Alpha Spectrum Filter

Advanced adaptive filter with multi-head composition, motion prediction, and Rényi-MTM probability framework

The Alpha Spectrum filter is OpenTrack’s most sophisticated filtering algorithm. It adapts smoothing strength from recent motion energy per axis and includes multiple “heads” (EMA, Brownian, Adaptive, Predictive) composed using a Rényi-Tsallis probability framework.

This filter is designed for advanced users who want maximum control and are willing to tune parameters. For most users, the Simplified Mode with default settings provides excellent results.

How It Works

The Alpha Spectrum filter uses an adaptive EMA (Exponentially Weighted Moving Average) update:

output += alpha * (input - output)
alpha = min + (max - min) * motion^curve

Where motion is a normalized innovation-energy estimate in [0, 1]:

• Low motion → alpha stays near Min (more smoothing, less jitter)
• High motion → alpha moves toward Max (faster response)

Multi-Head Composition

The filter implements a Hydra-style 4-head architecture:

1. EMA head: Standard exponential smoothing
2. Brownian head: Noise-energy contribution
3. Adaptive head: Sustained-motion responsiveness boost (15% higher activation threshold)
4. Predictive head: One-step-ahead prediction from previous frame

These heads are scored by generalized likelihood using Rényi/Tsallis neck scoring, then composed using MTM (Multiple Model) shoulder weighting.

The filter is currently in Phase A implementation. Full transition-matrix MTM with explicit regime semantics is not yet implemented.

Parameters

Simplified Mode (Recommended)

The default workflow uses simplified controls at the top of the dialog:

adaptive · boolean · default: "false"

Enable motion-history responsiveness boost during sustained movement.

• Enabled: Adds adaptive boosting for fast gameplay
• Disabled: Uses only base Min/Max/Curve mapping for predictable feel

advanced · boolean · default: "false"

Show detailed per-parameter controls. When off, detailed controls are disabled (greyed out).

ema_minmax_range · slider · default: "[0.085, 0.218]"

Controls both rotation and translation Min/Max together.

• Min range: 0.5% to 40% (0.005 to 0.4)
• Max range: 2% to 100% (0.02 to 1.0)

curve_deadzone_coupling · slider · default: "[4.26, 0.156, 1.041]"

Controls all four curve/deadzone parameters together:

• Rotation Curve (0.2 to 8.0)
• Translation Curve (0.2 to 8.0)
• Rotation Deadzone (0.0° to 0.3°)
• Translation Deadzone (0.0 to 2.0 mm)

Core EMA Controls

Rotation Parameters

rotation_min · float · default: "0.085"

Minimum alpha for rotations. Higher = less lag at rest but more jitter.

rotation_max · float · default: "0.218"

Maximum alpha for rotations. Higher = snappier turns and faster catch-up.

rotation_curve · float · default: "4.26"

Shape of alpha transition based on motion:

• Higher (>1): keeps heavy smoothing longer, opens up late
• Lower (<1): opens up earlier, more immediate feel

rotation_deadzone · float · default: "0.156"

Suppresses tiny rotational deltas before adaptation. Too high makes small movements feel ignored.

Translation Parameters

translation_min · float · default: "0.085"

Minimum alpha for X/Y/Z position. Higher = less lag but more shake.

translation_max · float · default: "0.218"

Maximum alpha for X/Y/Z position. Higher = faster positional response.

translation_curve · float · default: "4.26"

Shape of alpha transition for translation. Same behavior as rotation curve.

translation_deadzone · float · default: "1.041"

Suppresses tiny translational jitter. Too high creates a sticky center feel.

Advanced Hydra/NGC Controls

These controls appear in the left column when Advanced Mode is enabled. Start with defaults and tune only if needed.

brownian_head_gain · float

Scales Brownian head drive before alpha synthesis. Controls how much noise-energy contributes to adaptive response.

adaptive_threshold_lift · float

Raises the activation threshold for the Adaptive head. Higher = Adaptive head engages later during stronger motion.

predictive_head_gain · float

Scales influence of cached next-frame prediction. Watch Predictive error (rot/pos) status to tune.

mtm_shoulder_base · float

Sets minimum shoulder trust level before mode-dependent lift. Controls overall trust in MTM composition.

ngc_kappa · float

Controls depth-scale commutator coupling strength. Affects how Z-depth influences translational likelihood.

ngc_nominal_z · float

Reference distance used by NGC coupling term. Nominal Z-depth for depth-scale normalization.

Component Toggles

In Advanced Mode, you can enable/disable individual filter components:

enable_ema · boolean · default: "true"

EMA smoothing head

• On: Uses output += alpha * (input - output)
• Off: Pure pass-through (output = input) while status info still updates

enable_brownian · boolean · default: "true"

Brownian interface contribution

• On: Brownian term contributes to both adaptive drive and MTM measurement
• Off: Brownian status info computes, but contribution is disabled

enable_mtm · boolean · default: "true"

Rényi MTM shoulder composition

• On: Mode diffusion + posterior update influence adaptive responsiveness
• Off: MTM influence is fully removed (mode_e does not affect response)

Tuning Workflow

1. Start with Adaptive Mode off

   Disable Adaptive Mode initially. Enable it only if you need extra responsiveness during sustained motion.

2. Observe status info

   Watch the status line while moving and while still to understand current behavior.

   Mon|E1 B1 A1 P1 M1|rE0.350 rP0.350 pE0.534 pP0.500 k0.000
   

   Legend:

   • Mon: Status active
   • E/B/A/P/M: EMA, Brownian, Adaptive, Predictive, MTM toggles
   • rE, rP: Rotation mode expectation and peak
   • pE, pP: Translation mode expectation and peak
   • k: Live NGC coupling residual
3. Tune rotation first, then translation

   Adjust one family at a time to avoid chasing parameter interactions.

4. Fine-tune specific parameters

   Make small moves (~5-10% of slider range) and test with:

   • Still head pose (jitter check)
   • Slow pan
   • Fast snap turn
   • Lean in/out

Two-Column Advanced Tuning

When Advanced Mode is enabled, use this order:

Left Column (Hydra/NGC)

1. Start with defaults
2. Tune MTM Shoulder Base for overall trust level
3. Tune Brownian Head Gain to balance jitter vs response
4. Tune Adaptive Threshold Lift to control adaptive engagement
5. Tune Predictive Head Gain while watching predictive error status
6. Tune NGC Kappa and NGC Nominal Z last for translational coupling

Right Column (Core EMA)

1. Set rotation Min/Max/Curve/Deadzone for desired rotational feel
2. Set translation Min/Max/Curve/Deadzone for positional feel
3. Test with all movement types

If tuning regresses performance, use Reset sliders to defaults and repeat the process. The reset button writes default values to the active profile immediately.

Recommended Profiles

Stable / Simulator Focus

Maximum smoothness for precision work:

rotation_min: 0.03
rotation_max: 0.55
rotation_curve: 1.8
rotation_deadzone: 0.04

translation_min: 0.04
translation_max: 0.65
translation_curve: 1.5
translation_deadzone: 0.12

adaptive_mode: false

Balanced (Factory Default)

General purpose balanced settings:

rotation_min: 0.085
rotation_max: 0.218
rotation_curve: 4.26
rotation_deadzone: 0.156

translation_min: 0.085
translation_max: 0.218
translation_curve: 4.26
translation_deadzone: 1.041

adaptive_mode: false

Responsive / Fast Action

Minimal lag for competitive gaming:

rotation_min: 0.06
rotation_max: 0.85
rotation_curve: 0.9
rotation_deadzone: 0.02

translation_min: 0.07
translation_max: 0.90
translation_curve: 0.8
translation_deadzone: 0.06

adaptive_mode: true

Status Information

The status line uses a compact fixed-width format to avoid UI resizing:

Status Line Format

Mon|E1 B1 A1 P1 M1|rE0.350 rP0.350 pE0.534 pP0.500 k0.000

Status fields:

• Mon: Monitoring active
• E/B/A/P/M: Head toggles (1=enabled, 0=disabled)
• rE/rP: Rotation mode expectation/peak
• pE/pP: Translation mode expectation/peak
• k: NGC coupling residual

Brownian status:

• raw: Instantaneous noise energy
• filtered: Smoothed noise energy
• delta: Difference (raw - filtered)
• damped: Damped contribution

Troubleshooting

View jitters while still

• Increase Min smoothing or deadzone
• Check Brownian damped status info
• Reduce Brownian Head Gain

Feels laggy during turns

• Raise Max smoothing
• Lower Curve value
• Enable Adaptive Mode
• Increase Adaptive Threshold Lift

Feels too twitchy

• Lower Max smoothing
• Raise Curve value
• Disable Adaptive Mode

Small intentional movement ignored

• Reduce deadzone values
• Check that motion exceeds deadzone threshold

Implementation Notes

Rotation wrap-around is handled automatically. Angles crossing ±180° are properly unwrapped.

Recenter resets internal state on the next frame, clearing history and mode probabilities.

Code References

Relevant source files in the OpenTrack codebase:

• Core filter/update: filter-alpha-spectrum/ftnoir_filter_alpha_spectrum.cpp
• State definitions: filter-alpha-spectrum/ftnoir_filter_alpha_spectrum.h
• Dialog UI: filter-alpha-spectrum/ftnoir_filter_alpha_spectrum_dialog.cpp

Implementation Status

Currently implemented:

• Per-axis adaptive EMA smoothing
• Hydra-style four-head composition (EMA + Brownian + Adaptive + Predictive)
• True Rényi/Tsallis neck scoring across enabled heads
• MTM shoulder composition over neck-normalized head candidates
• NGC depth-scale commutator coupling term
• Alpha-spectrum mode probability vector (7 bins) with per-frame diffusion
• Measurement-driven mode likelihood updates and normalized posterior
• Runtime status info in settings dialog

Not yet implemented:

• Full transition-matrix MTM with explicit regime semantics
• Rényi-distance likelihood over expanded head sets
• IMM-style mode mixing across explicit motion regimes

Further Reading

Author Discussion

Technical deep-dive and research background for the Alpha Spectrum filter implementation