Phase Difference Processing Using Combined α-β Filter and Kalman Filter

In signal processing applications, precise measurement of phase difference and its rate of change is critical for airborne single-station passive positioning systems. To enhance measurement accuracy, a combined approach using α-β filter and Kalman filter can be implemented. The α-β filter serves as a simple yet effective tracking filter that performs initial smoothing of phase difference measurements, effectively reducing noise interference. However, its fixed gain characteristics may lead to insufficient accuracy in dynamic environments.

For further optimization, the output from the α-β filter can be used as input to the Kalman filter. The Kalman filter leverages system state models and observation models through recursive computation to minimize the mean squared error of estimation, thereby providing more accurate estimates of both phase difference and its rate of change. This hybrid strategy maintains the computational efficiency of the α-β filter while significantly improving tracking accuracy in dynamic scenarios through the adaptive capabilities of the Kalman filter. Implementation typically involves establishing state transition matrices and designing appropriate measurement update equations.

Mean squared error (MSE) serves as a crucial performance metric for evaluating this method. Experimental comparisons demonstrate that compared to using the α-β filter alone, the combined approach significantly reduces the MSE of phase difference estimation, thereby providing more reliable data support for passive positioning systems. This methodology shows significant application potential in scenarios requiring high real-time performance and accuracy, such as airborne single-station passive positioning systems. Code implementation would typically involve parameter tuning for both filters and validation through Monte Carlo simulations.