Loop Filter

The loop filters are provided by TrackingLoopFilters.jl. This includes:

first order loop filter FirstOrderLF
second order bilinear loop filter SecondOrderBilinearLF
second order boxcar loop filter SecondOrderBoxcarLF
third order bilinear loop filter ThirdOrderBilinearLF
third order boxcar loop filter ThirdOrderBoxcarLF
third order assisted bilinear loop filter ThirdOrderAssistedBilinearLF (combines PLL and FLL)

Default Configuration

The default Doppler estimator is ConventionalAssistedPLLAndDLL which uses:

ThirdOrderAssistedBilinearLF for the carrier loop (FLL-assisted PLL for improved dynamics)
SecondOrderBilinearLF for the code loop

When TrackState builds the default estimator from a signal-tuple declaration, the carrier loop is staged (see CarrierLoopStage): it pulls in as an FLL-assisted PLL at a wide 50 Hz with a 5 Hz FLL-assist bandwidth, drops the FLL once a phase-lock indicator reads lock, and later narrows to a narrow 18 Hz. The code bandwidth is a flat 1 Hz. All are one-sided noise bandwidths BL (Kaplan & Hegarty), for every signal. The stages only advance, and reset_loop_filters! keeps the stage reached; a satellite added anew starts over. Read a satellite's stage with carrier_loop_stage(get_doppler_estimator_state(sat)).

Where the replica wipes every sign modulation off the prompt (a dataless signal synced to its secondary code) the carrier discriminators turn four-quadrant.

The defaults are not scaled with the integration time; each is capped at filter time by its stability product BL · T_int: the PLL by 0.09, the FLL path by 0.02, the code loop by 0.018 (effective_carrier_loop_filter_bandwidth and siblings). The bandwidths that end up in the loop are:

Integration time	Wide BL	Narrow BL	FLL-assist BL	Code BL
1 ms (L1 C/A, L5I, …)	50 Hz	18 Hz	5 Hz	1 Hz
4 ms (E1B / E1C)	22.5 Hz	18 Hz	5 Hz	1 Hz
10 ms (L1C-D/P, B1C)	9 Hz	9 Hz	2 Hz	1 Hz
20 ms (L1 C/A or L2 CM after sync)	4.5 Hz	4.5 Hz	1 Hz	0.9 Hz
1.5 s (L2 CL)	0.06 Hz	0.06 Hz	0.013 Hz	0.012 Hz

The TrackingLoops manual ("Loop-filter bandwidths") gives the rationale for the bandwidths and caps.

Before TrackingLoops 4 the carrier filter was fed radians but its output read as Hz, making the loop about 5.6× wider than configured (≈ 100 Hz for 18 Hz); to get approximately that loop back, set both wide_carrier_loop_filter_bandwidth and narrow_carrier_loop_filter_bandwidth to 85.0Hz. Before TrackingLoops 5 the loop ran FLL-assisted at one carrier bandwidth throughout; pass equal wide and narrow bandwidths for one PLL bandwidth.

Override per signal by defining methods of default_wide_carrier_loop_filter_bandwidth, default_narrow_carrier_loop_filter_bandwidth, default_fll_assist_loop_filter_bandwidth / default_code_loop_filter_bandwidth, or override at construction time by passing your own doppler_estimator = to TrackState.

Doppler Estimators

In the TrackingLoops manual:

Resetting loop filters

After changing a signal's integration length with set_preferred_num_code_blocks_to_integrate!, reset the affected loop filters so the old integration length's filter state does not leak into the new one.

Tracking.reset_loop_filters! — Function

reset_loop_filters!(track_state)

Re-seed the Doppler-estimator state of every satellite (or one addressed satellite) from its current Doppler. For the conventional PLL/DLL this zeroes the loop-filter integrators and keeps carrier_doppler, code_doppler, any per-satellite bandwidth override and the carrier-loop stage. Each signal's last_fully_integrated_filtered_prompt is cleared, so the first FLL update does not measure a rotation spanning the old integration interval.

Use it when a signal's integration length changes mid-track, e.g. GPS L5I from 1 ms to 10 ms via set_preferred_num_code_blocks_to_integrate!: the integrator state does not carry over to the new update interval, and the transient can drag the loop out of lock.

No satellite id resets every satellite; (group, prn) or (single-group) prn resets one. Mutates track_state and returns it. Works for any AbstractDopplerEstimator through its init_estimator_state hook.

set_preferred_num_code_blocks_to_integrate!(track_state, 1, GPSL5I, 10)
reset_loop_filters!(track_state, 1)          # clean handoff for PRN 1
reset_loop_filters!(track_state)             # …or reset every satellite

source

Custom Configuration

You can customize the loop filters and bandwidths when creating the Doppler estimator:

julia> using Tracking, TrackingLoops, GNSSSignals, TrackingLoopFilters

julia> using Tracking: Hz

julia> # Use non-assisted PLL with custom loop filter types
       doppler_estimator = ConventionalPLLAndDLL(
           ThirdOrderBilinearLF,      # carrier loop filter type
           SecondOrderBilinearLF;     # code loop filter type
           wide_carrier_loop_filter_bandwidth = 30.0Hz,
           narrow_carrier_loop_filter_bandwidth = 15.0Hz,
           code_loop_filter_bandwidth = 0.5Hz
       );

julia> track_state = TrackState(; signal = GPSL1CA(), doppler_estimator);

julia> track_state = add_satellite!(track_state; prn = 1, code_phase = 50.0, carrier_doppler = 1000.0Hz);

Custom Loop Filters

You can implement a custom loop filter MyLoopFilter <: AbstractLoopFilter. In this case, a specialized filter_loop function is needed. For more information refer to TrackingLoopFilters.jl.

Custom Doppler Estimator

To replace the loop-filter-based estimator with a different algorithm (Kalman filter, joint-channel estimator, …), see the dedicated guide in custom_doppler_estimator.md.