feature_engineering.md

RadarSense — Feature Engineering & Schemas

This document lists the engineered feature schemas used to train the machine learning and quantum models for the RadarSense target classification pipeline.

1. Classical Model Schema (11 Features)

The deployed CatBoost classical model is trained on the following 11 engineered features (frozen schema contract).

Column	Feature	Type	Unit	Range	Description
1	doppler_velocity	float64	m/s	−50..50	Radial velocity, last step of an 8-step simulated track
2	doppler_freq_shift	float64	Hz	≈ −3333..3333	2·v·f_c/c at f_c = 10 GHz, derived from observed velocity
3	rcs_estimate	float64	dBsm	−20..20	Radar cross-section proxy; smaller = stealthier
4	micro_doppler_bandwidth	float64	Hz	0..500	Spectral spread from rotating/flapping parts — key drone discriminator
5	micro_doppler_jitter	float64	—	0..1	Normalized micro-motion irregularity
6	range_m	float64	m	50..5000	Target range
7	azimuth_deg	float64	deg	−180..180	Bearing
8	altitude_m	float64	m	0..3000	Estimated altitude
9	velocity_variance	float64	(m/s)²	0+	Variance of the simulated velocity track (derived, not sampled)
10	acceleration	float64	m/s²	−10..10	Mean derivative of the velocity track (derived, not sampled)
11	snr_db	float64	dB	−20..−10	Per-sample Signal-to-Noise Ratio; co-determined by range and RCS

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2. Quantum Model Schema (4 Features)

The Variational Quantum Classifier (VQC) and precomputed fidelity quantum kernel (QSVC) models use a subset of 4 specific physical features to match the ZZFeatureMap dimensionality (4 qubits).

Column	Feature	Type	Unit	Range	Description
1	doppler_velocity	float64	m/s	−50..50	Radial velocity, last step of an 8-step simulated track
2	rcs_estimate	float64	dBsm	−20..20	Radar cross-section proxy; smaller = stealthier
3	micro_doppler_bandwidth	float64	Hz	0..500	Spectral spread from rotating/flapping parts — key drone discriminator
4	micro_doppler_jitter	float64	—	0..1	Normalized micro-motion irregularity

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3. Alternative / Baseline Signal Model Schema (31 Features)

The detailed raw-signal statistical model (as processed in signal statistical feature extraction) generates 31 statistical features derived from 100-sample time-series waveforms across Amplitude, Velocity, and Energy signals.

Column	Feature	Type	Unit	Description
1	snr_db	float64	dB	Signal-to-Noise Ratio
2	amplitude_mean	float64	V	Mean of received signal amplitude waveform
3	amplitude_std	float64	V	Standard deviation of amplitude waveform
4	amplitude_min	float64	V	Minimum amplitude value
5	amplitude_max	float64	V	Maximum amplitude value
6	amplitude_range	float64	V	Amplitude range ($V_{\text{max}} - V_{\text{min}}$)
7	amplitude_energy	float64	V²	Total signal energy ($\sum x^2$)
8	amplitude_zcr	float64	—	Zero-Crossing Rate of amplitude around mean
9	amplitude_dominant_freq	float64	Hz	Peak dominant frequency from DFT
10	amplitude_spectral_bandwidth	float64	Hz	Spectral bandwidth spread from DFT
11	amplitude_diff_var	float64	V²	Variance of first-difference signal ($\text{var}(\Delta x)$)
12	velocity_mean	float64	m/s	Mean of radial velocity signal waveform
13	velocity_std	float64	m/s	Standard deviation of velocity waveform
14	velocity_min	float64	m/s	Minimum velocity value
15	velocity_max	float64	m/s	Maximum velocity value
16	velocity_range	float64	m/s	Velocity range ($v_{\text{max}} - v_{\text{min}}$)
17	velocity_energy	float64	(m/s)²	Total energy of velocity signal
18	velocity_zcr	float64	—	Zero-Crossing Rate of velocity around mean
19	velocity_dominant_freq	float64	Hz	Peak dominant frequency from velocity DFT
20	velocity_spectral_bandwidth	float64	Hz	Spectral bandwidth spread from velocity DFT
21	velocity_diff_var	float64	(m/s)²	Variance of first-difference velocity signal
22	energy_mean	float64	J	Mean of energy signal waveform
23	energy_std	float64	J	Standard deviation of energy waveform
24	energy_min	float64	J	Minimum energy value
25	energy_max	float64	J	Maximum energy value
26	energy_range	float64	J	Energy range ($E_{\text{max}} - E_{\text{min}}$)
27	energy_energy	float64	J²	Total signal energy of energy waveform
28	energy_zcr	float64	—	Zero-Crossing Rate of energy around mean
29	energy_dominant_freq	float64	Hz	Peak dominant frequency from energy DFT
30	energy_spectral_bandwidth	float64	Hz	Spectral bandwidth spread from energy DFT
31	energy_diff_var	float64	J²	Variance of first-difference energy signal

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4. Physical Grounding & Derivations

• Kinematic Trajectories: velocity_variance and acceleration are derived from an 8-step Ornstein–Uhlenbeck velocity track modeling specific class kinematics (e.g. drone hover-and-jerk behavior vs smooth aircraft velocity).
• SNR Coupling: SNR follows the physical radar-equation coupling form: $\text{SNR} \propto \text{RCS} - 40 \log_{10}(\text{Range})$, mapped affinely into the spec band.
• Measurement Noise: Noise levels on all features scale dynamically with the SNR deficit, making low-SNR targets much harder to predict.