41-EFT.WP.Comms.Navigation v1.0 | Chapter 13: Case Library — GNSS / UWB / 5G / Wi-Fi / Acoustic / Multi-Sensor

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Chapter 13: Case Library — GNSS / UWB / 5G / Wi-Fi / Acoustic / Multi-Sensor

I. Objectives & Scope

• Provide end-to-end reference implementations (data → cleaning/de-embedding → observation construction → fusion → evaluation → design recommendations) across GNSS/UWB/5G/Wi-Fi/Acoustic and their multi-sensor fusion with IMU/odometry/vision.
• All formulas/symbols/definitions are in English and wrapped in backticks. Whenever arrival time is involved, use the selected T_arr convention and explicitly record the path gamma(ell) and measure d ell.

II. Common Data Contract & Pipeline

• S130-1 (Case dataset card — required)
• unit_system: "SI"
• case_id: "<gnss|uwb|5g|wifi|acoustic|multisensor>"
• scene_tag: "<indoor|urban|highway|forest|factory|campus|UAV_outdoor>"
• anchors:
• - {id: "...", p_S: [x,y,z], array: "<ULA|URA|omni>", cal: "<file|hash>"}
• arrival_time:
• convention: "pulled_const|integrand"
• delta_form: "c_ref^-1 * ∫ n_eff dℓ" # or "∫ (n_eff/c_ref) dℓ"
• gamma: "piecewise: free|fixture|substrate|device|environment"
• d_ell: "m"
• channels:
• y_channels: ["TOA","TDOA","AOA","FOA","RSS","CP","IMU","WHEEL","VO"]
• Σ_y: "<block-diagonal or sparse>"
• cal_bundle:
• deembed: {scheme: "OSLT|TRL", refs: ["blank","substrate-only"]}
• sync: {cov_clock: {bb:"<s^2>", bd:"<s^2/s>", dd:"<s^2/s^2>"}}
• robust:
• nlos_flag: "<bool|score>"
• mixture: {pi_los: "<0..1>", mu_nlos: "<per-channel>", Sigma_nlos: "<blocks>"}
• priors:
• P0: "<state prior>", Qc: "<process PSD>", sync_cov: "<bb,bd,dd>"
• S130-2 (Cleaning & de-embedding)
  Phase unwrapping φ(ω) and group delay τ_g; path de-embedding to freeze T_arr^{(k≠segment)}; link asymmetry and drift models written into cal_bundle.
• S130-3 (Observations & matrices)
  Build y and H per Chapter 4; build J,B,Σ_y per Chapter 10.
• S130-4 (Fusion & robustness)
  Use Chapter 8 EKF/UKF/PF/FG frameworks; apply Chapter 9 reweighting/deflation and switchable constraints.
• S130-5 (Evaluation & design)
  NEES/NIS, ATE/RPE/CEP/PEB/SEB, GDOP/PDOP/HDOP/VDOP, and information/D/A/E-optimal design recommendations.
• M13-1 (Card → cleaning)
  Import card → de-embed/unwrap → inject sync priors → add segment-wise uncertainty into Σ_y.
• M13-2 (Cleaning → observations/matrix)
  Generate y,H and J,B,Σ_y; record the four arrival_time fields.
• M13-3 (Observations → fusion)
  Run the selected fusion mode, output {x̂,P} or {traj,cov}.
• M13-4 (Fusion → evaluation/design)
  Consistency/coverage & error budgets → emit design recommendations and an improvement list.

III. Case A: GNSS (Multi-Frequency / Carrier Phase)

• S130-6 (Channels & focus)
  TOA/FOA/CarrierPhase; dual-frequency iono correction; integer ambiguity N fixing and double differencing.
• S130-7 (Cleaning & sync)
  Satellite clock/ionosphere/troposphere corrections; common-view reference alignment.
• S130-8 (Fusion)
  Strong CP constraints + TOA/FOA aiding; on fixing failure fall back to float with inflated uncertainty.
• S130-9 (Evaluation)
  PDOP/VDOP and vertical observability; NEES/NIS, ATE.
• Outputs: {x̂(t), cov(t), N_hat, status} and design suggestions (elevation coverage, common-view, multi-band weights).

IV. Case B: UWB (Indoor TDOA/TWR)

• S130-10 (Channels)
  TDOA/TWR primary, optional AOA.
• S130-11 (Cleaning)
  CIR interpretation, excess delay τ_ex and τ_rms screening; NLOS reweighting.
• S130-12 (Fusion)
  ES-EKF/FG with ground constraints and pedestrian/vehicular motion models.
• S130-13 (Evaluation)
  HDOP and coverage heatmaps; CEP/PEB.
• Outputs: minimal anchor sets and redundancy designs; TWR rounds & duty-cycle advice.

V. Case C: 5G (AOA/OTDOA/PRS)

• S130-14 (Channels)
  AOA + (TOA/TDOA); arrays/beamforming and AOA calibration.
• S130-15 (Sync)
  PTP/gPTP + fronthaul; DL/UL asymmetry b_asym via table corrections.
• S130-16 (Fusion)
  AOA tangential + T(D)OA radial constraints; FOA enhances vertical information.
• S130-17 (Evaluation)
  Urban-canyon multipath: GDOP/HDOP and robust-kernel comparisons.
• Outputs: gNodeB placement (height/azimuth) and reference-sync configs.

VI. Case D: Wi-Fi (FTM/RTT + RSS)

• S130-18 (Channels)
  TOA (FTM/RTT) and RSS; AP clock/protocol differences.
• S130-19 (Cleaning)
  RSS Rician K and log-variance gating; indoor map/occlusion tables.
• S130-20 (Fusion)
  TOA-centric with RSS aiding; introduce AOA or vision in weak-geometry zones.
• S130-21 (Evaluation)
  PDOP/HDOP and multi-floor coverage; CEP.
• Outputs: AP siting and channel configs (bandwidth/duty/power).

VII. Case E: Acoustic (TOA/AOA/FOA)

• S130-22 (Channels)
  Underwater/room acoustics with strong dispersion and temperature profiles affecting n_eff(ω).
• S130-23 (Cleaning)
  Multipath peak decomposition and coherence-window limits; group-delay bias Δτ ≃ (1/c_ref) ∫ (∂ n_eff/∂ω) dℓ correction.
• S130-24 (Fusion)
  Fuse with IMU/VO to curb long-term drift.
• S130-25 (Evaluation)
  PEB/SEB and sensitivities to water-layer/room models.
• Outputs: transducer layout and bandwidth allocation.

VIII. Case F: Multi-Sensor (GNSS+5G+UWB+IMU+VO)

• S130-26 (Policy)
  Auto-select channel weights and robust kernels per scene_tag; FOA + AOA boost vertical/heading observability.
• S130-27 (Graph optimization)
  IMU preintegration + multi-channel factors + switchable constraints; rolling keyframes and Schur marginalization.
• S130-28 (SBC/benchmarks)
  Use Chapter 11 to generate synthetic sets and truths; assess coverage and consistency.
• Outputs: cross-platform config packs and design quotas (bands/timeslots/power/anchor count).

IX. Unified Outputs & Report Template

• S130-29 (Report schema)
• case_report:
• summary: {...}
• trajectory: {x_hat: "...", cov: "...", metrics: {ATE:"...", CEP:"...", PEB:"..."}}
• geometry: {DOP_maps: "...", worst_points: "...", advice: "..."}
• sync: {cov_clock: "...", residuals: "..."}
• robustness: {AUC:"...", ECE:"...", drops:"..."}
• design: {x_design*: "...", covθ*: "...", quotas: {band:"...", dwell:"...", anchors:n}}
• reproducibility: {scripts:"...", env:"...", anchors:["S130-*","M13-*","I13-*"], hash:"..."}
• M13-5 (Report generation)
  Aggregate metrics/DOP/coverage/consistency and design advice; emit a repro_bundle.

X. Implementation Bindings (Interface Prototypes)

• I13-1 load_case_card(path) -> {data, meta}
• I13-2 clean_and_deembed(data, cal_bundle) -> {clean, Σ_y, weights}
• I13-3 build_channels(clean, config) -> {y, H, J, B, Σ_y}
• I13-4 run_fusion(mode, y, H, Σ_y, priors) -> {x̂, P or traj, cov}
• I13-5 evaluate(traj, truths, dop_maps) -> {metrics, coverage}
• I13-6 recommend_design(metrics, F) -> {x_design*, quotas}
• I13-7 emit_case_report(all_artifacts) -> {report.yaml, repro_bundle}

XI. Quality Gates (This Chapter)

• Q1 Convention consistency: all cases involving T_arr must include convention/delta_form/gamma(ell)/d_ell.
• Q2 Units/dimensions: SI/engineering units s/Hz/rad/m/dBm/W present; pass check_dim.
• Q3 Covariance consistency: cleaning/reweight/censoring reflected in Σ_y blocks and graph/filter structures.
• Q4 Consistency & coverage: NEES/NIS and pass@coverage near nominal; report worst points and mitigations.
• Q5 Reproducibility: complete repro_bundle with scripts/params/env/anchors & hashes; one-click replay.

XII. Cross-Volume References & Anchors (This Chapter)

1. Cross-volume (fixed style): this volume Chs. 3–10 (propagation/observations/geometry/sync/dynamics/fusion/metrology chain) and Ch. 11 (simulation stack).
2. Anchors:
   • Minimal statements: S130-1—S130-29
   • Workflows: M13-1—M13-5
   • Interfaces: I13-1—I13-7

XIII. Summary
This chapter provides end-to-end, reproducible patterns and report templates spanning GNSS/UWB/5G/Wi-Fi/Acoustic/multi-sensor systems, connecting data contracts, de-embedding & conventions, synchronization & robustness, fusion & design. Together with the synthetic benchmarks (Ch. 11) and information metrics (Ch. 10), it enables auditable, repeatable deployment and comparative studies across scenarios.