2024 "Shuwei Cup" Problem A: Frequency Estimation Problem in Aircraft Laser Speed Measurement
- Read the signal data from the file and construct a known signal model. By subtracting the model signal from the original signal, the noise part is extracted.
- Then, perform statistical analysis on the noise by calculating its mean, variance, and autocorrelation function to understand the noise's intensity and temporal correlation.
- Next, perform frequency-domain analysis by calculating the noise's power spectral density through Fourier transform, revealing its frequency characteristics. Finally, use charts to display these results, including the signal and model comparison chart, noise time-domain waveform, autocorrelation function, and power spectral density chart, for a comprehensive analysis of the signal and noise characteristics.
- Read the signal data and filter out the portions that fall within the specified time and amplitude range. Then, apply a Butterworth bandpass filter to the signal to remove noise outside the target frequency band.
- Next, define an error function to evaluate the fit between the sine wave generated at a given frequency and the filtered signal.
- Then, use the Particle Swarm Optimization (PSO) algorithm to search for the optimal frequency within the predefined frequency range, minimizing the error function. PSO iteratively adjusts the positions and velocities of particles, combining individual and global best solutions to continuously optimize the search results. Finally, output the best matching frequency and its corresponding error value, thereby determining the optimal feature parameters of the signal.
- Load the signal data from flight phase 3 and perform Fast Fourier Transform (FFT) for frequency spectrum analysis to initially estimate the dominant frequency of the signal.
- Define an error function to calculate the mean squared error between the sine wave generated at a given frequency and the actual received signal.
- Use the Particle Swarm Optimization (PSO) algorithm to search within the frequency range estimated by the FFT to minimize the error function and find the optimal frequency. The program outputs the best frequency and its corresponding error value obtained through PSO optimization, providing a more accurate frequency estimate.
- Load the signal data from flight phase 4 and perform data cleaning by removing invalid data points.
- Use linear interpolation to reconstruct the signal and fill in the intermittent missing parts.
- Perform Fast Fourier Transform (FFT) on the reconstructed signal for frequency spectrum analysis, initially estimating the dominant frequency of the signal. Then, define an error function and use the Particle Swarm Optimization (PSO) algorithm to optimize the frequency estimation within the frequency range initially estimated by the FFT. Output the best frequency and its corresponding error value obtained through PSO optimization, providing an accurate frequency estimate.
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