Simulation-based evaluation of indoor positioning systems in connected aircraft cabins

Abstract

With regard to the demanding aircraft cabin environment, this paper delves into the rising use of location-aware radio communication systems to streamline operational processes. We propose a hybrid deterministic and stochastic simulation approach, incorporating model-based ray-tracing and empirical residual simulation. The methodology presented allows for the evaluation of localization methods based on geometric relations, serving as both a data generation and validation tool. We elaborate how different radio properties and propagation phenomena influence these geometric relations and the localization process. This paper includes a publicly available dataset derived from the simulation approach, facilitating transparency and further analysis in the field of aircraft cabin radio localization systems.

Keywords:

• Radio propagation simulation
• channel modeling
• radio localization
• ultra-wideband (UWB)
• connected cabin
• indoor positioning systems (IPS)
• passenger (PAX) boarding

1. Introduction

Efficient air traffic management and ground handling are crucial factors that drive the performance of airline operations. The integration of aircraft and passenger (PAX) trajectories presents a major challenge in future mobility management. The COVID-19 pandemic has significantly impacted the transportation network (Schwarzbach et al. 2020), highlighting the need for effective PAX handling processes at bottlenecks, such as boarding and disembarkation within the confined aircraft cabin (Milne, Cotfas, and Delcea 2021; Salari et al. 2021). A key metric known as aircraft turnaround constitutes all ground-handling processes, including freight and baggage unloading and loading, refueling, cleaning, catering, and PAX boarding and disembarking (Schultz et al. 2020). PAX behavior largely influences the duration of boarding, and convenient and fast boarding is a priority for both PAX and airlines (Schultz 2018c). Therefore, a high demand on both technological and operational solutions is mandatory.

Location-aware radio-based communication networks provide a technical solution for PAX state monitoring and handling. While several general survey studies for these so-called indoor positioning systems (IPS), including Geok et al. (2020); Mendoza-Silva, Torres-Sospedra, and Huerta (2019); Zafari, Gkelias, and Leung (2019), have been conducted, questions of technology selection, usable hardware, applicable positioning methods, as well as the holistic optimization of these emerging localization systems in the context of the connected cabin still remain unresolved. In addition, the accuracy and scalability of radio-enabled localization within the harsh cabin environment still pose a major research question. For the development and integration of IPS within the cabin, a variety of challenges arise. Among others this includes: the aircraft cabin is a restricted area so accessibility for integration and evaluation studies is limited. The availability of modern technologies, possible physical layer modifications or hardware components might not be available during field trials, which also causes limitations in the adaptability of the surveyed data.

To evaluate the radio propagation channel within the aircraft cabin, a variety of empirical studies for different radio technologies have been conducted (Chiu and Michelson 2010; Chuang et al. 2007; Cogalan, Videv, and Haas 2017; Jacob et al. 2009; Neuhold et al. 2016; Schulte et al. 2011). The focus of these works is empirical findings concerning general characteristics of the propagation environment. In addition, localization capabilities of 5G New Radio (5G NR) (Cavdar et al. 2018), WiFi (Wang et al. 2021) or Ultra-Wideband (UWB) (Geyer and Schupke 2022; Karadeniz et al. 2020) are discussed. However, these studies are limited to the technologies, constellation and hardware applied, so they allow no generalization.

This paper presents the capabilities of radio-based simulation with respect to localization functionalities with applications for air transport management and especially in-cabin systems. The foundation for this is a ray-tracing respectively ray-launching based radio propagation simulation, which is commonly applied for network coverage analysis, as well as probabilistic error sampling based on empirical findings. To provide a feasible data basis for radio-based localization, the conventional simulation approach is modified. A derived dataset from this simulation procedure has been published and is available (Schwarzbach and Ninnemann 2023). Concluding, this paper addresses the following main research objectives:

• Presentation of a holistic radio propagation approach for active localization systems addressing the present issues of spatial consistency and the influence of stochastic errors by combining multiple simulation procedures

• Merging of operational processes and simulations, e.g. boarding simulation with radio-based localization in a common framework

• Highlighting the potentials of the simulation framework to evaluate also radio sensing applications and data-driven approaches.

The rest of this paper is structured as follows: following this introduction, Section 2 provides a comprehensive overview on the operational aspects and potentials of location-awareness, as well as recent developments in radio-based localization and the corresponding radio channel modeling and simulation, with a specific emphasis on the connected aircraft cabin. Furthermore, Section 3 discusses the methodology of this work, including the proposed simulation portions and positioning capabilities. In Section 4, the carried out simulation and respective results are discussed. This paper concludes with a conclusion and suggestions for future research directions. The appendix includes both a table of abbreviations and symbols.

2. Literature review

The scope of this paper represents a cross-section of scientific disciplines and includes operational planning and turnaround optimization within air traffic management, the realm of radio-based indoor positioning systems, as well as the modeling and simulation of these systems. Therefore, this section provides a brief literature review of these research fields and highlights the resulting benefits of their integration.

2.1. Operational perspective

Numerous studies have investigated the most efficient sequencing of PAX during boarding and deboarding processes (Ferrari and Nagel 2005; Milne, Salari, and Kattan 2018; Tang et al. 2012; Van Landeghem and Beuselinck 2002). These studies typically analyze the effects of various operationally relevant input parameters, including seat load factor, group composition (such as families and couples), volume of carry-on baggage and use of baggage compartments. The objective of optimizing boarding/deboarding processes is generally to minimize the amount of time required. The duration necessary for establishing the sequence or the stability of the solution is commonly disregarded (see Schultz 2018c for variability in boarding time). Since the PAX cabin lacks sensors, optimization strategies cannot consider the current situation in the cabin. Therefore, a sequence often deemed advantageous might not be the optimal solution in a specific scenario. Implementing a cabin sensor system would facilitate the collection of movement data (such as walking speeds and position of bottlenecks , Schultz 2018a) and status data regarding cabin configuration (such as seat occupancy and baggage compartment usage).

As currently, sparse data on cabin processes are available, they could be utilized to calibrate airline-specific models (Schultz 2018b) and support dynamic optimization approaches (Notomista et al. 2016; Zeineddine 2017). These dynamic approaches can then update the sequence considering the current congestion situation. If congestion makes the rear rows to board problematic, priority should be given to front-row seat PAX. Similarly, data on the overhead storage compartments could be utilized. Operating at total capacity, these compartments indicate that nearby PAX may take longer to stow their luggage, potentially obstructing the aisle for an extended duration. In addition, the data of the cabin conditions can be recorded, used to develop data-driven models and finally predict the process flows, e.g. prediction of boarding times (Schultz and Reitmann 2019).

Apart from the cabin itself, PAX localization is also beneficial for modeling and prediction of PAX flows within the airport as discussed in Hu, Luo, and Bai (2022). In addition, Jiang, Zheng, and Kim (2022) discuss the introduction of radio-based localization to predict the PAX flow in a transportation station.

2.2. Radio-based localization

The determination of an absolute location information can be realized using radio-based systems. In this context, radio devices can be distinguished as stationary infrastructure units (anchors) and mobile tags to be located. In principle, range-based or range-free relations are derived from physical parameters of the systems, which can then be used to calculate the tag's location with the knowledge of the anchor's location (Mendoza-Silva, Torres-Sospedra, and Huerta 2019).

As a technological basis, wireless communication systems have garnered significant research attention over the past two decades due to their cost-effectiveness, energy efficiency, retrofitting capabilities, and versatility (Zafari, Gkelias, and Leung 2019).

This has led to the rapid emergence of the Internet of Things (IoT) across various research and application domains, enabled by affordable smart interconnections of devices, individuals, and operations (Al-Fuqaha et al. 2015; Lin et al. 2017). Researchers have explored using radio-based localization technologies to enhance intelligent and automated systems in various application areas, going beyond fundamental IoT functions like communication and sensor data acquisition (Li et al. 2021). Similar to the utilization of Global Navigation Satellite Systems (GNSS), the widespread adoption of smartphones (Davidson and Piché 2017; Xiao et al. 2016) and connected wearables (Ometov et al. 2021) has driven the comprehensive use of location-enabled communication technologies (Egea-Roca et al. 2022).

Terrestrial location-aware communication systems, historically confined to GNSS-denied scenarios, are commonly referred to as IPS (Farahsari et al. 2022). An additional research focus involves the ongoing transformation of mobile communication systems, particularly with the advent of 5G NR technology (Chettri and Bera 2020; del Peral-Rosado et al. 2018) and future beyond 5G systems (Chen et al. 2022; Kanhere and Rappaport 2021). These developments have transitioned from conventional assistance of positioning using signals of opportunity to fully integrated communication systems (Liu et al. 2022). In this context, integrated communication systems encompass the ability to provide both active, device-based localization and passive, device-free sensing (Shastri et al. 2022), which enhance the location-awareness of radio systems.

Regarding active localization, a plethora of survey papers on location capabilities in IPS and mobile cellular networks are available (Geok et al. 2020; Gonçalves Ferreira et al. 2017; Gu, Lo, and Niemegeers 2009; Laoudias et al. 2018; Shastri et al. 2022; Tariq et al. 2017; Xiao et al. 2016; Zafari, Gkelias, and Leung 2019). Analyzing these works reveals a lack of a unified taxonomy for defining location-aware communication systems. Instead, existing works are typically driven by either technology or application considerations. However, the abundance of research indicates that technologies, applications, and regulations are subject to continuous evolution. Concerning the establishment of a framework for spatial and geometric relations within a radio network, abstracted unified measurement types for data acquisition are necessary. These encompass measurement principles related to signal characteristics, physical attributes and connection-related properties of communication technologies.

In light of the aforementioned aircraft cabin environment, several empirical studies have been conducted to assess radio channel and propagation characteristics (Chiu and Michelson 2010; Chuang et al. 2007; Cogalan, Videv, and Haas 2017; Jacob et al. 2009; Neuhold et al. 2016; Schulte et al. 2011). These investigations also explored the localization capabilities of various radio technologies, including UWB (Geyer and Schupke 2022; Karadeniz et al. 2020), WiFi (Wang et al. 2021), and 5G NR (Cavdar et al. 2018). These studies primarily aim to provide empirical insights into radio propagation in the challenging aircraft cabin environment. However, their focus on assessing localization capabilities is limited.

2.3. Radio channel and modeling

The performance of wireless communication and localization is heavily dependent on the radio channel and various propagation effects. The three basic propagation phenomena for the interaction of the radio wave with objects in the environment are reflection, scattering, and diffraction. These phenomena lead to large-scale and small-scale channel characteristics including path loss, shadowing, and multipath fading.

Existing channel models take these effects into account and could be categorized into deterministic, stochastic, and hybrid approaches. Stochastic models use statistical approximations in form of statistical distributions to characterize the received signal and channel characteristics such as path loss, delay spread, and multipath components (MPCs). These models are based on measurements and empirical observations in specific types of environments (rural, urban, indoor, micro, macro, etc.). The channel is modeled at a random location of the sensor in a defined type of environment, so there is no spatial consistency between different sensor locations. Due to the low complexity of stochastic models and the suitability to model a communication channel, they are used for example for the 3GPP technical Report 38.901 channel model (3GPP 2019).

Hybrid channel models often extend stochastic models by taking the geometry into account. For example, quasi-deterministic channel models compute the dominant MPC with a highly simplified environment map and add clusters of stochastically modeled MPCs to the model (Han et al. 2022). For geometry-based stochastic models the most widely used academic simulator is QuaDRiGa (Jaeckel et al. 2017).

Deterministic models approximately solve the Maxwell's equations. These models achieve high accuracy, but require detailed knowledge of the geometry of the environment, the electromagnetic properties of the materials, and the spatial position of the sensors. The propagation paths are calculated based on the channel characteristics and the position of reflectors in the environment to obtain the channel impulse response (CIR). Deterministic approaches are spatially consistent, as they consider the propagation environment and transceiver geometry. This spatial consistency is crucial to evaluate localization with IPS in a specific environment such as the aircraft cabin. In general, the parameters of every propagation path are computed using geometrical optics with either ray-tracing or ray-launching. Details on these approaches are given in Han et al. (2022).

3. Methodology

3.1. Overview

To address the aforementioned challenges and shortcomings of conducted simulation approaches, an adaptive and technology-open simulation procedure is presented in this paper. This is realized by the consolidation of both deterministic, model-based 3D ray-tracing (Yun and Iskander 2015) to derive signal characteristics, such as time-of-flight or visibility, and probabilistic error modeling to address additional hardware- or propagation-specific influences (Schwarzbach, Weber, and Michler 2022). Unlike previous works, which focus on the general network coverage (Ußler et al. 2022) or passive radio sensing (Schwarzbach, Ninnemann, and Michler 2022) within the cabin, this contribution focuses on the specialized demands and requirements of active localization by combining the advantages of aforementioned simulations utilizing a hybrid simulation approach. Generally, deterministic approaches provide a strong correlation with the environment and geometry, as they are highly accurate but require complex modeling and computational efforts. Therefore these models are spatially consistent and can predict the channel's behavior with high accuracy. In addition, stochastic models are based on empirical channel measurements and the derived stochastic properties. They can easily be implemented and do not require specific modeling of the environment and can therefore possibly lead to inconsistency in their spatial representation.

In this light, we present three main pillars, which constitute a framework for application-driven location-based services within the cabin: operational simulation, radio propagation simulation, and localization. Figure 1 summarizes a high-level overview of the radio simulation and how it can be incorporated within an operational scenario, while highlighting the pillars of the approach.

Figure 1. High-level flowchart of the proposed radio localization simulation approach.

At first, operational requirements need to be addressed. This includes different use cases, the types of locatable objects and functional respectively quantitative requirements. The operation simulation allows the derivation of reference states from the operational inputs, e.g. a boarding sequence, where each PAX is associated to a reference position at each time step.

The main scope of the presented work is the adaptation of radio propagation simulation (as shown in blue in Figure 1). The developed approach utilizes both deterministic ray-tracing for spatial scene analysis, which is conventionally applied for network coverage analysis, and adaptive stochastic error sampling, partially based on empirical findings.

In contrary to previously mentioned works, this spatial consistency is achieved by adopting the observability results from deterministic simulation, here Line-of-Sight (LOS), Obstructed Line-of-Sight (OLOS), or Non-Line-of-Sight (NLOS) along additional parameters such as the channel impulse response or the delay spread. The obtained visibility constellations are then again used to further consider stochastic error influences with specific noise and error distributions for each propagation case as detailed in Section 3.3. Based on these inputs, different localization methods can be trained and applied to derive a location information.

Since UWB-based positioning systems have previously been discussed for applications within the connected cabin, e.g. Geyer and Schupke (2022), we also apply our simulation to the physical layer properties of UWB. In unison, we correspond to the principle of UWB two-way-ranging (Karapistoli et al. 2010).

While not being the main focus of the work, we still present the incorporation of both operational simulation and localization methods (orange and green in Figure 1) to emphasize the overall toolchain and interdependent principles of each pillar.

3.2. Radio propagation simulation

For deterministic radio propagation simulation, various inputs and pre-requisites for modeling are necessary to derive required channel parameters (Ußler et al. 2022). Figure 2 shows the processing for the deterministic radio propagation simulation to compute the visibility states.

Figure 2. Processing for the radio propagation simulation with inputs, prediction models, and results.

The inputs for the simulation include a detailed environmental model that includes both the geometry of the objects and their electromagnetic properties. For this purpose, a CAD model of the aircraft cabin with an associated database of material properties for different frequencies is used. In this case, the CAD model represents an Airbus A320 including all seats and luggage compartments (cf. Figure 3). However, PAX are not yet modeled. The electromagnetic properties include the relative permittivity, relative permeability, and roughness of the various surfaces and objects in the model. From these properties, it is possible to calculate the attenuation of the reflected wave and the loss due to transmission through the object with a defined thickness (Schwarzbach et al. 2020; Ußler et al. 2022).

Figure 3. CAD-Model of the Airbus A320 aircraft cabin: (a) exterior, (b) interior, (c) exemplary result of 3D ray-tracing.

The radio model consists of the signal parameters of the desired radio technology, the specification of the antenna, and other simulation parameters that parameterize the computation method. The radio technology is specified by a channel, the associated center frequency, and the transmission power. The modeling of the antenna is most accurately done by a 3D antenna pattern. From the antenna pattern, the antenna gain, the half-power beam width, and the size the sidelobes can be obtained. Further parameters of the simulation include the maximum number of reflections, transmissions, and diffraction per ray. Also, the specified sensitivity of the receiver determines the termination of the calculation of individual propagation paths.

Another specification for modeling the radio link is the location of the transmitter and receiver antennas. In our case, transmitting antennas are located at fixed positions, whereas the position of the receiver antenna is varying within an equidistant grid. Thus the visibility results and channel parameters are calculated for all receiver locations in the grid. For this, ray-launching provides different channel parameters, which are based on the calculation of the propagation paths with their respective length, amplitude, and phase (Yun and Iskander 2015). These parameters are listed in Table 1 and are conventionally used to plan and optimize the performance of communication networks, however, can also be applied for radio-based localization systems.

Table 1. Radio channel simulation results, which fully characterize the propagation channel and are required for the localization methods.

Results	Description
Delay	Delay of the respective ray
Delay Spread	Delay spread of all propagation paths either as Excess Delay Spread or RMS Delay Spread
Path loss	Attenuation of the propagation path due to free-space path loss, reflections, scattering, diffraction, etc.
Power/Field strength	Calculated power and field strength at receiver based on the path loss of all propagation paths
LOS/NLOS conditions	Differentiation whether there is an LOS, OLOS, or NLOS condition between transmitter and receiver
Interactions with objects	Location of interaction and type of interaction (reflection, scattering or diffraction) of the propagation path with objects
CIR	Delays and amplitudes of individual propagation paths plotted in the form of a power delay profile with Dirac pulses

Details and specifications on the applied parameters for the ray-launching simulation are summarized in Table A3 and are further elaborated in Section 4.

3.3. Ranging simulation

Based on the results of the deterministic radio simulation, visibility-specific additional error sampling simulation is performed to derive distance measurements. Specifically, stochastic sampling based on a semi-empirical simulation model has been studied in a previous work by examining the ranging capabilities of UWB in a harsh environment (Schwarzbach, Weber, and Michler 2022). In accordance, a collaborative ranging simulation in a smart parking environment has been performed using this approach (Jung, Schwarzbach, and Michler 2022).

Therefore, the semi-empirical sampling approach is only briefly outlined below and will further be enhanced in the following sections by combining it with radio propagation simulation. Unlike aforementioned works, this paper utilizes the semi-empirical approach with the previously introduced deterministic scene analysis and therefore allows more spatial consistency of the preserved observation data. The necessary steps for this task are briefly depicted in Figure 4.

Figure 4. High-level error sampling procedure.

The reference position is given from the operational scenario to be examined (cf. Figure 1) and can either be time-variant or time-invariant. For each measurement step (epoch), two parameters can be derived based on the constellation:

• Reference distance $\mathit{d}$, which is defined as the 3D distance between the reference position ${\mathbf{x}}_{\mathrm{ref}}$ and the position of available anchors ${\mathbf{x}}_a$: $\mathit{d}=\Vert {\mathbf{x}}_a-{\mathbf{x}}_{\mathrm{ref}}{\Vert }_2$.

• Observability analysis to each available infrastructure node is estimated from the given radio propagation simulation.

For the latter, there are generally four propagation phenomena observable (Qi, Kobayashi, and Suda 2006), of which three are illustrated in Figure 5:

• LOS: The signal is received via the direct path between transmitter and receiver (cf. Figure 5 a).

• OLOS: The signal is still received via the geometrical direct path, however it has penetrated at least one structure on its way (cf. Figure 5 b).

• NLOS: The direct signal is blocked in this case, however the signal still received via a reflected path (cf. Figure 5 c).

• Not receivable: Given the propagation environment and the radio model, the signal attenuation can exceed the receiver sensitivity and therefore leads to a signal not being receivable at a given location. This effect is typically caused by high distances or many obstructing objects between transceivers.

Figure 5. Schematic examples of different radio propagation phenomena: (a) LOS, (b) OLOS, and (c) NLOS.

In addition to these four propagation phenomena derived from deterministic radio simulation, additional effects and error sources are considered. At first, general measurement noise modeled as additive white gaussian noise (AWGN) to quantify the overall precision of the measurement technology is taken into account.

These intrinsic factors are hardware-related and are empirically quantifiable (Schwarzbach, Weber, and Michler 2022). Second, gross errors, also referred to as outliers, are substantial derivations between true and observable values. These effects can for example be caused by target confusion, network errors, or electromagnetic interferences. Given the aforementioned propagation scenarios and these additional error influences, we model a ranging measurement $r$ as follows (Qi, Kobayashi, and Suda 2006; Schwarzbach, Weber, and Michler 2022): (1) $\begin{array}{r}r=\{\begin{array}{ll}\mathrm{d}+\text{ϵ}& \mathrm{if}p>{\displaystyle \frac{\mathrm{d}}{{\mathrm{d}}_{\max }}}\\ \mathrm{\varnothing }& \mathrm{else},\end{array}\end{array}$(1) where the observation constitutes the true distance d and the additive errors $\text{ϵ}$. The error terms $\text{ϵ}$ exhibit a linear dependence on distance, relative to an empirical maximum range denoted as ${\mathrm{d}}_{\max }$. The parametrization of ${\mathrm{d}}_{\max }$ is application-, technology and frequency-specific. When the prescribed condition is not satisfied, measurement failure denoted as $\mathrm{\varnothing }$ is simulated. Furthermore, the probability p for occasional disturbances in measurements is represented as a Bernoulli experiment with $p\sim \mathcal{U}(0,1)$. Empirical evidence from our previous study (Schwarzbach, Weber, and Michler 2022) has substantiated the presence of distance-dependent characteristics in errors. This phenomenon in turn influences the success rate of simulated measurements.

Depending on the observed propagation scenario, we sample our scenario-specific ranging error following the decision tree given in Figure 6, in which we introduce the following quantities:

• ${\text{ϵ}}_{\mathrm{LOS}}$, ${\text{ϵ}}_{\mathrm{OLOS}}$, and ${\text{ϵ}}_{\mathrm{NLOS}}$ represent the ranging error for LOS, OLOS, and NLOS scenarios respectively

• $\mathcal{N}$ and $\mathcal{LN}$ denote a normal respectively a log-normal distribution

• ${\sigma }_r^2$ represents the noise-related error term

• ${\overline{R}}_r$ and ${\sigma }_{\overline{r}}^2$ represent the location and scale parameter of an $\mathcal{LN}$ distribution.

Figure 6. Error sampling decision highlighting the underlying stochastic models.

In addition, an empirical outlier probability $p_{\mathrm{out}}$ is defined, which accounts for gross outliers. Outliers characterize the robustness of the measurement system and can be caused by a variety of influences, such as measurement confusions (Schwarzbach, Weber, and Michler 2022). The quantity of this variable is again dependent on the environment and the measurement technology. Outliers are generally a major source for localization errors, especially in demanding scenarios, therefore, a proper simulation of them is essential.

Since outliers typically do not follow a generic stochastic model, we assume a uniform error distribution within a physically measurable domain. Therefore outliers $\text{ϵ}$ are additionally modeled as (2) ${\text{ϵ}}_{\mathrm{OUT}}\sim \mathcal{U}(-\mathrm{d},{\mathrm{d}}_{\max }-\mathrm{d}).$(2) Further details on the stochastic sampling approach, derived from a real-world measurement campaign using UWB, are presented in Schwarzbach, Weber, and Michler (2022).

In summary, the following error types are considered within the simulation: LOS noise, OLOS noise, NLOS right-skewed noise, uniformly distributed outliers with respect to an outlier probability and measurement failures with respect to signal attenuation (maximum range) and random failures. Resulting overall error (residual) distribution derived from the presented simulation approach are presented in Section 4.

3.4. Positioning

In the literature, a variety of applicable state estimation approaches for radio positioning exist. Most commonly, these can be divided in the following categories: deterministic approaches use explicit observables and calculate geometric relationships between fixed infrastructure and mobile devices on this basis (Stojmenović 2005). In addition, probabilistic approaches also use the aforementioned observables, but consider the system states as stochastic random variables and describe them as well as the observables by means of probability density functions (Chen 2003). Lastly, the localization problem can also be solved by applying data-driven localization methods derived from machine learning and artificial intelligence (Burghal et al. 2020).

Since the focus of this paper is on highlighting the simulation procedure to enable positioning applications (cf. Section 3), this manuscript will not further elaborate applicable state estimation methods, but rather build up on existing frameworks allowing a discussion of the simulated effects on the localization process.

For dynamic systems, Recursive Bayes' Filter (RBF) poses a common framework for localization problems, including Kalman, Histogram, or Particle Filters (Chen 2003). In this work, we apply a pre-defined, equidistant grid representation of the state space, representing possible locations and allowing a multi-dimensional implementation of an Histogram Filter (Thrun, Burgard, and Fox 2005), also known as Point-Mass Filter or Grid Filter. This representation is used for the given application because of two reasons. This non-parametric filtering approach provides inherent robustness to non-gaussian error types compared to parametric filtering. With multiple locatable objects within the confined cabin space, the grid can be used as a uniform state space for all objects. When presented with various objects within the network, this approach can reduce computational load compared to, for example, a Particle Filter.

Since this localization method has been previously detailed for several radio-based localization problem, we only briefly outline the necessary calculation steps and refer to previous works for implementational details (Schwarzbach, Michler, and Michler 2020) and Schwarzbach, Michler, and Michler (2023).

For this method, the domain of the state space representing realizations of the state vector $\mathcal{X}$ is decomposed in a discrete and finite set of M-equidistant grid points $X_M$: $\mathrm{dom}\left(\mathcal{X}\right)={\mathit{X}}_1\cup {\mathit{X}}_2\cup \dots {\mathit{X}}_M$.

Given this state–space initialization, the Grid Filter follows the general iterative RBF structure depicted in Figure 7, where the corresponding calculations are given in Equations  (3(3) $\begin{array}{rl}{\overline{\mathit{p}}}_t& ={\mathit{p}}_{t-1}\sum _m\mathit{P}\left({\mathcal{X}}_{t,m}|{\mathcal{X}}_{t-1}\right)\end{array}$(3) ), (4(4) $\begin{array}{rl}{\mathit{p}}_t& =\eta {\overline{\mathit{p}}}_t\sum _m\mathit{P}\left({\mathcal{Z}}_t|{\mathcal{X}}_{t,m}\right)\end{array}$(4) ) and (5(5) $\begin{array}{rl}{\stackrel{\mathbf{ˆ}}{\mathcal{X}}}_t& =\mathrm{argmax}{\mathit{p}}_t\end{array}$(5) ) (Thrun, Burgard, and Fox 2005). (3) $\begin{array}{rl}{\overline{\mathit{p}}}_t& ={\mathit{p}}_{t-1}\sum _m\mathit{P}\left({\mathcal{X}}_{t,m}|{\mathcal{X}}_{t-1}\right)\end{array}$(3) (4) $\begin{array}{rl}{\mathit{p}}_t& =\eta {\overline{\mathit{p}}}_t\sum _m\mathit{P}\left({\mathcal{Z}}_t|{\mathcal{X}}_{t,m}\right)\end{array}$(4) (5) $\begin{array}{rl}{\stackrel{\mathbf{ˆ}}{\mathcal{X}}}_t& =\mathrm{argmax}{\mathit{p}}_t\end{array}$(5) where

• ${\overline{\mathit{p}}}_t$ denotes the predicted belief following a motion model at timestep t,

• ${\mathit{p}}_t$ denotes the resulting belief using the given observations modeled via

• $\mathit{P}\left({\mathcal{Z}}_t|{\mathcal{X}}_{t,m}\right)$, which denotes the observation Likelihood with respect to the normalization constant η

• ${\stackrel{\mathbf{ˆ}}{\mathcal{X}}}_t$ denotes the state estimation derived from maximizing the current belief.

Figure 7. General RBF structure.

Figure 8 depicts an exemplary output of the applied state estimation framework. Here, the given state space is depicted as the (mostly) purple discrete grid. Reference points (red) perform faulty ranging measurements (grey) in accordance with Section 3.3, which influence the grid likelihood as indicated by the yellow areas, which represent a higher likelihood. Finally, the reference position is indicated in black.

Figure 8. Exemplary output of the observation step of the Grid Filter using faulty ranging measurements. Anchors are depicted in red, reference point in black. The discrete state space is represented by an equi-distant grid (purple), where the likelihoods of ranges (grey) are color-coded.

4. Simulation and results

4.1. Simulation overview

In accordance with previous works, we constitute our simulation within the previously mentioned Airbus A320 model (Schultz 2018c; Schwarzbach et al. 2020). In total, three scenarios are covered as summarized in Table 2.

Table 2. Test cases on testbed for automated and connected driving.

	Name	Description	Samples
I	Static, above seat	Antenna height 112 cm	5000 positions, 40,000 ranges
II	Static, below seat	Antenna height 70 cm	5000 positions, 40,000 ranges
III	Dynamic, 148 PAX	Boarding process	40,184 positions, 321,472 ranges

At first, two static scenarios are examined to achieve a reproducible scenario for different receiver heights. Scenario I refers to a receiver height slightly above the seats within the cabin. This generally leads to a high percentage of LOS reception, while scenario II applies a receiver height indicated a position below the seat, e.g. for the localization of life vests (Ninnemann et al. 2022). Both scenarios I and II refer to an empty cabin without PAX. Scenario III then covers an entire boarding process, as previously described in Schultz (2018a). In total, 148 PAX are incorporated in the boarding sequence, which are continuously tracked during the process.

Concerning the radio propagation simulation, ray-launching is used to calculate radio parameters for all possible receiver locations within the cabin represented by an equidistant grid. To limit the computational effort and time, the maximum number of interactions with objects is set to 2 and the grid of possible receiver positions has a resolution of 10 cm. Since the implementation of ray-launching is not the main scope of this work, we used the commercially available software Altair WinProp 2022.3 (Altair Engineering Inc 2023), which provides necessary features for ray-tracing and ray-launching. Alternatively, open-source frameworks to perform ray-tracing, such as MaxRay (Arnold et al. 2022), for 5G mmWave (Hossain et al. 2019) or 3D ray-tracing (Geok et al. 2022) are also available. Table A3 lists the details and parameter sets used for the radio propagation simulation in the aircraft cabin.

4.2. Visibility analysis

The results derived from the deterministic radio simulation are the visibility states between anchors and the reference positions. To illustrate these constellations, the visibility for scenarios I and II is compared in Figure 9. For each anchor indicated in black, the observation state throughout the grid is given by the respective color.

Figure 9. Visibility analysis provided by radio propagation simulation: scenario I (left) and scenario II (right) for the entire reception plane. The visibility states are color-coded with respect to the given colorbar.

Given these results, the difference in relative antenna height between anchors and the reception plane is apparent. While scenario I comprises LOS reception in an empty cabin, scenario II constitutes hardly any LOS states due to the obstruction of objects between anchors and the reference plane. For scenario II, we also considered a distant-dependent threshold between OLOS and NLOS observations, as additional signal attenuation due to longer travel distances for the OLOS path would lead to a higher likelihood for NLOs reception. This threshold was empirically set to 6 m.

4.3. Ranging sampling

Based on the derived results from the visibility analysis, the stochastic error sampling as detailed in Section 3.3 is performed. To provide insight on the different visibility states, Figure 10 depicts the ranging residuals (measurement errors) for each individual scenario. Further highlighting the underlying data, Table 3 briefly outlines the corresponding quantities. This further emphasizes the presence of both measurement failures in the confined cabin area (21.4% –22.5% across all three scenarios) as well as the presence of measurements outliers, which are not explicitly shown in Figure 10 due to readability.

Figure 10. Residuals for simulated scenarios. Values are clipped at $[-5,15]$ m.

Table 3. Quantities of ranging measurements for each scenario.

Scenarios	Total measurements	Valid measurements	Depicted measurements
I	$40,000\left(100\mathrm{\%}\right)$	$31,437\left(78.6\mathrm{\%}\right)$	$30,269\left(75.7\mathrm{\%}\right)$
II	$40,000\left(100\mathrm{\%}\right)$	$31,469\left(78.7\mathrm{\%}\right)$	$28,353\left(70.9\mathrm{\%}\right)$
III	$322,376\left(100\mathrm{\%}\right)$	$233,569\left(72.5\mathrm{\%}\right)$	$224,683\left(70.0\mathrm{\%}\right)$

It is observable that the measurement residuals follow distinct distributions influenced by the simulated scenarios and corresponding visibility states. Scenario I constitutes a majority of LOS reception (as indicated in Figure 9), while still being prone to environmentally unrelated outliers and measurement failures. In contrast, scenario II is prone to a majority of comparably higher noise due to OLOS as well as manifold NLOS receptions. Lastly, caused by the presence of additional obstacles, for example PAX, within the propagation environment, scenario III reveals a mix of the two previous scenarios. For this, it is assumed that PAX generally case an absorption or attenuation of the radio signal, therefore the overall reception range is lower and additional noise is added.

4.4. Positioning results

At last, the discussion of derivable positioning results based on the introduced positioning method from Section 3.4 is presented. Figure 11 depicts the qualitative localization results for the simulated scenarios. Furthermore, a quantitative analysis of the positioning results is conducted. For this the $\left|\right|\cdot |{|}_2$ norm between the estimated and reference positions is utilized as error metric $\mathcal{Q}$ (18305:2016  2016). This metric is also referred to as root mean square error (RMSE) and is commonly applied for radio positioning, as it also highlights the influence of outliers (Chai and Draxler 2014).

Figure 11. Qualitative positioning results for each simulation scenario: scenarios I and II represent the static receiver position at different heights, while for scenario III the trajectory of one exemplary PAX is depicted.

For this matter, Figure 12 depicts statistical error measures expressing the positioning accuracy as well as an empirical cumulative density function of the positioning error. The comparison of scenarios I and II in Figure 11 clearly reveals the influence of different measurement error distributions on the positioning results, as the right-skewed error distribution in scenario II also leads to a higher scattering of positioning results. This is also supported by Figure 12, where scenario I yields an average positioning error of ${\overline{\mathcal{Q}}}_{\mathrm{I}}=0.17$ m compared to ${\overline{\mathcal{Q}}}_{\mathrm{II}}=0.34$ m for scenario II. The overall descriptive statistics for all scenarios are summarized in Table 4, including average $\overline{\mathcal{Q}}$ (RMSE), median $\widetilde{\mathcal{Q}\mathcal{,}}$ and the error variances ${\sigma }_{\mathcal{Q}}^2$. In addition, the σ quantiles and the $25,50,75$ percentiles of the error distributions are given.

Figure 12. Statistical evaluation of the positioning error for all three scenarios: (a) raincloud plot and individual error points and (b) empirical cumulative density function (ECDF). Positional errors are clipped at 5 m.

Table 4. Quantitative evaluation scenarios I, II, and III.

	$\overline{\mathcal{Q}}$	$\tilde{\mathcal{Q}}$	${\sigma }_{\mathcal{Q}}^2$	Quantile [m]			Percentile [m]
Measure	[m]	[m]	[m]${}^2$	σ	$2\sigma$	$3\sigma$	25	50	75
I	0.17	0.16	0.01	0.20	0.35	0.45	0.10	0.16	0.23
II	0.34	0.31	0.04	0.40	0.69	0.93	0.19	0.31	0.44
III	0.29	0.21	0.69	0.28	0.54	0.89	0.13	0.21	0.31

Furthermore, scenario III is briefly discussed. Figure 11 reveals clustering points in different areas, where the PAX has to wait before moving on due to other PAX. These occurrences can be monitored for operational planning and turnaround estimation respectively the optimization of the overall boarding strategy.

While Figure 11 only depicts the estimated trajectory for one PAX, the given statistical measures include the positional errors for all 148 simulated PAX during the boarding sequence. From the available results, it can be inferred that the presence of PAX within the cabin has an additional negative impact on visibility, and consequently, on ranging accuracy.

5. Conclusion and research directions

Radio propagation simulation is an ubiquitous tool in various engineering fields, predominantly used for coverage and network analysis, but it also provides numerous advantages for radio-based location applications. However, single-handily applied deterministic, empirical, and stochastic models have dedicated disadvantages for simulating the necessary inputs for radio-based localization. Therefore, this paper proposes the integrated combination of the aforementioned approaches to provide spatially consistent geometric relations, yet enabling alternating residual distributions. Due to the adaptability of both the deterministic and stochastic simulation components, different scenarios and error sampling distributions can easily be applied and assessed. The framework also enables a cheap setup optimization, e.g. geometrical layout of anchors, and parameter tuning, e.g. for outlier detection.

The implemented simulation toolchain can be used not only to evaluate the performance of localization algorithms based on visibility states but is also scalable in terms of evaluation opportunities. These opportunities encompass assessing other signal parameters, such as RSSI or CIR (as shown in Table 1), and evaluating different propagation environments and radio technologies, including specific antenna hardware.

In summary, the presented results encompass three scenarios, each yielding different visibility states, resulting in demanding and partially right-skewed error distributions based on the proposed sampling distributions. This further underscores the need for robust positioning and effective outlier mitigation strategies.

We want to further emphasize that this paper only covers one specific network constellation, one radio technology and a specific distance measurement principle. Derived from that, a fixed set of proposal distributions and one localization scheme is presented. However, due to the nature of the toolchain, manifold of the expects can be altered and compared. This also allows the simulation toolchain to be applied for the implementation and evaluation of data-driven localization approaches and machine learning in general by addressing the data generation bottleneck (Michler et al. 2023).

Dataset

The dataset consists of three csv files containing the visibility analysis from ray-launching, the anchor states, and the results of the probabilistic range sampling. The file visibility.csv contains visibility states inside a grid with the resolution of 10 cm of the two simulated heights in the cabin. The columns of the file include the following data:

• x: Position of the predicted grid cell in x

• y: Position of the predicted grid cell in y

• height: Height of the simulated prediction plane. Is used to investigate the viability of the tag for two different height in the cabin

• anchor_id: ID of the anchor for which the visibility is specified

• visibility: Computed visibility state (LOS=1/OLOS=2/NLOS=3) based on the radio propagation simulation with ray-launching.

The second .csv file includes the sampled ranges based on the observability and is named ranges.csv. Each line of the file contains the following data:

• ref_pos_x: Static reference position of the PAX in x

• ref_pos_y: Static reference position of the PAX in y

• height: Height of the used prediction plane

• anchor_id: ID of the anchor for which the range is sampled.

• range: Sampled range between the anchor and the tag at the PAX. This range is used in the localization module to estimate the position of the PAX based on the simulated radio channel characteristics and visibility state from the radio propagation simulation.

Additionally the 3D position of the anchors in the cabin is provided in separate file called anchors.csv. The dataset is open-access available to download on the research data repository OpARA of Dresden University of Technology: http://dx.doi.org/10.25532/OPARA-275 (Schwarzbach and Ninnemann 2023).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been funded by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) following a resolution of the German Federal Parliament within the projects CANARIA (FKZ: 20D1931C) and INTACT (FKZ: 20D2128D).

Appendices

Table of abbreviations

Table B1. Table of abbreviations.

Abbreviations	Description
3GPP	3rd Generation Partnership Project
5G	5th Generation standard of mobile cellular communication
BLE	Bluetooth Low Energy
CAD	Computer-aided Design
CIR	Channel Impulse Response
ECDF	Empirical Cumulative Density Function
GNSS	Global Navigation Satellite Systems
IPS	Indoor Positioning Systems
IoT	Internet of Things
LiFi	Light Fidelty
LOS	Line-of-Sight
LPWAN	Low Power Wide Area Network
LTE	Long-Term Evolution
MPC	Multipath Components
NFC	Near-Field Communication
NLOS	Non-Line-of-Sight
NR	New Radio
OLOS	Obstructed Line-of-Sight
PAX	Passenger
RBF	Recursive Bayes' Filter
RMSE	Root mean square error
RSSI	Received Signal Strength Indicator
Rx	Receiver
Tx	Transceiver
UWB	Ultra-Wideband
WLAN	Wireless Local Area Network
WPAN	Wireless Personal Area Network

Table of symbols

Table C1. Table of symbols.

Symbol	Description
$\mathrm{\varnothing }$	Measurement failure
$\Vert \cdot {\Vert }_2$	Euclidean norm
$\mathit{d}$	Reference distances between anchors and tag
${\mathrm{d}}_{\max }$	Maximum range
ε	Additive errors
η	Normalization factor
M, m	Amount of discrete grid realizations, counting variable
$\mathcal{N}(\cdot )$	Normal distribution
$\mathcal{LN}(\cdot )$	Log-Normal distribution
p	Probability of Bernoulli experiment
$\mathit{p}$	Corrected belief
$\overline{\mathit{p}}$	Predicted belief
$\mathit{P}(\cdot )$	Likelihood function
$p_{\mathrm{out}}$	Outlier probability
$\mathcal{Q}$	Error metric
$\overline{\mathcal{Q}}$	RMSE
$\tilde{\mathcal{Q}}$	Median
${\sigma }_{\mathcal{Q}}^2$	Empirical error variance
r	Ranging measurement
${\overline{R}}_r$	Location parameter of Log-Normal distribution
${\sigma }_r^2$	Variance of noise-related error
${\sigma }_{\overline{r}}^2$	Scale parameter of Log-Normal distribution
t	Timestep
$\mathcal{U}(\cdot )$	Uniform distribution
X	Grid realizations
$\mathcal{X}$	State vector
$\stackrel{\mathbf{ˆ}}{\mathcal{X}}$	Estimated state vector
${\mathbf{x}}_{\mathrm{ref}}$	Reference position of the mobile device
${\mathbf{x}}_a$	Positions of anchors a
$\mathcal{Z}$	Observations

Appendix 3. Details of radio propagation simulation

The radio propagation simulation with ray-tracing was performed on a 32-core CPU in workstation using Altair WinProp 2022.3. The parameters in Table A3 specify the inputs of the simulation including the geometric and radio model.

Table D1. Parameters and inputs of the radio propagation simulation with Altair WinPop 2022.3.

	Parameter	Value
Geometric model	CAD model	Airbus A320
Radio properties	Center Frequency	6500 MHz (UWB Channel 5)
	Tx Power	–14.7 dBm
	Antenna	Omnidirectional Antenna
	Position of Anchors [m]	A1: −1.36;11.11;1.50
		A2: 1.37;13.77;1.50
		A3: −1.33;16.55;1.50
		A4: 1.33;19.28;1.50
		A5: −1.36;21.99;1.50
		A6: 1.33;24.69;1.50
		A7: −1.32;27.41;1.50
		A8: 1.35;30.06;1.50
Simulation parameters	Rx Grid Resolution	10 cm
	Rx Prediction Plane Heights	70 cm and 112 cm above floor
	Prediction Model	Ray-Launching
	Max. # of Reflections	2
	Max. # of Transmissions	2
	Max. # of Diffractions	0