits are better suited to linearization, i.e. they would have smaller curvature and less intersecting roads or other roads nearby, which could lead to confusion in matching hazard approach paths.

Table 6 shows the total number of the observations in the Cologne and Detroit simulation runs. If the erroneous heading does not exceed 10[degrees] and the offset of the current position does not exceed 40.0 m in more than 95.54 % of observations, the hazard warning application achieves a ratio of 95.6 % correct True Positive to ground truth positive classifications at every sampled position value in Cologne. The ratio of false positive among all positive observations, are 1.28 % in the same simulation run.

For the Detroit simulation run, the proportions are 97.5 % true positive of ground truth positive, and 1.27 % for false positive among all positive observations.

SUMMARY/CONCLUSIONS

We have conducted simulation experiments for hazard warning application performance in both North American and European settings, i.e. Detroit, Michigan and Cologne, Germany. We have shown, that the simplistic hazard matching approach presented here can be well suited for the use case of hazard warning, given that heading error and perpendicular location offset are within reasonable bounds.

The results both apply to road geometry in North America and Europe. The North American results showed even higher accuracy, which needs further investigation to find out the causal factors. We have found indications, such as the smaller linearization error for approach paths.

Future Work

Running the same simulations for more and different areas around the world, as well as distinguishing urban from rural scenarios would be desirable. Distinguishing different scenarios could be accompanied with another parameter study for approach path generation. Similarly, the results of this study should be validated in real drive experiments.

Future work could include a comparison of the performance of state of the art map matching, like Hidden Markov Model (HMM), with the performance of the simplistic approach presented here.

Next to filtering the position information, to eliminate noise and hence false classification, filtering techniques could also apply to the output of the trace match algorithm and the match quality value at every instant.

With the advent of the autonomous vehicle and highly accurate localization techniques using highly accurate maps, the hazard warning use cases should perform increasingly better. This would also enable use cases with much lower latency, like electronic brake light warnings, or collision mitigation combining sensor data of multiple vehicles.

REFERENCES

[1.] National Highway Traffic Safety Administration, Proposed Regulation on Federal Motor Vehicle Safety Standards: Vehicle-to-Vehicle (V2V) Communications, vol. 161, Washington D.C.: Department of Transportation, 2014.

[2.] THE EUROPEAN PARLIAMENT AND THE COUNCIL, "Regulation (EU) concerning type-approval requirements for the deployment of the eCall in-vehicle system based on the 112 service and amending Directive 2007/46/EC," 19 05 2015. [Online]. Available: http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32015R0758. [Accessed 25 10 2016].

[3.] Jiang D. and Delgrossi L., "IEEE 802.11p: Towards an International Standard for Wireless Access in Vehicular Environments," in IEEE Vehicular Technology Conference (VTC Spring), Singapore, 2008.

[4.] Popovski P., "Ultra-reliable communication in 5G wireless systems," in 5G for Ubiquitous Connectivity (5GU), Akaslompolo, 2014.

[5.] CAR 2 CAR Communication Consortium, "Memorandum of Understanding on Deployment Strategy for cooperative ITS in Europe," 27 07 2011. [Online]. Available: https://www.car-2-car.org/index.php?id=231. [Accessed 13 10 2016].

[6.] Lochert C., Caliskan M., Scheuermann B., Barthels A., Cervantes A. and Mauve M., "Multiple Simulator Interlinking Environment for Inter Vehicle Communication," in Proceedings of the Second ACM International Workshop on Vehicular Ad Hoc Networks, Cologne, 2005.

[7.] Mattos P., "Integrated GPS and dead reckoning for low-cost vehicle navigation and tracking," in Vehicle Navigation and Information Systems Conference, Yokohama, 1994.

[8.] Newson P. and Krumm J., "Hidden Markov map matching through noise and sparseness," in Proceedings of the 17th ACM SIGSPATIAL international conference on advances in geographic information systems, Seattle, 2009.

[9.] Drive C2X Partners, "Drive C2X Project," 01 07 2014. [Online]. Available: http://www.drive-c2x.eu/project [Accessed 14 10 2016].

[10.] Haklay M. and Weber P., "Openstreetmap: User-generated street maps," IEEE Pervasive Computing, pp. 12-18, 2008.

CONTACT INFORMATION

Corresponding Author:

Dr. Andreas Barthels Ford of Europe Product Development Electrical and Electronic Systems Engineering Connected Vehicle & Services

Mailing Address:

Ford-Werke GmbH D-MC-3/C10 50725 Koln Germany

DEFINITIONS/ABBREVIATIONS

AECS - Accident Emergency Call System

CAM - Cooperative Awareness Message (ETSI Standard EN 302 637-2)

DOT - U.S. Department of Transportation

DENM - Decentralized Environment Notification Message (ETSI Standard EN 302 637-3)

DSRC - Dedicated Short Range Communication

ETSI - European Telecommunications Standards Institute

HMI - Human Machine Interface

HMM - Hidden Markov Model

NHTSA - US National Highway Traffic Safety Administration

OBU - onboard unit

OSGi - Open Systems Gateway interconnect

VII - Vehicle Infrastructure Integration

Andreas Barthels, Christian Ress, Martin Wiecker, and Manfred Muller

Ford Motor Company
Table 1. Offset Diverge parameter set used for illustration

Random Variable             Distribution Parameter

[O.sup.OD.sub.lat]          N(10m, 5 m)
[O.sup.OD.sub.lon]          N(10m, 5 m)
[O.sub.heading]             N(0.0 [degrees], 5.0 [degrees])
[O.sub.samplecount]         N(30, 5)

Table 2. White Noise parameter set used for illustration

Random Variable     Distribution Parameter

[O.sup.WN.sub.lat]  N(0, 1 m)
[O.sup.WN.sub.lon]  N(0, 1 m)

Table 3. Parameters used for approach path generation along a road

Parameter              Threshold value

STRAIGHT_DENM_SPACING  200 m
BEARING_THRESHOLD       10[degrees]

Table 1. Total approach path length depending on road class, after
which recursive traversal is terminated

Road Class   Termination Length

Motorway     3'000 m
Trunk          500 m
Primary      1'000 m
Secondary      750 m
Tertiary       500 m
Residential    500 m
Link           500 m

Table 2. Simulation parameters used for all simulation runs

Parameter                         Value

Step Size / GPS Sample Frequency     1 Hz
Maximum Simulated Time            2400 s
Vehicle Agents in Simulation       100
Hazard Count in Simulation           0.57 hazards per k[m.sup.2]
Match Quality Threshold           [T.sub.match](p)
                                  [greater than or equal to] 70

Table 3. Simulation parameters used for Cologne Area Experimentation

Parameter                            Value

Latitudel                             51.017513
Longitudel                             6.798379
Latitude2                             50.879462
Longitude2                             7.121144
Area covered (uniform distribution)  347.87 k[m.sup.2]
Hazard Count in Simulation           200

Table 4. Simulation parameters used for Detroit Experimentation Area

Parameter                            Value

Latitudel                             42.443015
Longitudel                           -82.959993
Latitude2                             42.340823
Longitude2                           -83.278405
Area covered (uniform distribution)  297.8 k[m.sup.2]
Hazard Count in Simulation           171

Table 5. Observation Counts for
[mathematical expression not reproducible]

Cologne Experimentation Area

Observation     Count

True Positive     164
False Positive     50
False Negative  3'351

Detroit Experimentation Area

Observation     Count
True Positive      58
False Positive     29
False Negative  1'598

Table 6. Observation Counts for Simulation Run with Error Model OD

Cologne Experimentation Area

Observation     Count
True Positive   3'863
False Positive     50
False Negative    119

Detroit Experimentation Area

Observation     Count
True Positive   1'477
False Positive     19
False Negative     37
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Author:Barthels, Andreas; Ress, Christian; Wiecker, Martin; Muller, Manfred
Publication:SAE International Journal of Passenger Cars - Electronic and Electrical Systems
Article Type:Technical report
Date:Aug 1, 2017
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