BTP

Kalman Filter Frequency Tracking

This repository contains implementations of various Kalman Filter (KF) approaches for tracking the frequency and phase characteristics of signals affected by Doppler shift.

Project Overview

The project explores different state-space models and filtering techniques to track frequency variations in a BPSK signal affected by sinusoidal Doppler shift. The implementations progress from simple to more complex models, with increasingly realistic noise simulation and parameter tuning approaches.

Implementation Workflow

The project's implementation progression is visualized in kalman_filter_workflow.png, showing how different Kalman Filter implementations evolved:

1. Started with a 2-State KF using a harmonic oscillator model
2. Transitioned to a constant velocity model with SNR-based noise configuration
3. Enhanced to a 3-State KF with realistic noise and complex signal processing
4. Added state constraints and BER analysis
5. Finally implemented adaptive methods with Sage-Husa and WAF

Each stage brought specific improvements and features, making the implementation progressively more sophisticated and realistic.

Implementation Variants

Harmonic Oscillator Models

• KF Version: kf_2state_frequency_track.py
• Model: 2-state model tracking frequency deviation and its rate
• Features: Accurately tracks sinusoidal frequency variations

Constant Velocity Model

• File: kf_const_vel_freq_track.py
• Model: 2-state KF tracking frequency and frequency rate
• Features: Configurable SNR, improved tracking with tuned process noise

Constant Acceleration Model with Realistic Noise

• File: kf_random_walk_doppler_track.py
• Model: 3-state KF tracking frequency, frequency rate, and acceleration
• Features: Realistic noise simulation, iterative Q/R parameter tuning
• Note: Simulates complex signal waveform with AWGN based on SNR

Constant Acceleration Model with Base Q Tuning

• File: kf_realistic_noise_track.py
• Model: 3-state KF with comprehensive parameter tuning
• Features: Extends tuning to base process noise components, most refined frequency tracking implementation

Phase/Frequency/Rate Model

• File: akf_phase_freq_rate_track.py
• Model: 3-state KF tracking phase difference, frequency shift, and frequency rate
• Features: Uses phase angle measurements directly, handles phase wrapping
• Note: Potentially advantageous in low SNR scenarios

Key Features

• Realistic Signal Generation: Complex BPSK signal with sinusoidal Doppler shift
• Noise Modeling: AWGN added to complex waveform with configurable SNR
• Parameter Tuning: Iterative optimization of process and measurement noise parameters
• Performance Evaluation: Visualization of tracking performance and estimation errors
• Phase Handling: Special considerations for phase wrapping in phase-based tracking

Usage

Each implementation can be run independently. For example:

python kf_realistic_noise_track.py

This will:

1. Generate a simulated BPSK signal with Doppler shift
2. Run the parameter tuning process (if applicable)
3. Apply the Kalman filter with optimized parameters
4. Generate performance plots in the plots/ directory

Parameters

Key configurable parameters across implementations:

• Carrier Frequency: 10 GHz
• Doppler Amplitude: 5 kHz
• Doppler Frequency: 0.5 Hz
• Data Rate: 16 kbps
• Samples per Bit: 8
• Waveform SNR: Configurable (typically 10-15 dB)

Project Structure

The repository contains:

• Individual implementation files for each model variant
• A comprehensive project report (BTP.pdf) detailing the theoretical background, implementation details, and results analysis
• A memory bank file (project_memory_bank.md) documenting the development process
• Generated plots in the plots/ directory (not included in repository)
• A visual workflow diagram (kalman_filter_workflow.png) showing the evolution of implementations

Future Work

Potential improvements and extensions:

• Systematic performance comparison across models at different SNR levels
• Implementation of adaptive tuning methods for Q and R parameters
• Refinement of phase measurement techniques to handle BPSK modulation
• Exploration of alternative frequency estimation algorithms

Requirements

• Python 3.x
• NumPy
• Matplotlib