41-EFT.WP.Comms.Navigation v1.0 | Chapter 1: Introduction & Scope

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Chapter 1: Introduction & Scope

I. Scenarios & Objectives

• Covered scenarios: cooperative on-road (GNSS / 5G AOA / IMU fusion), indoor localization (UWB TDOA/TWR, Wi-Fi FTM, visual/odometry), UAV (outdoor/under-canopy multipath), industrial RTLS (multi-floor/metal-rich environments).
• Overall objective: establish a unified pipeline path terms → arrival time/frequency → geometry → fusion → metrology/inversion, yielding cross-band/platform-reusable observable–parameter mapping y = M(θ) and implementation bindings Ixx-*.
• P10-1 (Scope principle): Any comms/navigation observation can be written as a measurable function of propagation along an explicit path gamma(ell) coupled with clock/geometry; its statistics are fully specified by the data contract and error budget.

II. Main Thread & Observation-Stack Master Equation

1. S10-1 (Observation-stack master equation)
   y = h(x, θ, ν; x_design) + ε, where:
   • x = state (p_WB, v_WB, q_WB, …), θ = parameters (geometry/clock/channel), ν = instrument/environment nuisances;
   • x_design = design variables (layout/bands/protocols);
   • ε ~ 𝒟(0, Σ_y) is observation noise (possibly robust mixtures).
2. Two arrival-time conventions (choose exactly one and keep fixed):
   • Pulled-constant: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • Integrand form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
     Both require explicit gamma(ell) and measure d ell.
3. Typical channels: TOA/TDOA/AOA/FOA/RSS/CarrierPhase. Multipath/NLOS enter as equivalent bias/variance in Σ_y or via outlier masks.
4. Geometry & observability: quantify with H = ∂h/∂x, F = H^T Σ_y^{-1} H; deploy/run-time indicators GDOP/PDOP/HDOP.

III. Volume Structure & Data-Contract Overview

1. Structure:
   • Ch.2: unified terminology/symbols/metrology;
   • Chs.3–4: propagation and per-channel equations (S3x-* / S4x-*) with path/measure declarations;
   • Chs.5–6: layout (geometry) and synchronization;
   • Chs.7–9: dynamics modeling and robust cleaning;
   • Ch.10: measurement matrix J = ∂y/∂θ and experiment design;
   • Ch.11: simulation stack & synthetic data;
   • Ch.12: interfaces & implementation bindings;
   • Ch.13: case library.
2. Data contract (cross-volume fixed fields):
   • unit_system:"SI", references:["volume vX.Y: anchor"];
   • Arrival-time fields: convention, delta_form, gamma(ell), d_ell;
   • Error-budget card: channel uncertainties, covariance Σ_y, coverage factor and combination rules;
   • Chinese is forbidden in formulas/symbols: wrap phi(x,t), Xi(x,t), T_arr, n_eff, T_trans in backticks.
3. M1-1 (Reading & reuse guide)
   • Choose scenario & channels, instantiate Dataset/Pipeline/Error-Budget cards;
   • Per Chs.3–4, pick convention and path segmentation;
   • Use Ch.10 to generate J, Σ_y, assess cond(F) and D/A/E-optimal designs;
   • Run inversion & fusion via Ch.12 I12-* interfaces;
   • Write results back to Ch.13 case library and the error-budget card.

IV. Unified Constants & Metrology Baseline

• Constants: c_ref = 299792458.0, k_B (when thermal noise is modeled), carrier f_c; clock state b_t (bias), \dot b_t (drift), optional \ddot b_t.
• Frames/attitude: world W, body B, base/anchor S; attitude by q_WB or R_WB (right-handed); direction unit vector n̂.
• Collision rules: never mix T_fil (tension) with T_trans (transmittance), nor n (number density) with n_eff (effective refractive index).
• Dimensions/units: all formulas must pass check_dim; tables/fields must include SI units; angles in rad, frequency in Hz, power in dBm or W (state conversion).

V. Testable Predictions & Evaluation Metrics

• Pred. 1 (Sync→TOA co-variation): with equal bandwidth/SNR, adding common-view/differential time reduces var(T_arr) ~ (1/N_ref), mapping to σ_ρ = c_ref · σ_{T_arr}.
• Pred. 2 (GDOP-optimal geometry): with fixed range variance, near-regular polygon anchor layouts minimize GDOP and reduce cond(F).
• Pred. 3 (Multi-band fusion): coherence-weighted fusion over ω via W_coh(ω) yields tr(F) exceeding any single-band bound, shrinking the posterior position ellipsoid volume.
• Pred. 4 (FOA elevates vertical observability): adding FOA increases the diagonal terms of the altitude block in the Fisher matrix, mitigating 2D→3D degeneracy.
• Pred. 5 (Robust cleaning gain): robust mixture likelihoods or M-estimators with NLOS_flag removal increase NEES/NIS pass rates toward nominal coverage.
• Metrics: GDOP/PDOP/HDOP, RMSE/CEP/PEB/SEB, NEES/NIS, LOO/WAIC (model comparison), pass@coverage (coverage).

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

• Cross-volume (fixed style): EFT.WP.Core.Metrology v1.0 Ch.1–3,5 (dimensions/units/uncertainty); EFT.WP.Core.Equations v1.1 Ch.2 S20-* (path/measure & the two T_arr conventions); companion whitepaper Energy Threads, Ch.2 S/P (paths & propagation kernels).
• Anchors: P10-1; S10-1; M1-1.

VII. Summary
This chapter establishes a unified problem statement and execution thread for communications-navigation fusion. Built on the two T_arr conventions with explicit path/measure, it connects observation modeling, geometry & synchronization, fusion estimation, and metrology-driven design, and enforces cross-platform reuse and auditability via data contracts and I12-* interfaces. Subsequent chapters follow this thread and are directly deployable across scenarios and device stacks.