Berthold Horn

Prof. Berthold Horn

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Research Focus & Metrics

Academic Career Length

20Years (2007-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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9 March 2020 in Sensors
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Journal Article
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BHBerthold Horn
Berthold Horn
Determination of indoor position based on fine time measurement (FTM) of the round trip time (RTT) of a signal between an initiator (smartphone) and a responder (Wi-Fi access point) enables a number of applications. However, the accuracy currently attainable—standard deviations of 1–2 m in distance measurement under favorable circumstances—limits the range of possible applications. An emergency worker, for example, may not be able to unequivocally determine on which floor someone in need of help is in a multi-story building. The error in position depends on several factors, including the bandwidth of the RF signal, delay of the signal due to the high relative permittivity of construction materials, and the geometry-dependent “noise gain” of position determination. Errors in distance measurements have unusal properties that are exposed here. Improvements in accuracy depend on understanding all of these error sources. This paper introduces “frequency diversity,” a method for doubling the accuracy of indoor position determination using weighted averages of measurements with uncorrelated errors obtained in different channels. The properties of this method are verified experimentally with a range of responders. Finally, different ways of using the distance measurements to determine indoor position are discussed and the Bayesian grid update method shown to be more useful than others, given the non-Gaussian nature of the measurement errors.

1 June 2007 in 2007 IEEE Intelligent Vehicles Symposium
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Conference Paper
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BHBerthold Horn
Berthold Horn
YFYajun Fang
Yajun Fang
IMIchiro Masaki
Ichiro Masaki
We show how to determine the time to contact from time varying images using only accumulated sums of suitable products of image brightness derivatives. There is no need for feature or object detection, tracking of features, estimation of optical flow, or any "higher level" processing. This so-called "direct" method for determining the time to contact is based on analysis of the motion field resulting from rigid body motion under perspective projection and the constant brightness assumption. The method has essentially no latency, since it can be based on analysis of just two frames of a video sequence, and does not require a calibrated camera. An implementation of the method is demonstrated on synthetic image sequences and stop motion sequences - where the ground truth is accurately know - as well as on video sequences taken by a camera mounted on moving vehicles.

7 October 2019 in IEEE Transactions on Automatic Control
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Journal Article
Closed access
WLWang Liang
Wang Liang
BHBerthold Horn
Berthold Horn
In this paper, we study mixed traffic flow in which some cars are under car-following control and others are under bilateral control. We also provide the necessary (modular string) stability condition for this type of mixed traffic, which can be viewed as an extension of the condition for pure car-following control based traffic. This necessary stability condition provides some indication of how the introduction of self-driving cars (under bilateral control) will affect today's traffic.

6 December 2017 in IEEE Transactions on Intelligent Transportation Systems
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Journal Article
Open access
BHBerthold Horn
Berthold Horn
WLWang Liang
Wang Liang
Traffic congestion wastes fuel and commuters' time, and adds to CO₂ emissions. Stop-and-go traffic instabilities can be suppresses using bilateral control--which differs from ``car following'' and adaptive cruise control in that, counter-intuitively, it uses information about the following vehicle (as well as about the leading vehicle). Stability can be proven mathematically, and can be demonstrated in simulation. A physical analog of a sequence of vehicles using bilateral control is a chain of masses connected by springs and dampers--a system which is inherently stable, since it lacks an external energy source. Here, in order to further understand bilateral control and its capacity to suppress instabilities, we move from a microscopic view (interaction of individual vehicles) to a macroscopic view (densities and flow rates). This leads us to the damped wave equation governing traffic under bilateral control. That equation allows us to determine the speed of propagation of disturbances, as well as their rate of decay. The equation is also useful in fine tuning parameters of bilateral control systems.

18 April 2022 in Sensors
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Journal Article
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BHBerthold Horn
Berthold Horn
Indoor localization using fine time measurement (FTM) round-trip time (RTT) with respect to cooperating Wi-Fi access points (APs) has been shown to work well and provide 1–2 m accuracy in both 2D and 3D applications. This approach depends on APs implementing the IEEE 802.11-2016 (also known as IEEE 802.11mc) Wi-Fi standard (“two-sided” RTT). Unfortunately, the penetration of this Wi-Fi protocol has been slower than anticipated, perhaps because APs tend not to be upgraded as often as other kinds of electronics, in particular in large institutions—where they would be most useful. Recently, Google released Android 12, which also supports an alternative “one-sided” RTT method that will work with legacy APs as well. This method cannot subtract out the “turn-around” time of the signal, and so, produces distance estimates that have much larger offsets than those seen with two-sided RTT—and the results are somewhat less accurate. At the same time, this method makes possible distance measurements for many APs that previously could not be used. This increased accessibility can compensate for the decreased accuracy of individual measurements. We demonstrate here indoor localization using one-sided RTT with respect to legacy APs that do not support IEEE 802.11-2016. The accuracy achieved is 3–4 m in cluttered environments with few line-of-sight readings (and using only 20 MHz bandwidths). This is not as good as for two-sided RTT, where 1–2 m accuracy has been achieved (using 80 MHz bandwidths), but adequate for many applications A wider Wi-Fi channel bandwidth would increase the accuracy further. As before, Bayesian grid update is the preferred method for determining position and positional accuracy, but the observation model now is different from that for two-sided RTT. As with two-sided RTT, the probability of an RTT measurement below the true distance is very low, but, in the other direction, the range of measurements for a given distance can be much wider (up to well over twice the actual distance). We describe methods for formulating useful observation models. As with two-sided RTT, the offset or bias in distance measurements has to be subtracted from the reported measurements. One difference is that here, the offsets are large (typically in the 2400–2700 m range) because of the “turn-around time” of roughly 16 μs (i.e., about two orders of magnitude larger than the time of flight one is attempting to measure). We describe methods for estimating these offsets and for minimizing the effort required to do so when setting up an installation with many APs.

8 September 2016 in Studies in Applied Mathematics
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Journal Article
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WLWang Liang
Wang Liang
BHBerthold Horn
Berthold Horn
GSGilbert Strang
Gilbert Strang
Many authors have recognized that traffic under the traditional car‐following model (CFM) is subject to flow instabilities. A recent model achieves stability using bilateral control (BCM)—by looking both forward and backward [1]. (Looking back may be difficult or distracting for human drivers, but is not a problem for sensors.) We analyze the underlying systems of differential equations by studying their eigenvalues and eigenvectors under various boundary conditions. Simulations further confirm that bilateral control can avoid instabilities and reduce the chance of collisions.