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# Design, Implementation, and Evaluation of a Real Time Localization System for the Optimization of Agitation Processes

Andreas Heller, Ludwig Horsthemke, Peter Glösekötter

► To cite this version:

Andreas Heller, Ludwig Horsthemke, Peter Glösekötter. Design, Implementation, and Evaluation of a Real Time Localization System for the Optimization of Agitation Processes. 6th International Embedded Systems Symposium (IESS), Sep 2019, Friedrichshafen, Germany. pp.39-50, 10.1007/978-3-031-26500-6_4. hal-04489021

HAL Id: hal-04489021

https://inria.hal.science/hal-04489021v1

Submitted on 4 Mar 2024

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# Design, Implementation, and Evaluation of a Real Time Localization System for the Optimization of Agitation Processes

Andreas Heller, Ludwig Horsthemke, and Peter Glösekötter

Münster University of Applied Sciences, Steinfurt, Germany

andreas.heller@fh-muenster.de

l.horsthemke@fh-muenster.de

peter.gloesekoetter@fh-muenster.de

**Abstract.** This work describes the setup of an ultrawideband (UWB) realtime localization system (RTLS) for tracking of particles. We describe how the RTLS obtains distances and positions through radio waves and the setup and evaluation of a real world system is stated in detail. In the proposed system the particles track a substrates surface flow inside a biogas plant for verification of agitation processes.

**Keywords:** UWB · RTLS · Biogas plant optimization.

## 1 Introduction

The mixing process in biogas plants plays an important role in its effectiveness [2]. Simulations for different biogas mixing concepts are carried out, with the aim of maximizing the gas yield. The here described system provides a means to assessing the surface flow of substrates in biogas plants to validate such simulations [3]. Lemmer et al. [7] pointed out that a combination of intrusive and non-invasive research methods tends to be applied for the research on mixing quality in biogas digesters as done in this work.

The UWB RTLS consists of fixed nodes mounted above the biogas plant and small floating units which positions are tracked over time. By reconstructing the path from the captured positions and calculating the time derivative, flow velocities can be deducted. With a high number of tags and long runtimes a dependable data base for evaluation of simulations can be constructed. UWB has been chosen in contrast to other ranging techniques like received signal strength indication, (assisted) global navigation satellite system (GNSS) or ultrasound due to its high accuracy (≤ 15 cm) relatively low cost and low power [10].

## 2 Main

This section offers a detailed look into the systems logic. First the distance determination via ultra wide band communication (UWB) with subsequent position determination is explained. In following, the system structure is described and key parameters are examined. Finally, results of a real world test are provided.
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## 2.1 Distance determination

The proposed system is based on UWB localization, which relies on time measurement to extract distances between two communication partners. To calculate these distances, we simply measure the time a signal needs to travel from one communication partner to another. To extract the distance based on the measured time, we take the signals velocity into account. That however is, like it is for all electromagnetic waves, the speed of light *c*. Lastly a simple multiplication of *c* and time *t* provides the distance *ρ*, we are looking for (*ρ* = *c* · *t*).

Measuring the distance like proposed above would simply not be possible, since the two communicating sides do not know send or receive times of the opposing side. Thus a scheme called Alternative Double Sided Two Way Ranging (AltDS-TWR) is deployed. In comparison to other TWR-schemes, such as Single Sided-TWR (SS-TWR), Symmetric Double Sided-TWR (SDS-TWR), or Asymmetric Double Sided-TWR (ADS-TWR), AltDS-TWR offers good robustness and accuracy [9]. Another widely presented method for UWB based distance measurement is called Time Difference of Arrival (TDoA). It offers great performance and usually good accuracy, however all the components in a TDoA based system have to be properly synchronized to achieve reasonable accuracies. The two communication partners are called *tag* and *anchor*, where *tag* usually

<figure><img src="image_3.png" /><figcaption>Fig. 1: Alternative Double Sided Two Way Ranging.</figcaption></figure>

refers to the mobile node which position is tracked and the anchor's positions are known. Figure 1 shows the DS-TWR scheme in which three messages are exchanged. The respective nodes note the times at which messages are received or transmitted. The results of this scheme are six time stamps, from which intervals can be calculated. These are marked in Figure 1 as $t_{XS}$ and $t_{XR}$. When subtracting the tags first send- and the receive-time stamp, the result is a *round trip time*, marked as $T_{Ra}$, same goes for the round trip time for the anchor, marked as $T_{Rb}$. The time interval noted as $T_{Dx}$ is the processing time each component
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needs to compute a received message, prepare and send the answer message. If we subtract a processing time from a round trip and take the result by half, we calculate the time of flight tof for SS-TWR. To take maximum advantage of DS-TWR however we have to take into account, that the clock speeds of the two communication partners will vary. Errors from diverging clocks are called clock- and frequency drifts which play a huge role in the optimization of UWB based localization systems. Since the signal travels with the speed of light, small deviations in measured time can cause great errors in calculated distances. Lastly the following formula will take all this into account and calculate the time of flight as

$$ tof = \frac{T_{Ra} \cdot T_{Rb} - T_{Ra} \cdot T_{Rb}}{T_{Ra} + T_{Rb} + T_{Da} + T_{Db}}. \qquad (1) $$

If the anchor calculates the distance, the sent-time stamp for the final message can be pre calculated and embedded into the final message, thus the anchor knows all time slots and is able to calculate without needing to wait for another message.

## 2.2 Lateration

In previous section we covered the measurement of distances between two components. Here we will take distances from components with static positions, called anchors, to one tracked component, called tag. In this section an example with three anchors and one tag is presented, where the tag can be tracked in two dimensions. We will also cover how to track the tags position in the third dimension and what restrictions the system has in each case. Figure 2 schematically shows this system. The measured ranges from each anchor $A_i$ to the tag $T_0$, is marked as $\rho_X$. As marked in the figure, the ranges can be interpreted as circles around the anchors positions. Thus the intersection of all the circles mark the tags position. Mathematically a circle is described as

$$ \rho_i^2 = (x - x_{A_i})^2 + (y - y_{A_i})^2 \qquad (2) $$

where $x_{A_i}$ and $y_{A_i}$ are the coordinates of the i-th anchors location. When solving Equation 2, there will be squared terms left for the x- and y- coordinates, which we are looking for. The difference to another circle will solve this problem. In this example we subtract the circle in the origin, this way the terms for the anchors position are set to zero

$$ x_{A_0} = y_{A_0} = 0 \qquad (3) $$

thus resulting to a solvable linear equation system with two equations and two variables

$$ \rho_1^2 - \rho_0^2 = -2x(x_{A_1} - x_{A_0}) - 2y(y_{A_1} - y_{A_0}) + x_{A_1}^2 + y_{A_1}^2 - x_{A_0}^2 - y_{A_0}^2, \qquad (4) $$

$$ \rho_2^2 - \rho_0^2 = -2x(x_{A_2} - x_{A_0}) - 2y(y_{A_2} - y_{A_0}) + x_{A_2}^2 + y_{A_2}^2 - x_{A_0}^2 - y_{A_0}^2. \qquad (5) $$

Additional to the resulting equation system, also the context to the amount of anchors and the trackable dimensions becomes clear. If we want to track a tag in N dimensions, we have to provide N + 1 anchors.
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<figure><img src="image_4.png" /><figcaption>Fig. 2: Trilateration visualization.</figcaption></figure>

A more straightforward view is achieved by displaying the system using a matrix equation

$$ \mathbf{b} = \mathbf{A} \cdot \begin{pmatrix} x \\ y \end{pmatrix} \qquad (6) $$

where

$$ \mathbf{b} = \begin{pmatrix} \rho_1^2 - \rho_0^2 - x_{A_1}^2 - y_{A_1}^2 + x_{A_0}^2 + y_{A_0}^2 \\ \rho_2^2 - \rho_0^2 - x_{A_2}^2 - y_{A_2}^2 + x_{A_0}^2 + y_{A_0}^2 \\ \vdots \\ \rho_n^2 - \rho_0^2 - x_{A_n}^2 - y_{A_n}^2 + x_{A_0}^2 + y_{A_0}^2 \end{pmatrix} \qquad (7) $$

and

$$ \mathbf{A} = -2 \cdot \begin{bmatrix} x_{A_1} - x_{A_0} & y_{A_1} - y_{A_0} \\ x_{A_2} - x_{A_0} & y_{A_2} - y_{A_0} \\ \vdots & \vdots \\ x_{A_1} - x_{A_0} & y_{A_1} - y_{A_0} \end{bmatrix} \qquad (8) $$

The system displayed in Figure 2 can now be described as

$$ \mathbf{b} = \mathbf{A} \cdot \begin{pmatrix} x \\ y \end{pmatrix} \qquad (9) $$

$$ \begin{pmatrix} \rho_1^2 - \rho_0^2 - x_{A_1}^2 - y_{A_1}^2 + x_{A_0}^2 + y_{A_0}^2 \\ \rho_2^2 - \rho_0^2 - x_{A_2}^2 - y_{A_2}^2 + x_{A_0}^2 + y_{A_0}^2 \end{pmatrix} = \begin{bmatrix} x_{A_1} - x_{A_0} & y_{A_1} - y_{A_0} \\ x_{A_2} - x_{A_0} & y_{A_2} - y_{A_0} \end{bmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix} \qquad (10) $$

This equation is now solved by multiplying it with $\mathbf{A}^{-1}$. This however is not as trivial. One requirement for inverting matrices requires it to be symmetric. With
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more anchors the matrix **A**, only grows in one direction. Moores pseudoinverse **A**<sup>+</sup> however does not require symmetry. It is calculated as

$$ \mathbf{A}^{+} = (\mathbf{A}^{T} \cdot \mathbf{A})^{-1} \cdot \mathbf{A}^{T}. \qquad (11) $$

Now tag positions are obtainable no matter the dimensions of matrix **A**.

In conclusion the system can track positions in two dimensions with any amount of anchors (more than three). In the case of this paper however it is substantial to track the tags in three dimensions leeding to a single adjustment to the mathematical foundation. So instead of the circles, denoted by the ranges from anchors to the tag, the third dimension will create a sphere around each anchor. Thus the adjusted system builds up on

$$ \rho_i^2 = (x - x_{A_i})^2 + (y - y_{A_i})^2 + (z - z_{A_i})^2. \qquad (12) $$

Finally the matrix equation changes to

$$ \mathbf{b} = \mathbf{A} \cdot \begin{pmatrix} x \\ y \\ z \end{pmatrix} \qquad (13) $$

with adjustments to **b** and **A** as

$$ \mathbf{b} = \begin{pmatrix} \rho_1^2 - \rho_0^2 - x_{A_1}^2 - y_{A_1}^2 - z_{A_1}^2 + x_{A_0}^2 + y_{A_0}^2 + z_{A_0}^2 \\ \rho_2^2 - \rho_0^2 - x_{A_2}^2 - y_{A_2}^2 - z_{A_2}^2 + x_{A_0}^2 + y_{A_0}^2 + z_{A_0}^2 \\ \vdots \\ \rho_n^2 - \rho_0^2 - x_{A_n}^2 - y_{A_n}^2 - z_{A_n}^2 + x_{A_0}^2 + y_{A_0}^2 + z_{A_0}^2 \end{pmatrix}, \qquad (14) $$

$$ \mathbf{A} = -2 \cdot \begin{bmatrix} x_{A_1} - x_{A_0} & y_{A_1} - y_{A_0} & z_{A_1} - z_{A_0} \\ x_{A_2} - x_{A_0} & y_{A_2} - y_{A_0} & z_{A_1} - z_{A_0} \\ \vdots & \vdots & \vdots \\ x_{A_1} - x_{A_0} & y_{A_1} - y_{A_0} & z_{A_1} - z_{A_0} \end{bmatrix}. \qquad (15) $$

## 2.3 System structure

Anchors and tags are based on simple printed circuit boards which include a DecaWave DWM1000 UWB transceiver module, a STM32F103 ARM Cortex-M3 processor and a low quiescent current, low drop out voltage regulator as shown in Figure 3. Anchors are additionally equipped with circuitry for RS485 communication and buck converters for power supply from the backbone.

Figure 4 shows the basic structure concept. It can be divided into a backbone and the mobile tags. The backbone is comprised of a Single Board Computer (SBC) as a central unit which delivers power to the anchor nodes and connects to them via RS485. The anchors are distributed around the perimeter of the biogas reactor, usually on the outside with direct line of sight (LOS) to the substrates surface, except for the film hood on the reactor and the nodes plastic enclosures. The anchors positions have to be determined manually when setting
<figure><img src="image_5.png" /><figcaption>Fig. 3: a) Tag PCB and battery in supporting frame. b) Tag assembly in enclosure. c) Closed enclosure of tag. d) Anchor PCB with additional circuitry. e) Opened anchor assembly.</figcaption></figure>

up the system. Distance records are stored in the anchors memory until the SBC retrieves and stores them at a period of 10 s. Additionally the stored records and information about the system's state are uploaded to a server via cellular connection. This way the system can be constantly monitored and the gathered data are available for offline processing while the measurements are still running. Also a backup battery ensures the uninterrupted operation of the system for several days, should a power outage occur.

The mobile tags are powered by 61.2 Wh Li-SOCl₂ primary cells which enable runtimes of several months. The weight distribution in the case was chosen in a way that the top part tends to always protrude from the substrate to ensure the best possible reception of the radio. The cases are made of ABS and feature a smooth surface which prevents the substrate in the biogas reactor from adhering to it and attenuating the RF propagation.

In the ranging process a tag carries out AltDS-TWR successively with each of the four anchors. This process takes approximately 20 ms with the radio settings listed in Table 1 which means that a capacity of 50 tags can not be exceeded. These settings are chosen as a compromise to give high ranges and high accuracies while keeping the transmission time low to give the aforementioned capacity of tags and the best ranging performance. As Mikhaylov et al. [12] already mentioned on channel 5 the standard deviations of the results do not seem to change much with the distance between tag and anchor and show an overall lower deviation of the measurements. This behaviour was also observed in this work after less extensive tests which is why channel 5 was chosen for this system.
<figure><img src="image_6.png" /><figcaption>Fig. 4: Basic structure of the system.</figcaption></figure>

<table><caption>Table 1: Communication configuration of radio.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Channel number</td><td>5</td></tr><tr><td>Center frequency</td><td>6.489 GHz</td></tr><tr><td>Bandwith</td><td>499.2 MHz</td></tr><tr><td>Pulse repetition frequency</td><td>16 MHz</td></tr><tr><td>Preamble length</td><td>1024</td></tr><tr><td>Preamble acquisition chunk size</td><td>32</td></tr><tr><td>Preamble code in RX and TX</td><td>3</td></tr><tr><td>Data rate</td><td>110 kbps</td></tr></tbody></table>

## 2.4 Distance and accuracy

For a maximum distance estimation the link margin which is the difference of received signal level $P_R$ and the receiver sensitivity can be examined. $P_R$ can be calculated from the path loss formula

$$R_P[\text{dBm}] = T_P[\text{dBm}] + G[\text{dB}] - L[\text{dB}] - 20 \log_{10} \frac{4\pi f_C d}{c} \quad (16)$$

with transmit power $T_P$, gain of receive and transmit antennas $G$, losses from PCB, cables and connectors $L$, the center frequency of the used channel $f_C$, distance $d$ and speed of light $c$ [1]. At channel 5 the center frequency equals 6.489 GHz and the transmit power was set to the legal limit of -41 dBm/MHz. From the DWM1000 datasheets antenna diagram combined loss and antenna gain of 0 dB to -5 dB per transceiver is assumed. The receiver sensitivity at the used configuration is determined from the datasheet as -100 dBm [4] with a crystal trimmed to ±2ppm. The resulting link margin leads to communication
<figure><img src="image_7.png" /><figcaption>(a) HDOP distribution for fill level of 0.8 m (b) HDOP distribution for fill level of 3.4 m (3 m between anchor and tag planes). (0.4 m between anchor and tag planes).</figcaption></figure>

Fig. 5: Simulation of HDOP for two different fill levels of constellation from Figure 8a. Anchor positions are set to (0,-5),(5,0),(0,5),(-5,0) with the origin in the center of the tank.

ranges of 79 m to 23 m. State of the art biogas plants include fermenter tanks of up to 40 m diameter though most of todays plants are smaller. The attenuation by the enclosures and the film hood cover of the biogas plant is expected to be low as they are made of ABS and PVC respectively which offer low dissipation factors tan δ and dielectric constants near to 1. With the anchor placement right at the tanks perimeter and high expected fill levels the maximum needed ranges are of the same dimensions. This could imply a necessary change of the radio configuration in favor of range with the disadvantage of lower accuracy or system capacity.

The quality of measurements also depends on the constellation of anchor and tag positions which can be quantified by the dilution of precision (DOP). It is an indicator for the error gain of a certain constellation and has been introduced for time of arrival (TOA) based systems like GNSS [6]. As in this work the height of the tags will be at the constant or slowly changing fill level of biogas tanks and the planes of anchor placement and tags will be parallel to each other, only the horizontal part (HDOP) is of interest. The HDOP is defined as the ratio of error in the horizontal plane to the error of pseudoranges [8]

$$HDOP = \frac{\sqrt{\sigma_X^2 + \sigma_Y^2}}{\sigma_\rho} \qquad (17)$$

with the errors in x- and y-direction σ_X, σ_Y. The best HDOP can be achieved when the two mentioned planes are coplanar. A stochastic simulation for the constellation depicted in Figure 8a has been carried out for two different fill levels. The results in Figure 5 show the best values can be expected in the center of the slurry tank while amplifications of error rise up to HDOP = 2 at the edge of the tank. With decreasing fill levels the distances between the planes
<figure><img src="image_8.png" /><figcaption>Fig. 6: Power consumption of tag as a function of sample period from 10 Hz⁻¹ to 1 h.</figcaption></figure>

and so the HDOPs increase.

Another source of error is message loss, which can occur due to submerged tags. This system's backbone however, can detect message loss and only takes sets of messages into account, that provide feasible position calculations.

## 2.5 Power management and TDMA

To minimize power consumption and thus ensure long runtimes the tags initiate the ranging process at a regular interval and enter a low power state in between. For wait times between the ranging processes the microprocessor was put into the lowest power state from which it can only be woken up by an external interrupt which is generated by the DW1000 built in sleep timer. After calibration as explained in [5, P.39] the timers actual frequency is determined. As the frequency can be approximately 7 kHz to 13 kHz and the upper 16 bits of the 28 bit counter can be set, the minimum wait duration can be 585 ms to 315 ms. Using this timer the rest of the DW1000 can be put to sleep in addition to the host microcontroller.

An update rate of 1 Hz was chosen for this system because it gives good temporal resolution at the expected flow velocities at the surface of biogas plants. From the variation of the timers frequency follows that the exact wait times for 1 Hz operation can not be met. Also the collision of two tags ranging initiations has to be prevented. This makes it necessary to introduce a time division multiple access (TDMA) scheme. It is coordinated by one of the anchors which acts as a master and sends synchronization information during the ranging procedure. This master has to know of all active tags and based on the number of tags and the systems update rate assign each a unique time slot. Should a tag's ranging initiation drift over time leaving its assigned slot the master anchor will calculate a wait time which is used once by the tag for resynchronization.

The power consumption of a tag is dominated by the active ranging which was measured to be 27.7 mW at the given update rate. This leads to an operational
<figure><img src="image_9.png" /><figcaption>(a) Real distance $r = 4.2$ m, Mean measured distances $\bar{\rho}_1 = 4.21$ m, $\bar{\rho}_2 = 4.19$ m, Mean mea- sured distances $\bar{\rho}_1 = 10.1$ m, $\bar{\rho}_2 = 10.06$ m, $\bar{\rho}_3 = 10.08$ m, $\bar{\rho}_4 = 10.07$ m, Standard deviations $\sigma_{\rho,1} = 17$ mm, $\sigma_{\rho,2} = 15$ mm, $\sigma_{\rho,3} = 14$ mm, $\sigma_{\rho,4} = 13$ mm.

(b) Real distance $r = 10.1$ m, Standard deviations $\bar{\rho}_1 = 10.1$ m, $\bar{\rho}_2 = 10.06$ m, $\bar{\rho}_3 = 10.08$ m, $\bar{\rho}_4 = 10.07$ m.</figcaption></figure>

Fig. 7: Histograms and fitted probability density functions of $n = 120$ rangings between one tag floating in water and four anchors at two fixed distances.

time of 92 days with the chosen battery. During sleep times the power could be reduced to 724 µW. Figure 6 shows the power consumption of tag as a function of sample period. The mean dynamic power used by the ranging drops below the static power at a sample period above 40 s. Self discharge of the battery has not been accounted for.

## 2.6 Evaluation

To assess the expected quality of distance measurements a tag was placed inside an open tank of 10 m by 5 m filled with water at two different fixed locations. Four anchors were placed 2 m above the ground next to each other and to the perimeter of the tank. Figure 7 shows the resulting histograms of 120 measurements at each location. The results show standard deviations of less than 20 mm and maximum differences of mean and real value under 50 mm. These results show a comparable performance to open space measurements deducted by Michler et al. [11]. This leads to the conclusion that the placement of the UWB transceiver right above a plane of water has no detrimental effect on the ranging performance.

In a next step a test with two tags in a slurry tank was performed. This tank has similiar properties to those of biogas plants and the advantage of an open top. So it was possible to have an unmanned aerial vehicle capture a video for later comparison to the reconstructed positions. Figure 8 shows a schematic
<figure><img src="image_10.png" /><figcaption>Fig. 8: Test setup and reconstructed position records in slurry tank.</figcaption></figure>

of the tank with dimensions, fill level indication and anchor placements as well as reconstructed traces of two tags overlayed after 2 minutes of operation. The anchors were placed 0.5 m to the inside and 0.4 m above the walls of the tank which would also be the positions right on top of the hood cover if the tank was a biogas plant. The low fill level resulted in a difference of 3 m between the plane of anchors and the substrate surface. This can be considered a worst case scenario in terms of the HDOP as biogas plants are expected to operate at medium to high fill levels. No systematic loss of messages due to too high distances could be detected in this test.

A reconstruction of the traces was projected onto the horizontal plane and overlayed to the stabilized video capture of the UAV. Traces and video were synchronized in time and scaled accordingly using two timestamps with known positions. Because errors from perspective distortion have not been accounted for, the reconstructed path gives only an indication of the dynamic deviation to the actual position.

## 3 Conclusion and future work

This paper describes the concepts and system structure of a UWB based real-time localization system for the tracking of substrate flow on the surface of biogas plant digesters. The system can operate continuously over a period of three months with up to 50 concurrent tags and offers a sufficient accuracy for the evaluation of flow simulations. The field of use however does not end with substrate flow tracking as it can be used for all kind of tracking tasks where other systems e.g. global navigation satellite systems fail.

Future work includes the implementation of a novel ranging scheme (TOF-CR) described by Rebel et al. [13] to benefit of the accurate ranging of DS-TWR while keeping transmit times and power consumption low. Furthermore
the amount of anchors will be increased and the number of anchors a tag communicates to will be made flexible and chosen at runtime based on the anchors in reach and the resulting DOP. Therefore most of the system control will be moved to the SBC in the backbone. The system will then be used extensively to build a database for simulation verification.

**Acknowledgement:** This project has been funded by the Federal Ministry of Education and Research in Germany, the grant ID reads 03FH002IX4.

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