Geometric Dilution Of Precision Research Articles

Ultrasonic Array-Based Multi-Source Fusion Indoor Positioning Technology

Underground mining involves numerous risks, such as collapses, gas leaks, and explosions, posing significant threats to worker safety. In this work, we develop an indoor localization system that uses Bluetooth for coarse positioning and ultrasonic arrays for precision calibration. This system is particularly useful for automated mining operations in underground environments where satellite positioning signals are unavailable. The indoor localization system consists of ultrasonic receiver arrays and an improved multi-transmitter-multi-receiver algorithm, enabling accurate localization within the mining environment. Geometric Dilution of Precision (GDOP) analysis is incorporated to optimize the network layout, and an inertial navigation module is integrated to track the posture of moving objects, enabling precise trajectory determination over large areas, such as coal mines. In the experiment, three traditional methods were compared, and the proposed tracking approach demonstrated a positioning accuracy within 10 cm, reducing error by 20% compared to conventional techniques. This high-precision indoor localization method proves beneficial for underground mining applications.

A star selection strategy based on MDS and fast convex hull algorithm in COSPAS-SARSAT system

Abstract The space segment of the current COSPAS-SARSAT system is mainly supported by the Galileo system, and the positioning technology used is generally three-star time-difference positioning. Most of the antennas equipped in the Mission Control Centre (MCC) are not omnidirectional. In the case of Source of Search and Rescue (SAR) in a heavily shaded environment, it is necessary to use the different orbit time-sharing single satellite geolocations using TDOA, and the time-sharing will generate more satellite position data. In order to achieve the higher positioning accuracy of the solution, it is necessary to select the appropriate time and optimal geometrical distribution from the satellite positions. In this paper, we propose a satellite selection strategy based on Multiple Dimensional scaling (MDS) data degradation and a fast convex hull algorithm. The three-dimensional satellite data are downscaled to two-dimensional while maintaining their relative positional relationships, and the two-dimensional convex hull algorithm is used for Geometric Dilution of Precision (GDOP) minimum search star selection. By simulating the satellite position data in different orbits and time-sharing to complete the localization solution, the results show that compared with the traditional satellite selection method, the satellite selection strategy proposed in this paper is able to achieve better localization accuracy in a shorter period of time.

Long-range LBL underwater acoustic navigation considering Earth curvature and Doppler effect

The accuracy of underwater acoustic navigation is significantly influenced by geometry configuration and systematic errors coming from geophysical environment. Long baseline (LBL) systems exhibit superior positioning precision than other acoustic navigation systems, primarily attributable to the better Geometric Dilution of Precision (GDOP). However, the geometry configuration tends to degrade when the underwater vehicle is far away from the seafloor beacons. Factors such as acoustic ray bending error, Doppler effect and Earth curvature may seriously affect the navigation accuracy. To address these issues, we present a robust Kalman filter with systematic error compensation for long-range LBL systems. Firstly, a reversed acoustic ray tracking method is proposed for a unique phenomenon in acoustic wave propagation. Following that, we construct an acoustic positioning model with a time bias parameter, to weaken the impact of Doppler effect on acoustic ranging. This additional parameter was estimated with the state of the user vehicle in real time. At last, an observation equation of pressure gauge considering Earth curvature is presented for depth constraint. Long-range LBL experiments conducted in the South China Sea is employed to validate the performance of the proposed methods, taking the positioning results of inverted ultra-short baseline (iUSBL) system as reference. The results show that the proposed method outperform traditional method with a decrease of about 60 % in the three-dimensional root mean square (3DRMS) of navigation errors. With mentioned three improvements, the 3DRMS of the long-range LBL system with the longest distance of 20 km from the beacon center is less than 14 m. These findings can provide theoretical basis for other long-range LBL systems.

Geometry Optimization of Stratospheric Pseudolite Network for Navigation Applications

A stratospheric pseudolite (SP) is a pseudolite installed on a stratospheric airship. A stratospheric pseudolite network (SPN) is composed of multiple SPs, which shows promising potential in navigation applications because of its station-keeping capability, long service duration, and flexible deployment. Most traditional research about SPN geometry optimization has centered on geometric dilution of precision (GDOP). However, previous research rarely dealt with the topic of how SPN geometry configuration not only affects its GDOP, but also affects its energy balance. To obtain an optimal integrated performance, this paper employs the proportion of energy consumption in energy production as an indicator to assess SPN energy status and designs a composite indicator including GDOP and energy status to assess SPN geometry performance. Then, this paper proposes an SPN geometry optimization algorithm based on gray wolf optimization. Furthermore, this paper implements a series of simulations with an SPN composed of six SPs in a specific service area. Simulations show that the proposed algorithm can obtain SPN geometry solutions with good GDOP and energy balance performance. Also, simulations show that in the supposed scenarios and the specific area, a higher SP altitude can improve both GDOP and energy balance, while a lower SP latitude can improve SPN energy status.

Design of a Cislunar space navigation constellation based on special long-period orbits

This paper proposes a method for designing a navigation constellation in the Cislunar space. Firstly, the dynamic characteristics of the Cislunar space were analyzed. Northern Halo orbits and southern Halo orbits around L1 and L2 libration point are designed. Then, based on the invariant manifold theory, the homoclinic low-energy transfer trajectories of L1 Halo orbits and the low-energy heteroclinic transfer trajectories between L1 and L2 Halo orbits are provided respectively. Afterthat, two types of special long-period orbits are attained for the constellation design. Based on the geometric dilution of precision and the minimum number of visible satellites, design requirements for two parts are given. Next, two navigation constellation configurations are proposed. Lastly, simulations are conducted on the performance of two constellation configurations with different number of satellites. Compared to constellations in one orbit, constellations that configured in two orbits require fewer satellites to meet the design requirements. In different lunar transfer orbits, the performance of the dual orbit constellation was validated.

An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets

Continuous advancements in GNSS systems have led, apart from the broadly used GPS, to the development of other satellite systems (Galileo, BeiDou, GLONASS), which have significantly increased the number of available satellites for GNSS positioning applications. However, despite GNSS satellites’ redundancy, a potential poor GNSS satellite signal (i.e., low signal-to-noise ratio) can negatively affect the GNSS’s performance and positioning accuracy. On the other hand, selecting high-quality GNSS satellite signals by retaining a sufficient number of GNSS satellites can enhance the GNSS’s positioning performance. Various methods, including optimization algorithms, which are also commonly adopted in artificial intelligence (AI) methods, have been applied for satellite selection. In this study, five optimization algorithms were investigated and assessed in terms of their ability to determine the optimal GNSS satellite constellation, such as Artificial Bee Colony optimization (ABC), Ant Colony Optimization (ACO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). The assessment of the optimization algorithms was based on two criteria, such as the robustness of the solution for the optimal satellite constellation and the time required to find the solution. The selection of the GNSS satellites was based on the weighted geometric dilution of precision (WGDOP) parameter, where the geometric dilution of precision (GDOP) is modified by applying weights based on the quality of the satellites’ signal. The optimization algorithms were tested on the basis of 24 h of tracking data gathered from a permanent GNSS station, for GPS-only and multi-GNSS data (GPS, GLONASS, and Galileo). According to the comparison results, the ABC, ACO, and PSO algorithms were equivalent in terms of selection accuracy and speed. However, ABC was determined to be the most suitable algorithm due it requiring the fewest number of parameters to be set. To further investigate ABC’s performance, the method was applied for the selection of an optimal GNSS satellite subset according to the number of total available tracked GNSS satellites (up to 31 satellites), leading to more than 300 million possible combinations of 15 GNSS satellites. ABC was able to select the optimal satellite subsets with 100% accuracy.

An Improved Genetic Method for Satellite Selection in Multi-Global Navigation Satellite System Positioning for Mobile Robots

An Improved Genetic Method for Satellite Selection in Multi-Global Navigation Satellite System Positioning for Mobile Robots

Effect of satellite availability and time delay of corrections on position accuracy of differential NavIC

Abstract The position accuracy of standalone Navigation with Indian Constellation (NavIC) may not be met for certain applications like civil aviation. To improve the position accuracy of the user receiver, the technique used is Differential NavIC, which makes use of Differential corrections. The position accuracy of the user receiver also depends on the satellite availability (i.e. number of satellites available at a certain time instant to estimate the user position) and delay in transmission of differential corrections. In this article, the analysis of differential NavIC using different numbers of visible satellites (satellite availability) and different time delays for transmission of corrections is carried out. For this analysis, three cases are considered, Case I is when all (six) NavIC satellites are visible, Case II is when five satellites (3 Geosynchronous Orbit (GSO) and 2 Geostationary Earth Orbit (GEO)) are visible, and Case III is when five satellites (3 GEO and 2 GSO) are visible. The comparative analysis for these three cases is carried out with respect to the position accuracy parameters and Geometric Dilution of Precision. It is observed that, with the satellite availability in case I and case III, the user receiver accuracy is approximately the same. In case III, the accuracy of the user receiver (3.08 m) is similar to the accuracy (3.09 m) in case I. For time delay in transmission of corrections, different time delays (0, 5, 10, 20, …, 300 s) are considered to observe the effect on the positional accuracy of the user receiver. Due to the increase in this time delay, there is a significant degradation in the user receiver position accuracy of differential NavIC.

Station layout optimization for underwater acoustic positioning system based on combined cone configuration

The theoretical minimum of the geometric dilution of precision (GDOP) for target positioning cannot be achieved because of the coplanar constraint for underwater station configurations, and the conventional single-cone configuration leads to an infinite GDOP. Therefore, this study extends the single-cone configuration to the combined cone configuration. The proposed configuration is theoretically proven to be superimposable, rotatable, and GDOP-rotation-invariant. A criterion based on the global GDOP for underwater targets is constructed to address the problem of a single criterion for station layout optimization. However, traditional optimization algorithms are prone to local optimality and low convergence efficiency. Therefore, an improved adaptive particle swarm optimization (APSO) algorithm is proposed to optimize the configuration of the underwater acoustic positioning systems. Finally, it is verified that the proposed APSO can enhance the global optimality and improve the convergence efficiency of the algorithm. Combined with the measured data of the long baseline system, it is shown that the optimal combined cone configuration significantly reduces the global GDOP and improves the positioning accuracy compared with traditional configurations.

Low orbit regional enhanced navigation constellation for BDS3 design based on Bayesian optimization algorithm

The application of Low Earth Orbit (LEO) satellite navigation can enhance geometric structure, increase observations and contribute to navigation and positioning. To improve the performance of the navigation constellation in China, this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm. In this paper, four different optimal LEO constellation configurations are designed, and their enhancements to BDS3 navigation performance are analyzed, including Geometric Dilution of Precision (GDOP), the numbers of visible satellites, and the rapid convergence of precision point positioning (PPP). Additionally, the enhancement advantages in China compared to other regions are further discussed. The results demonstrate that regional enhanced constellations with 70, 72, 80, and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation. Globally, the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0 %, 18.3 %, 19.9 %, and 20.3 %. Similar results can be obtained using the genetic algorithm (GA), but the computational efficiency of Bayesian optimization algorithm is 53.9 % higher than that of the genetic algorithm. The number of visible satellites of enhanced constellations in China has increased by more than four on average, which is better than that in other regions. In the PPP experiment, the convergence time of the stations in China and other regions is shortened by 83.0 % and 76.2 %, respectively, and the navigation performance of hybrid constellations in China is better.

Quality Control for Ocean Current Measurement Using High-Frequency Direction-Finding Radar

High-frequency radars (HFRs) are important for remote sensing of the marine environment due to their ability to provide real-time, wide-coverage, and high-resolution measurements of the ocean surface current, wave height, and wind speed. However, due to the intricate multidimensional processing demands (e.g., time, Doppler, and space) for internal data and effective suppression of external noise, conducting quality control (QC) on radar-measured data is of great importance. In this paper, we first present a comprehensive quality evaluation model for both radial current and synthesized vector current obtained by direction-finding (DF) HFRs. In the proposed model, the quality factor (QF) is calculated for each current cell to evaluate its reliability. The QF for the radial current depends on the signal-to-noise ratio (SNR) and DF factor of the first-order Bragg peak region in the range–Doppler (RD) spectrum, and the QF for the synthesized vector current can be calculated using an error propagation model based on geometric dilution of precision (GDOP). A QC method is then proposed for processing HFR-derived surface current data via the following steps: (1) signal preprocessing is performed to minimize the effect of unwanted external signals such as radio frequency interference and ionospheric clutter; (2) radial currents with low QFs and outliers are removed; (3) the vector currents with low QFs are also removed before spatial smoothing and interpolation. The proposed QC method is validated using a one-month-long dataset collected by the Ocean State Monitoring and Analyzing Radar, model S (OSMAR-S). The improvement in the current quality is proven to be significant. Using the buoy data as ground truth, after applying QC, the correlation coefficients (CCs) of the radial current, synthesized current speed, and synthesized current direction are increased by 4.33~102.91%, 1.04~90.74%, and 1.20~62.67%, respectively, and the root mean square errors (RMSEs) are decreased by 2.51~49.65%, 7.86~27.22%, and 1.68~28.99%, respectively. The proposed QC method has now been incorporated into the operational software (RemoteSiteConsole v1.0.0.65) of OSMAR-S.

A fast satellite selection algorithm for positioning in LEO constellation

In the near future, a much larger scale of low earth orbit (LEO) satellites will be deployed, and satellite selection is an effective way to overcome challenges to processing capability and channel limitation of receivers caused by superabundant satellites in view. However, existing algorithms do not take into account the fact that a large-scale LEO constellation satellite selection subset can be closer to the theoretical optimal configuration than the traditional brute force search and recursive algorithm computational overhead is too large for end devices. In this study, the solution of the minimum optimization problem of the GDOP (Geometric Dilution of Precision) under the condition of limited elevation angle is first analyzed to determine the optimal ratio configuration scheme of top and bottom satellites under the optimal geometric satellite positioning problem. Subsequently, a fast satellite selection algorithm is proposed, which selects a subset of satellites that meet the different numbers of observation satellites and is close to the optimal geometric configuration by geometric method. The comparative simulation shows that, in the 1586 LEO constellation system, the proposed algorithm has an average GDOP of 1.52 when the satellite subset size is 10 and 0.95 when the subset size is 30. Compared with the recursive, the Rotating Partition algorithm and the Quasi-optimal algorithm, the proposed algorithm achieves better accuracy when its size is not close to the total number of observable satellites.

Efficient near-field localization aided with reconfigurable intelligent surface using geometric dilution of precision

ABSTRACT Reconfigurable intelligent surfaces (RISs) are anticipated to constitute a critical component of forthcoming communication networks due to their ability to establish controllable wireless environments. Furthermore, RIS can be leveraged to solve infeasible localization problems. This paper presents a novel adoption of the geometric dilution of precision (GDoP) analysis in the design of non-line of sight (NLoS) single anchor millimetre wave (mmWave) large RIS-aided localization in the near-field. Considering downlink transmission, the time difference of arrival (TDoA) is used to estimate the positioning by extracting the signal contribution of each RIS tile. Considering the enriched time of arrival (ToA) measurements provided by RIS, the RIS tiles involved in TDoA-based estimation should be selected properly. Therefore, the GDoP adopted in this context is to select RIS tile combinations that achieve minimum GDoP values. It has been shown via numerical simulation that the proposed design of the RIS-aided localization outperforms other state-of-the-art techniques that adopt the signal-to-noise ratio (SNR) for the selection of the RIS tiles. It is demonstrated that the proposed scheme can provide sufficient localization accuracy involving only 10% of RIS tiles, whereas the SNR method requires about (70–80) % of the tiles to approximately achieve the same accuracy.

Evaluation of Ionospheric Delay Extraction Model Using Dual-Frequency Multisystem Observations

Ionospheric delay presents complex spatiotemporal variation characteristics and is a critical error source restricting the improvement of global navigation satellite system (GNSS) positioning, navigation, and timing performance. It is a prerequisite to constructing an accurate ionospheric delay extraction model that supports the study of the ionospheric delay characteristics. By using modernized dual-frequency and multi-system signals and inter-system bias (ISB) calibration, the performance of the ionospheric delay extraction model can be enhanced further. This study focuses on quantitatively analyzing the influence of the geometric dilution of precision (GDOP) and the redundancy of observations on the accuracy of ionospheric delay extraction, by constructing two state-of-the-art high-precision dual-frequency multi-system ionospheric delay extraction models using the tightly coupled un-difference and un-combination precise point positioning (UPPP) and carrier-to-code leveling (CCL) methods. GNSS datasets from eight international GNSS service (IGS) stations were selected to evaluate their accuracy and analyze their influencing factors. The results show that the ionospheric delay extraction model using the UPPP method is more accurate than the CCL method for both single and multiple systems. The ionospheric delay extraction model using the CCL method is insensitive to time and coordinates. The ionospheric delay extraction model using the UPPP method shows inconsistent accuracy at different times and coordinates, which reflects a correlation with the GDOP effect.

Geometric triangulation uncertainty for sustainable urban underwater localization in presence of malicious virtual node

Sustainability of urban underwater sensor networks (uUWSNs) depends critically on the efficient triangulation during the localization process. There is very limited literature on sustainable range-free localization in uUWSNs. To address this issue, we improve localization method based on triangulation approach through convex optimization with Geometric Dilution of Precision (GDOP). We define “geometric triangulation uncertainty”. A sustainable scheme is proposed for identification of underwater nodesto modify a two-mode Gaussian Mixture Model. The proposed method is then compared to a weighted least square model for different threshold levels of maximum node range and associated triangulation uncertainties. The convex formulation is then solved using semidefinite programming to obtain optimal position of target in presence of a malicious virtual node. Theproposed method is verified using Cramer’s Rao lower bound in terms of RMS errors and cumulative errors. It exhibits close to ideal performance whenever perturbations associated with geometric triangulation uncertainty is bounded. The performance of the proposed method exceeds that of the weighted least squares method, which means that the proposed technique shall find immense application in intelligent computation of urban underwater scenarios, where the amount of sensor information exchange critically depends upon terrain environment and surrounding disturbances.

LEO navigation augmentation constellation design and precise point positioning performance analysis based on BDS-3

Low Earth orbit (LEO) satellites have high signal strength and faster geometry changes over short periods, offering unique advantages in navigation augmentation. Integrating LEO satellites into the navigation system can help augment the performance of the global satellite navigation system and break the dilemma of the existing navigation system with limited services in challenging environments. Constellation design is the key before establishing a complete LEO navigation augmentation platform. Therefore, in this study, two LEO navigation augmentation constellations, Polar/Walker (S1) and Walker/Walker (S2) with different inclinations, are designed and optimized using the non-dominated sorting genetic algorithm III (NSGA-III). The global average geometric dilution of precision (GDOP) of BDS-3 is reduced from 1.56 to 0.92 and 0.95, and the average visible satellite number is improved from 11.74 to 27.83 and 25.72 with the navigation augmentation of the optimized constellations. To further validate the navigation augmentation effect of two LEO constellations on BDS-3 precision point positioning (PPP), nine stations at different latitudes were selected for LEO augmented BDS-3 PPP simulation experiments. The results show that after adding S1 and S2 constellations to BDS-3, respectively, the convergence times of the nine stations are reduced by 35.5%∼96.5% and 43.7%∼96.2%, and the positioning accuracy is improved by 5.7%∼71.9% and 24.2%∼69.5%, respectively. Overall, each S1 and S2 constellations can significantly improve the global service performance and PPP performance of BDS-3.

Acquisition of Weak BDS Signal in the Lunar Environment

Autonomous navigation using the GNSS has been increasingly used in lunar exploration missions, as it is considered an efficient method for spacecraft to operate without relying on ground facilities. However, so far, only GPS and Galileo have been studied and implemented in lunar missions, whereas the potential of BDS-3 for such missions remains largely unexplored. This paper presents an analysis and evaluation of the navigation service capabilities for spacecraft at lunar altitudes by utilizing existing GNSS satellite resources in orbit. In detail, we investigate the number of GNSS signals received by low lunar orbit (LLO) receivers, as well as the carrier-to-noise ratio (C/N0), Doppler shift, and geometric dilution of precision (GDOP) of the received signal. Additionally, a digital intermediate frequency (IF) signal simulation program to emulate the BDS B1I signal is utilized, which allows to freely set the carrier-to-noise ratio, Doppler shift, and code phase. Based on this framework, we discussed a high-sensitivity BDS B1I signal receiver and validated its performance with simulated signals. We verified the capabilities of coherent integration, non-coherent integration, differential integration, and semi-bit methods to detect weak BDS B1I signals in a lunar environment. The results indicate that the semi-bit coherent differential integration method is still capable of acquiring signals at a C/N0 of 15 dB-Hz and can effectively suppress the navigation data bit sign transition.

Buried gas pipe leak localization using dual-wave spectrum estimation

To accurately locate leaks in buried gas pipes, a three-dimensional (3D) localization method using dual-wave velocity pairing and multi-array fusion localization was developed in this study to locate leak-induced vibroacoustic sources. Two velocities at which the P1 and S waves propagated along soil were estimated when the peaks of the dual-wave spectrum coincided with each other. Root-MUSIC algorithm was introduced to quickly determine the superimposed peak, thereby reducing the computational complexity. To address the issue of 3D localization using the P1 wave that propagated in soil according to a far-field model, least-squares (LS) estimation for the 3D coordinates was performed using the fusion localization method. A numerical model of geometrical dilution of precision (GDOP) was constructed to analyze the performances of multi-array layouts. A uniform circular array of eight accelerometers was utilized to visualize the leak-induced vibroacoustic source, and the imaging showed that the vibroacoustic source coincided with the leak. Accurate direction of arrival (DOA) estimation under multiple soil conditions was achieved, which proved that the velocity near the array was accurately estimated. An equilateral-triangle multi-array layout was selected using GDOP analyzing, and the results of localization experiments revealed that the equilateral-triangle layouts with 1.5-m and 2-m spacings achieved relatively good accuracy. Compared to the 3D localization method using a single array, the fusion localization method showed better accuracy for the remote leak, and the maximum reduction in error is 84.75 %. GDOP of fusion localization was found less than 0.1 m when the internal pipe pressure ≥ 0.4 MPa and the signal-to-noise ratio (SNR) ≥ 0 dB under the conditions of experiments in this study.

Cooperative Navigation for Heterogeneous Air-Ground Vehicles Based on Interoperation Strategy

This paper focuses on the cooperative navigation of heterogeneous air-ground vehicle formations in a Global Navigation Satellite System (GNSS) challenged environment and proposes a cooperative navigation method based on motion estimation and a regionally optimal path planning strategy. In air-ground vehicle formations, unmanned ground vehicles (UGVs) are equipped with low-precision inertial navigation measurement units and wireless range sensors, which interact with unmanned aerial vehicles (UAVs) equipped with high-precision navigation equipment for cooperative measurement information and use the UAVs as aerial benchmarks for cooperative navigation. Firstly, the Interacting Multiple Model (IMM) algorithm is used to predict the next moment’s motion position of the UGVs. Then regional real-time path optimization algorithms are introduced to design the motion position of the high-precision UAVs so as to improve the formation’s configuration and reduce the geometric dilution of precision (GDOP) of the configuration. Simulation results show that the Dynamic Optimal Configuration Cooperative Navigation (DOC-CN) algorithm can reduce the GDOP of heterogeneous air-ground vehicle formations and effectively improve the overall navigation accuracy of the whole formation. The method is suitable for the cooperative navigation environment of heterogeneous air-ground vehicle formations under GNSS-challenged conditions.

Cramér–Rao Lower Bounds on 3D Position and Orientation Estimation in Distributed Ranging Systems

As radio frequency (RF) hardware continues to improve, many technologies that were traditionally impractical have suddenly become viable alternatives to legacy systems. Two-way ranging (TWR) is often considered a poor positioning solution for airborne and other vehicular navigation systems due to its low precision, poor angular resolution, and precise timing requirements. With the advent of modern RF hardware and advanced processing techniques, however, modern studies have experimentally demonstrated TWR systems with an unprecedented, sub-centimeter ranging precision with low size, weight, power, and cost (SWaP-C) consumer-grade hardware. This technique enables a new class of positioning, navigation, and timing (PNT) capabilities for urban and commercial aircraft but also instigates new system design challenges such as antenna placement, installation of new electronics, and design of supporting infrastructure. To inform these aircraft design decisions, we derive 2D and 3D Cramér–Rao lower bounds (CRLBs) on position and orientation estimation in a multi-antenna TWR system. We specifically formulate these bounds as a function of the number of antennas, platform geometry, and geometric dilution of precision (GDoP) to inform aircraft design decisions under different mission requirements. We simulate the performance of several classic position and orientation estimators in this context to validate these bounds and to graphically depict the expected performance with respect to these design considerations. To improve the accessibility of these highly theoretical results, we also present a simplified discussion of how these bounds may be applied to common airborne applications and suggest best practices for using them to inform aircraft design decisions.