Fast acquisition of weak eLoran signals via a uniform partitioned overlap-save algorithm exploiting temporal sparsity

Enhanced Loran (eLoran) provides resilient, wide-area positioning, navigation, and timing (PNT) services in the low-frequency band. However, receiver acquisition remains computationally demanding because of the long group repetition intervals (GRIs) and high sampling rates required for signal processing. Although the uniform partitioned overlap-save (UPOLS) algorithm has potential for matched filtering, its application to eLoran acquisition has not yet been explored. In this study, we propose the first UPOLS-based acquisition scheme tailored for eLoran signals. To address the computational bottleneck, we exploit the inherent temporal sparsity of eLoran pulses and develop a sparsity-aware acquisition method, termed the sparsity partitioned overlap-save (SPOLS) algorithm. Extensive simulations were conducted under additive white Gaussian noise (AWGN) and mixed noise-interference conditions, and performance was evaluated in terms of peak detection probability, root-mean-square error (RMSE), runtime, and memory footprint. Under AWGN conditions, SPOLS consistently detected the correlation peak at or near the true time of arrival (TOA) over a wide range of signal-to-noise ratios (SNRs), whereas the envelope delay correlation (EDC) method degraded rapidly as noise increased, showing peak shifts and spurious detections. At a fixed SNR with decreasing signal-to-interference ratio (SIR) from 10 to -25 dB, SPOLS maintained reliable detection with minimal bias, while EDC exhibited progressively distorted results. RMSE analysis showed that SPOLS achieved accuracy comparable to UPOLS and substantially outperformed EDC under moderate-to-low SNR and interference conditions. In addition, SPOLS reduced normalized runtime by approximately 45% relative to UPOLS and required less memory. These results demonstrate that SPOLS provides an effective balance among estimation accuracy, robustness, and computational complexity, making it well suited for TOA-based positioning and ranging in low-SNR and interference-prone environments, particularly in resource-constrained embedded systems.