Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained.

An adaptive digital phase-locked loop (DPLL) continually adjusts the noise bandwidth of the loop filter in global navigation satellite system (GNSS) receivers to track signals by measuring the signal-to-noise ratio and/or dynamic stress. Such DPLLs have a relatively large amount of computational complexity compared with the conventional DPLL. A table-based adaptive DPLL is proposed that adjusts the noise bandwidth value by extracting it from the pre-generated table without additional calculations. The values of the noise bandwidth table are computed in an optimal manner in consideration of the thermal noise, oscillator phase noise, and dynamic stress error. The calculation method of the proper integration time to maintain the stability of the loop filter is presented. Additionally, the simulation is configured using the trajectory analysis results from the Moon exploration mission and shows that the proposed algorithm operates stably in harsh environments, while a conventional fixed bandwidth loop cannot. The proposed algorithm has a similar phase jitter performance to the existing adaptive DPLL algorithms and has an execution time that is approximately 2.4–5.4 times faster. It is verified that the proposed algorithm is computationally efficient while maintaining jitter performance.

This study addresses a signal processing technique in a search and rescue system. An international disaster rescue communications support programme such as COSPAS‐ search and rescue satellite‐aided tracking (SARSAT) estimates the position of a beacon based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA) techniques. To backtrack signals from encrypted beacons without knowing the encryption codes, the cross ambiguity function (CAF) is proposed to estimate the TDOA and FDOA, in which high sampling rates are needed to increase the positioning accuracy of existing CAF algorithms, which entail high calculation loads. To overcome this, an interpolation method is proposed for peaks of Fourier transform capable of maintaining high accuracy at low calculation loads after a well‐performed initial acquisition. The numerical simulation shows an improved estimation accuracy of the proposed algorithm compared with existing peak detection methods.