Set-Valued Shadow Matching using Zonotopes

Bhamidipati, Sriramya; Kousik, Shreyas; Gao, Grace Xingxin

doi:10.33012/2021.17933

Cited by 4 publications

(19 citation statements)

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“…We first describe our model and assumptions of the GNSS satellite signals, the initial area of interest, and the 3D building map. We then summarize the procedure for extracting GNSS shadows, which is based on our prior work [32]. We finally explain the details of our tree data structure that takes in the GNSS shadows as input to construct the exact shadow matching distribution (i.e., no discretization), which provides certifiable guarantees on the receiver position.…”

Section: Proposed Mosaic Zonotope Shadow Matching Algorithmmentioning

confidence: 99%

“…To reach risk-aware 3DMA-GNSS, one must meet the following two objectives: (1) formulate precise models of the uncertainty in real-time while tractably scaling with increasing numbers of available signals and (2) provide guarantees on the uncertainty bounds of the urban localization solution across a vast space of AI-driven LOS classifier designs. using set-valued representations, namely constrained zonotopes [32]. We denote the building in gray, the shadow direction with the black thick arrow, the shadow volume in cyan, the ground plane in brown, and the extracted GNSS shadow in magenta.…”

Section: Introductionmentioning

confidence: 99%

“…ZSM recursively refines the area of interest with GNSS shadows, but assumes an ideal LOS classifier, and is thus brittle against any LOS classifier inaccuracies. (Figure adapted from [32]).…”

Section: Introductionmentioning

confidence: 99%

“…Our recent work proposes a new shadow matching paradigm: set-based shadow matching [32]. A setvalued approach computes a continuum of state estimates rather than considering a grid of position candidates.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, constrained zonotopes generalize zonotopes to represent any convex polytopes, thereby avoiding the limitation of symmetry [34]. Our prior work [32] developed a novel Zonotope Shadow Matching (ZSM) algorithm that computes the set-based GNSS shadow based on the 3D building map, as shown in Figure 1. ZSM parameterizes each satellite/building pair with constrained zonotopes, extends the building along shadow direction from the GNSS satellite, and performs set intersection with the ground plane.…”

Section: Introductionmentioning

confidence: 99%

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Mosaic Zonotope Shadow Matching for Risk-Aware Autonomous Localization in Harsh Urban Environments

Neamati¹,

Bhamidipati²,

Gao³

2022

Preprint

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Risk-aware urban localization with the Global Navigation Satellite System (GNSS) remains an unsolved problem with frequent misdetection of the user's street or side of the street. Significant advances in 3D mapaided GNSS use grid-based GNSS shadow matching alongside AI-driven line-of-sight (LOS) classifiers and server-based processing to improve localization accuracy, especially in the cross-street direction. Our prior work introduces a new paradigm for shadow matching that proposes set-valued localization with computationally efficient zonotope set representations. While existing literature improved accuracy and efficiency, the current state of shadow matching theory does not address the needs of risk-aware autonomous systems. We extend our prior work to propose Mosaic Zonotope Shadow Matching (MZSM) that employs a classifier-agnostic polytope mosaic architecture to provide risk-awareness and certifiable guarantees on urban positioning. We formulate a recursively expanding binary tree that refines an initial location estimate with set operations into smaller polytopes. Together, the smaller polytopes form a mosaic. We weight the tree branches with the probability that the user is in line of sight of the satellite and expand the tree with each new satellite observation. Our method yields an exact shadow matching distribution from which we guarantee uncertainty bounds on the user localization. We perform high-fidelity simulations using a 3D building map of San Francisco to validate our algorithm's risk-aware improvements. We demonstrate that MZSM provides certifiable guarantees across varied data-driven LOS classifier accuracies and yields a more precise understanding of the uncertainty over existing methods. We validate that our tree-based construction is efficient and tractable, computing a mosaic from 14 satellites in 0.63 seconds and growing quadratically in the satellite number.

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Section: Proposed Mosaic Zonotope Shadow Matching Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mosaic Zonotope Shadow Matching for Risk-Aware Autonomous Localization in Harsh Urban Environments

Neamati¹,

Bhamidipati²,

Gao³

2022

Preprint

Self Cite

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Set-Valued Shadow Matching Using Zonotopes for 3D-Map-Aided GNSS Localization

Bhamidipati

Kousik

Gao

2022

navi

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GNSS-based localization is often unreliable in dense urban areas. As illustrated in Figure 1, direct line-of-sight (LOS) GNSS signals can be blocked or reflected by tall buildings (Hofmann-Wellenhof et al., 1992), creating non-line-of-sight (NLOS) and multipath effects, thereby lowering the number of visible GNSS satellites available for localization (Zhu et al., 2018). In particular, LOS satellite signals in the cross-street direction are more likely to be blocked or reflected by buildings than signals along the street. Consequently, positioning accuracy is degraded in urban areas, especially in the cross-street direction.Robustness to degraded accuracy is important for safety-critical GNSS applications such as autonomous driving and drone delivery. As detailed later in our discussion of related work, set-valued position estimates enable robustness guarantees by ensuring an entire set of possible positions lies outside of obstacles or inside

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Multi-Epoch Kriging-Based 3D Mapping-Aided GNSS and Doppler Measurement Fusion using Factor Graph Optimization

Ng,

Hsu,,

Zhang

2023

navi

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Navigation and positioning are integral activities in the current society, and global navigation satellite systems (GNSSs) are widely used to perform globally referenced positioning. However, the performance of GNSSs in urban positioning is often unsatisfactory. The poor performance occurs because a GNSS signal does not travel in a line-of-sight (LOS) route directly to the receiver in such scenarios but is reflected or attenuated over buildings and obstacles. Signal propagation errors, such as non-LOS (NLOS), multipath, and diffraction reception errors, for GNSS signals deteriorate the positioning performance (Groves, 2013a). Moreover, the reflected signal experiences an additional time delay and must travel further, leading to the generation of positioning errors exceeding 50 m. Nevertheless, GNSS methods must be implemented in locations with tall buildings to provide absolute coordinates in the global frame for location-based services (LBSs). Therefore,

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Set-Valued Shadow Matching using Zonotopes

Cited by 4 publications

References 0 publications

Mosaic Zonotope Shadow Matching for Risk-Aware Autonomous Localization in Harsh Urban Environments

Mosaic Zonotope Shadow Matching for Risk-Aware Autonomous Localization in Harsh Urban Environments

Set-Valued Shadow Matching Using Zonotopes for 3D-Map-Aided GNSS Localization

Multi-Epoch Kriging-Based 3D Mapping-Aided GNSS and Doppler Measurement Fusion using Factor Graph Optimization

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