Skywave Delay Research Articles

Ionospheric delay estimation of Loran skywave using simple cosine model

ABSTRACT Ionospheric delay is the most significant source of error affecting the Loran skywave timing. To improve timing service, we propose a new ionospheric delay estimation method in this paper. It is a cosine model that combines the ionospheric physical characteristics and skywave delay variation law. This semi-empirical and semi-measured model has characteristics of accuracy and simplicity compared with the traditional method. The experimental results show that estimation error of the model is less than 1 µs for a single day and less than 2 µs for 3 days in the stable time. It is sufficient to correct more than 90% of delay when skywave passes through the ionosphere and is less affected by the season. This paper also gives some suggestions on the propagation of ionospheric coefficients required for the model. It allows broadcasting only by modifying the data channel message structure under the normal operation of Loran system.

Enhanced Loran skywave delay estimation based on artificial neural network in low SNR environment

This study proposes a high precision algorithm to estimate the Enhanced Loran skywave delay. It is based on the artificial neural network. The algorithm establishes a neural network model between the receiving Enhanced Loran signal and the skywave propagation delay. By training a large number of data, the neural network model can more accurately reflect the relationship between the receiving signal and the skywave delay. This is an innovative application of the skywave delay estimation algorithm in the Enhanced Loran receiving system, especially in low signal-to-noise ratio (SNR) environments. The experimental results show that the accuracy of this algorithm is about hundreds of nanoseconds in the condition of normal receiving SNR. The accuracy of the algorithm is about us in the condition of low SNR, while the previous algorithm cannot be used in this case. It has also been proved by the off-air data.

Skywave delay estimation in Enhanced Loran based on Extended Invariance Principle Weighted Fourier transform and Relaxation algorithm

A high precision algorithm is proposed to estimate the Enhanced Loran skywave delay, which is based on an Extended Invariance Principle Weighted Fourier transform and Relaxation (EXIP-WRELAX) algorithm. It is an innovation on the application of the skywave interference estimation algorithm in the Enhanced Loran receiver. Compared with existing algorithms, this algorithm has higher accuracy and lower computational complexity. Simulation results show that the proposed algorithm reduces the estimated error accuracy from ∼1000 to 50 m. At the same time, accurate search over the entire frequency domain is avoided, which greatly reduces the computational complexity. The algorithm is also proved by the off-air data.

Loran‐C skywave delay estimation using hybrid‐WRELAX algorithm

A hybrid weighted Fourier transform and relaxation (hybrid-WRELAX) method applied to Loran-C skywave delay estimation is presented. The performance of this method is demonstrated and compared with the spectrum analysis method. The hybrid-WRELAX method has been proved to provide higher accuracy to estimate the Loran-C skywave delay. Results testify this conclusion using off-air data.

A study of changes in apparent ionospheric reflection height within individual lightning flashes

Ionospheric reflection heights estimated using the zero-to-zero and peak-to-peak methods to measure skywave delay relative to the ground wave were compared for 108 first and 124 subsequent strokes at distances greater than 100km. For either metric there was a considerable decrease in average reflection height for subsequent strokes relative to first strokes. We showed that the observed difference cannot be explained by the difference in frequency content of first and subsequent return-stroke currents. Apparent changes in reflection height (estimated using the peak-to-peak method) within individual flashes for 54 daytime and 11 nighttime events at distances ranging from 50km to 330km were compared, and significant differences were found. For daytime conditions, the majority of the flashes showed either decrease (57%) or non-monotonic variation (39%) in reflection height with respect to the immediately preceding stroke. With respect to the first stroke, 91% of the flashes showed monotonic decrease in height. For nighttime flashes, patterns in reflection height changes with respect to the immediately preceding stroke were as follows: 46% no change, 27% monotonic decrease, and 27% non-monotonic variation. When changes were measured with respect to the first stroke, 54% of nighttime flashes showed monotonic decrease and 46% no change. Ionospheric reflection height tends to increase with return-stroke peak current. The observed daytime effects can be explained by (a) the dependence of EMP penetration depth on source intensity, which decreases with stroke order, (b) additional ionization associated with elves, or (c) combination of (a) and (b) above.

Low complexity sparse noise reduction method for Loran‐C skywave delay estimation

A sparse noise reduction method applied to Loran-C skywave delay estimation is presented, which is both simple and practicable. Signal sparsity is utilised to reduce the noise inside the Loran frequency band and significant improvement in the performance of estimation is achieved. The proposed method shows increased estimation accuracy with reduced computational complexity owing to no matrix inversion in the computation process.

High resolution techniques for Loran-C skywave delay estimation

Two high-resolution estimation techniques are applied to the problem of estimating the delays of the skywave components of signals input to Loran-C receivers. Their performance is evaluated and compared with that of a Fourier-based spectral-division technique. Simulation results show that the high-resolution algorithms improve the accuracy of the estimates significantly and estimate the skywave delay successfully in situations in which the Fourier-based method fails.

Loran-C skywave delay estimation using the AR algorithm

The autoregressive algorithm is applied to the problem of estimating the delay of skywaves in Loran-C receivers. The performance of the new technique is demonstrated and compared with an earlier FFT spectral-division method. The AR algorithm is shown to provide better resolution and to estimate the skywave delay successfully in situations in which the Fourier-based method fails. Results using off-air data confirm these conclusions.

Analysis of Envelope-to-Cycle Difference (ECD) in the Far Field

With the recent mid-continent expansion of LORAN in the United States and the worldwide increase in the use of LORAN in terrestrial and aviation applications, the understanding of propagation over land of LORAN signals has received renewed attention. This study focuses on two aspects of the ability of a LORAN receiver to select the correct zero crossing to track. First, it has long been thought that the negative change in Envelope to Dcyle Difference (ECD) s more rapid over land than seawater. Recent data has shown this not to be true and one purpose of this study is to develop a more accurate model of the variation of ECD with distance and ground conductivity. Second, with more groundwave attenuation over land than over seawater, skywave to groundwave ratios are larger and skywaves are potentially more of a problem. In our study we have developed a highly accurate model of pulses from solid state transmitters which allows the isolation of skywave from groundwave. This allows us to collect statistical data on skywave to groundwave ratio, skywave delay, and skywave ECD. These statistics, together with a knowledge of the frequency response of the receiver front end and the ECD estimation method, allow us to predict ECD bias and cycle selection problems due to skywave interference.

Effect of skywave interference on the coverage of loran-c

Receivers for the Loran-C terrestrial radio-navigation system are designed to distinguish pulses received by groundwave propagation from skywave interference components which arrive later. The technique, however, has significant limitations when implemented in receivers of finite bandwidth. The International Electrotechnical Commission and other authorities specify minimum standards of receiver performance in this respect. Drawing data from a range of sources, including Decca Navigator records, the paper proposes methods of predicting skywave-togroundwave ratio and skywave delay, the key elements of these specifications. This information is used to calculate the range limits due to skywave interference at various times and seasons, considering individual transmitters and both present and proposed Loran-C chains. The results demonstrate that the use of high transmitter powers is generally not justified. The paper points out ambiguities in the current minimum performance standards for receivers. It demonstrates that they are inadequate to protect users against the effects of skywave interference and identifies areas in which improved specifications are required.

The accuracy of sky-wave delay measurements

The paper describes an experimental investigation of the limitations imposed by the ionosphere upon the accuracy of sky-wave path-time measurements.The measurements were made at intervals between August, 1942, and the middle of 1944, covering the frequency range 2–16 Mc/s, and consisted of observations at vertical incidence and at oblique incidence over ranges up to 6000 km.The limiting accuracy of path-time measurement at vertical incidence was found to be of the order of ± 5 μsec, while at oblique incidence it was in the region of ± 10 to ± 20 μsec under normally favourable conditions.The instrumental techniques involved in the various phases of the work are briefly described, and the probable mechanism of the shortperiod variations about the mean path-time is discussed.