SBF Field Decoding Reference¶

Every value stored in obs_ds and the sbf_obs metadata dataset is derived from raw SBF integers through a well-defined transformation. This page documents each formula with the source field type, the arithmetic applied, and the firmware page reference.

All page references are to the Septentrio AsteRx SB3 ProBase Firmware v4.14.0 Reference Guide (abbreviated RefGuide-4.14.0) unless stated otherwise.

Epoch Timestamps¶

Source: MeasEpoch header — WNc (u2) + TOW (u4, milliseconds). Source block: ReceiverTime (ΔLS), RefGuide-4.14.0 p.369.

GPS Time uses a fixed epoch and has no leap seconds; UTC is obtained by subtracting the current GPS–UTC offset ΔLS:

\[ t_\text{UTC} = t_\text{GPS epoch} + \frac{WN_c \times 604800 \times 10^3 + TOW}{10^3} - \Delta_\text{LS} \]

Symbol	Meaning	Value
\(t_\text{GPS epoch}\)	GPS reference epoch	1980-01-06 00:00:00 UTC
\(WN_c\)	Continuous GPS week number	from `MeasEpoch.WNc`
\(TOW\)	Time of Week	ms, from `MeasEpoch.TOW`
\(\Delta_\text{LS}\)	GPS − UTC leap-second offset	18 s (valid from 2017-01-01; updated from `ReceiverTime` when present)

Signal Number Decoding¶

Source: MeasEpochChannelType1.Type (u1) and ObsInfo (u1), p.262.

The 5 least-significant bits of Type carry a signal index:

\[ \text{SigIdxLo} = \text{Type} \;\&\; 0x1F \]

If \(\text{SigIdxLo} = 31\) the signal number is extended via ObsInfo:

\[ \text{sig_num} = \left(\frac{\text{ObsInfo} \gg 3}{} \;\&\; 0x1F\right) + 32 \]

Otherwise \(\text{sig_num} = \text{SigIdxLo}\). The mapping from signal number to constellation / band / tracking code is defined in the signal type table (RefGuide-4.14.0 §4.1.10, p.256).

C/N₀ (SNR)¶

Source: MeasEpochChannelType1.CN0 (u1), p.264. Dataset variable: SNR (units: dB-Hz).

The raw byte encodes carrier-to-noise density in two different scales depending on the signal type:

\[ C/N_0 = \begin{cases} \text{CN0}_\text{raw} \times 0.25 + 10 & \text{all signals except 1 and 2} \\ \text{CN0}_\text{raw} \times 0.25 & \text{signals 1 (GPS L1P) and 2 (GPS L2P)} \end{cases} \]

Signals 1 and 2 are tracked semi-codeless and have a lower intrinsic \(C/N_0\); the firmware omits the +10 dB offset and enforces a minimum of 1 dB‑Hz.

Do-Not-Use: raw value 255 → stored as NaN.

CN0HighRes correction (MeasExtra)¶

Source: MeasExtra.MeasExtraChannelSub.Misc bits 0–2 (u3), p.265.

When MeasExtra (Block 4000) is logged, the reader applies an additional sub-quantisation correction that extends resolution from 0.25 dB to 1/32 dB:

\[ C/N_{0,\,\text{final}} = C/N_0 + \underbrace{({\rm Misc} \;\&\; 0x07)}_{\text{CN0HighRes}\;\in\{0,\ldots,7\}} \times 0.03125 \]

If MeasExtra is absent the correction is zero (NaN guard prevents modification).

Resolution	Source
0.25 dB-Hz	`MeasEpoch.CN0` alone
0.03125 dB-Hz (1/32 dB-Hz)	after CN0HighRes correction

Pseudorange¶

Source: MeasEpochChannelType1.Misc bits 0–3 (CodeMSB, u4-equivalent), CodeLSB (u4), p.262.

\[ PR = \bigl(\text{CodeMSB} \times 2^{32} + \text{CodeLSB}\bigr) \times 10^{-3} \quad [\text{m}] \]

where \(\text{CodeMSB} = \text{Misc} \;\&\; 0x0F\).

Do-Not-Use: CodeMSB = 0 and CodeLSB = 0 → NaN.

Type2 (slave signal) pseudorange¶

Source: MeasEpochChannelType2.OffsetsMSB bits 0–2 (CodeOffsetMSB, 3-bit two's-complement, range −4 to +3), CodeOffsetLSB (u2), p.264.

\[ PR_2 = PR_1 + \bigl(\text{CodeOffsetMSB} \times 65536 + \text{CodeOffsetLSB}\bigr) \times 10^{-3} \quad [\text{m}] \]

Do-Not-Use: CodeOffsetMSB = −4 and CodeOffsetLSB = 0 → NaN.

Doppler Shift¶

Source: MeasEpochChannelType1.Doppler (i4), p.263.

\[ D = \text{Doppler}_\text{raw} \times 10^{-4} \quad [\text{Hz}] \]

Positive Doppler indicates a closing range (approaching satellite).

Do-Not-Use: raw = −2 147 483 648 (\(= -2^{31}\), i4 minimum) → NaN.

Type2 (slave signal) Doppler¶

Source: MeasEpochChannelType2.OffsetsMSB bits 3–7 (DopplerOffsetMSB, 5-bit two's-complement, range −16 to +15), DopplerOffsetLSB (u2), p.264.

The Type2 Doppler includes a frequency-ratio correction to account for the different carrier frequency of the slave signal:

\[ D_2 = D_1 \times \frac{f_2}{f_1} + \bigl(\text{DopplerOffsetMSB} \times 65536 + \text{DopplerOffsetLSB}\bigr) \times 10^{-4} \quad [\text{Hz}] \]

where \(f_1, f_2\) are the carrier frequencies of the Type1 (master) and Type2 (slave) signals respectively.

Do-Not-Use: DopplerOffsetMSB = −16 and DopplerOffsetLSB = 0 → NaN.

Carrier Phase¶

Source: MeasEpochChannelType1.CarrierMSB (i1), CarrierLSB (u2), p.263–264.

The carrier phase is encoded as a fractional offset relative to the pseudorange, expressed in cycles. Let \(\lambda = c / f\) be the carrier wavelength:

\[ L = \frac{PR}{\lambda} + \bigl(\text{CarrierMSB} \times 65536 + \text{CarrierLSB}\bigr) \times 10^{-3} \quad [\text{cycles}] \]

\[ \lambda = \frac{c}{f} \quad \text{where } c = 299\,792\,458 \;\text{m/s} \]

Do-Not-Use: CarrierMSB = −128 and CarrierLSB = 0 → NaN.

Type2 carrier phase¶

\[ L_2 = \frac{PR_2}{\lambda_2} + \bigl(\text{CarrierMSB}_2 \times 65536 + \text{CarrierLSB}_2\bigr) \times 10^{-3} \quad [\text{cycles}] \]

Uses \(PR_2\) (Type2 pseudorange, above) and the slave signal wavelength \(\lambda_2\).

GLONASS FDMA Carrier Frequencies¶

Source: ChannelStatus.ChannelSatInfo.FreqNr, RefGuide-4.14.0 §4.1.10 p.256 and ChannelStatus Block 4013 p.393.

GLONASS uses Frequency Division Multiple Access (FDMA). The centre frequency depends on the frequency slot \(K = \text{FreqNr} - 8\).

FreqNr range differs by firmware version

RefGuide-4.14.0 allows slot range −7 to +13 (FreqNr 1–21). RefGuide-4.15.1 restricts this to −7 to +6 (FreqNr 1–14), matching the current GLONASS ICD allocation.

\[ f_{L1}(K) = 1602 + K \times \frac{9}{16} \quad [\text{MHz}] \]

\[ f_{L2}(K) = 1246 + K \times \frac{7}{16} \quad [\text{MHz}] \]

These frequencies are used as \(f\) in the carrier phase wavelength formula and as \(f_1, f_2\) in the Type2 Doppler formula.

GLONASS L3 CDMA (signal 12) has a fixed frequency of 1202.025 MHz and does not use this formula.

Satellite Geometry (SatVisibility → θ, φ)¶

Source: SatVisibility.SatInfo.Elevation (i2, scale 0.01 °/LSB), Azimuth (u2, scale 0.01 °/LSB), RefGuide-4.14.0 p.400.

Polar angle θ¶

The SBF block stores elevation above the horizon. canvod-readers converts to the polar angle (co-elevation) used in the Tau-Omega VOD formula:

\[ \theta\,[\text{rad}] = \text{deg2rad}\!\left(90 - \text{Elevation}_\text{raw} \times 0.01\right) \]

θ	Geometry
\(\theta = 0\)	satellite at zenith (directly overhead)
\(\theta = \pi/2\)	satellite at the horizon

Azimuth φ¶

\[ \phi\,[\text{rad}] = \text{deg2rad}\!\left(\text{Azimuth}_\text{raw} \times 0.01\right) \]

The stored azimuth is the geographic (compass) convention: 0 = North, π/2 = East, measured clockwise. Both θ and φ are stored in radians as broadcast_theta and broadcast_phi in the sbf_obs metadata dataset.

MeasExtra Signal-Quality Fields¶

All fields below are sourced from MeasExtra Block 4000, MeasExtraChannelSub sub-block, p.265.

Multipath correction (pseudorange)¶

\[ \Delta PR_\text{MP} = \text{MPCorrection}_\text{raw} \times 10^{-3} \quad [\text{m}] \]

Raw field: i2. Add to the stored pseudorange to recover the unmitigated measurement before firmware multipath filtering.

Smoothing correction (pseudorange)¶

\[ \Delta PR_\text{smooth} = \text{SmoothingCorr}_\text{raw} \times 10^{-3} \quad [\text{m}] \]

Raw field: i2. Add to the stored pseudorange to recover the raw unsmoothed measurement before Hatch-filter carrier smoothing.

Code tracking variance¶

\[ \sigma_\text{code}^2 = \text{CodeVar}_\text{raw} \times 10^{-4} \quad [\text{m}^2] \]

Raw field: u2. Estimated noise variance of the code-phase measurement. Maximum representable value is 6.5534 m² (raw = 65534). Do-Not-Use: 65535 → NaN.

Carrier tracking variance¶

\[ \sigma_\text{carrier}^2 = \text{CarrierVar}_\text{raw} \quad [\text{mcycles}^2] \]

Raw field: u2, direct copy (scale = 1 mcycle²/LSB). Maximum 65534 mcycles². Do-Not-Use: 65535 → NaN.

The corresponding Doppler variance is:

\[ \sigma_D^2 = \sigma_\text{carrier}^2 \times D_\text{VarFactor} \quad [\text{Hz}^2] \]

where DopplerVarFactor (MeasExtra block header, p.264) is a per-epoch scale factor that converts mcycles² to Hz².

Lock time¶

\[ T_\text{lock} = \text{LockTime}_\text{raw} \quad [\text{s}] \]

Raw field: u2. Duration of uninterrupted carrier phase tracking. Reset to 0 on reacquisition. Clipped to 65534 s. Do-Not-Use: 65535 → NaN.

Cumulative loss-of-continuity counter¶

\[ N_\text{slip} = \text{CumLossCont}_\text{raw} \quad \text{(modulo 256)} \]

Raw field: u1, direct copy. Increments at every reacquisition or cycle slip. A change \(\Delta N_\text{slip} \neq 0\) between consecutive epochs is a direct indicator of a carrier-phase discontinuity (cycle slip).

Carrier multipath correction¶

\[ \Delta L_\text{MP} = \frac{\text{CarMPCorr}_\text{raw}}{512} \quad [\text{cycles}] \]

Raw field: i1, scale \(1/512\) cycles/LSB (\(\approx 1.953 \times 10^{-3}\) cycles/LSB). Add to the stored carrier phase to recover the unmitigated phase.

Auxiliary Scalar Fields¶

Fields stored with a simple scale or offset:

Variable	Source block	Raw field	Formula	Unit
`pdop`, `hdop`, `vdop`	DOP (Block 4001), fallback PVTGeodetic	u2	raw × 0.01	1
`h_accuracy_m`	PVTGeodetic (Block 4007) `HAccuracy`	u2	raw × 0.01; DNU 65535	m
`v_accuracy_m`	PVTGeodetic (Block 4007) `VAccuracy`	u2	raw × 0.01; DNU 65535	m
`mean_corr_age_s`	PVTGeodetic (Block 4007) `MeanCorrAge`	u2	raw × 0.01	s
`temperature_c`	ReceiverStatus (Block 4014) `Temperature`	u1	raw − 100; DNU 0	°C

Page references: DOP block p.349, PVTGeodetic pp.337–339, ReceiverStatus pp.396–399.

Summary: Non-trivial Transformations¶

Observable	Non-trivial step
SNR	Signal-dependent formula (±10 dB offset); two-pass correction from MeasExtra
Pseudorange	40-bit reconstruction from two fields (CodeMSB × 2³² + CodeLSB); Type2 adds delta
Carrier phase	Mixed-unit formula: pseudorange converted to cycles via λ = c/f, then phase delta added
Type2 Doppler	Frequency-ratio scale factor applied before adding delta
θ (polar angle)	Elevation → co-elevation (90° − elevation), then degrees → radians
φ (azimuth)	Scale 0.01°/LSB, degrees → radians
GLONASS frequencies	Slot-dependent FDMA formula required for λ and Type2 Doppler
Epoch	GPS week + TOW (ms) → UTC datetime via leap-second subtraction
CN0HighRes	Bit-field extraction (bits 0–2) then scale 1/32 dB-Hz/LSB
CarMPCorr	Integer division by 512 to convert i1 to fractional cycles

References¶

Septentrio AsteRx SB3 ProBase Firmware v4.14.0 Reference Guide
Septentrio AsteRx SB3 ProBase Firmware v4.15.1 Reference Guide
IS-GPS-200 Rev. N §20.3.3.5.2.4 — GPS time and leap seconds
RINEX 3.04 signal nomenclature — used verbatim for SID code strings