41-EFT.WP.Comms.Navigation v1.0 | Chapter 2: Terminology, Symbols & Metrology Baseline

Home ／ Docs-Technical WhitePaper ／ 41-EFT.WP.Comms.Navigation v1.0

Chapter 2: Terminology, Symbols & Metrology Baseline

I. Scope & Dependency Anchors

• This chapter freezes the volume’s terminology, symbols, and metrology baseline: frames/attitude, time/frequency, observation-family labels, units/dimensions, uncertainties, and data-contract fields.
• All formulas/symbols/definitions are in English and wrapped in backticks; cross-volume citations use the fixed style “volume + version + anchor (P/S/M/I)”.
• Dependency anchors: S20-1—S20-10 (this chapter), M2-1—M2-2 (this chapter). Cross-references: EFT.WP.Core.Metrology v1.0 Ch.1–3,5 and EFT.WP.Core.Equations v1.1 Ch.2 S20-*.
• Collision rules (mandatory): T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective refractive index).

II. Frames, Attitude, Time/Frequency (Baseline Definitions)

• S20-1 (Frames & attitude)
  World frame W, body frame B, anchor/base frame S; attitude by quaternion q_WB or right-hand rotation matrix R_WB; direction unit vector n̂.
• S20-2 (Position & velocity)
  p_WB ∈ ℝ^3 (m), v_WB ∈ ℝ^3 (m·s⁻¹).
• S20-3 (Time & clock)
  t_rx = t_tx + T_prop + b_t + ε_t, with clock bias b_t (s), drift \dot b_t (s/s), optional second-order \ddot b_t.
• S20-4 (Frequency & offsets)
  Carrier f_c, carrier frequency offset f_CFO (positive at receiver), Doppler f_D = - ( f_c / c_ref ) ( v_rel · n̂ ).
• S20-5 (Angle definitions)
  Azimuth θ ∈ (-π, π] about W–z; elevation φ ∈ [-π/2, π/2]; unit rad.

III. Observation Families & Path Conventions

1. S20-6 (Observation families)
   TOA/TDOA/AOA/FOA/RSS/CarrierPhase; unified measurement equation y = h(x, θ, ν) + ε.
2. S20-7 (Two arrival-time conventions — path/measure mandatory)
   • Pulled-constant: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • Integrand form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
     They are equivalent but must not be mixed; both require explicit gamma(ell) and d ell.
3. S20-8 (Piecewise paths)
   gamma = ⊕_k gamma_k, covering {free|fixture|substrate|device|environment}; isolate segments by differencing: ΔT_arr = T_arr^{case} - T_arr^{ref}.
4. S20-9 (LOS/NLOS/multipath)
   Model via equivalent bias b_NLOS and variance inflation into Σ_y, or carry an NLOS_flag mask in the stream.
5. S20-10 (Statistical models)
   ε ~ 𝒟(0, Σ_y) may be Gaussian, Gaussian mixture, or Student-t; robust loss ρ(·) must be explicit (Huber/Tukey).

IV. Units, Dimensions & Uncertainty (Metrology Baseline)

1. Base/derived units: m, s, Hz, rad, A, K, W, dBm; every table/field must include SI units.
2. Dimension checks: all expressions must pass check_dim. Typical verifications:
   • ρ = c_ref · T_arr ⇒ [m] = [m·s⁻¹][s].
   • f_D = - ( f_c / c_ref )( v_rel · n̂ ) ⇒ [Hz] = [Hz][m·s⁻¹]/[m·s⁻¹].
3. Uncertainty notation: standard u(x), combined u_c, expanded U = k · u_c (coverage factor k); covariance matrix Σ_y.
4. SNR & thermal noise: when needed, use k_B, bandwidth B, and noise spectral density N_0 (unit W·Hz⁻¹).

V. Symbol Table (Incremental)

The table lists only symbols newly introduced or specialized in this volume; global symbols are in Core.Terms v1.0.

VI. Arrival-Time & Path Recording (Mandatory Data-Contract Fields)

unit_system: "SI"

arrival_time:

convention: "pulled_const" # or "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"

observables: ["T_arr(ω)","TOA","TDOA","AOA","FOA","RSS"]

covariance:

Σ_y: "<block-diagonal or sparse>"

references:

- "EFT.WP.Core.Equations v1.1:Ch.2 S20-*"

- "EFT.WP.Core.Metrology v1.0:Ch.1–3,5"

VII. Observations & Jacobians (Checkable Forms)

• TOA: y_TOA = T_arr + b_t + ε_t; ∂y_TOA/∂p_WB = (1/c_ref) ∂ρ/∂p_WB = (1/c_ref) n̂^T.
• TDOA: y_TDOA = ΔT_ij + ε (reference station j=0).
• AOA: y_AOA = [θ, φ]^T + ε; directional derivatives from unit-sphere parametrization.
• FOA: y_FOA = f_D + ε.
• Unified H = ∂h/∂x and Fisher F = H^T Σ_y^{-1} H are used for cond(F) and D/A/E-optimal design (see Chapter 10).

VIII. Quality Gates (This Chapter)

• Q1 Metrology checks: all formulas pass check_dim; tables/fields include SI units.
• Q2 Path declaration: any T_arr/TOA/TDOA/FOA usage includes convention/delta_form/gamma(ell)/d ell.
• Q3 Collision bans: never mix T_fil/T_trans or n/n_eff in the manuscript.
• Q4 Covariance consistency: block structure of Σ_y matches channel grouping; robust mixtures specify weights and component covariances.
• Q5 Citation style: all cross-volume citations carry “volume + version + anchor.”

IX. Dataset/Pipeline Card Supplemental Fields (Recommended)

clocks:

model: "bias+drift(+drift2)"

priors: {b_t: "N(0,σ_b^2)", dot_b_t: "N(0,σ_d^2)"}

geometry:

anchors: "<positions, cov>"

bands:

ω: ["L1","UWB","5G","Wi-Fi"]

robust:

nlos_flag: "<bool or score>"

loss: "Huber|Tukey"

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

• Cross-volume (fixed style): EFT.WP.Core.Metrology v1.0 Ch.1–3,5; EFT.WP.Core.Equations v1.1 Ch.2 S20-*.
• Anchors in this chapter: S20-1—S20-10; M2-1—M2-2 (M2-2: placeholder for check_dim/contract self-check scripts).