TDoA with propagation delays based on IRI2016 electron densities

This is a follow-up of this blog post where the method referred to there is applied to TDoA maps. The first example is a STANAG 4285 signal (FUO Toulon) centered on 8436.4 kHz (USB: 8432.6 kHz)

TDoA maps using ground-wave propagation delays

TDoA using propagation delays based on IRI2016

The maps using propagation delays based on IRI2016 electron densities match better the (assumed) true position of the transmitter. It is a small effect but noticeable, and can be seen better in the side-by-side comparison below:

TDoA comparison

Another example are the TDoA maps from the last blog post where the TDoA maps based on more realistic propagation delays are more consistent between the two measurements; both indicate a position on the South coast of Cornwall:

TDoA comparison

TDoA comparison

TDoA code update

The TDoA code now does not explicitly use gnuplot any more. All plotting is done in octave. This will it make easier to extend the code (work in progress).

Recently some interesting signals have been independently observed by several people, see, e.g., tweet. These are frequency hopping signals.

Tuning a KiwiSDR to 7812 kHz two of the signal fit into its passband. Below are TDoA maps for these signals. Note that these maps are likely biased by the fact that some of the KiwiSDRs might receive the ground-wave signal and others a sky-wave signal.

TDoA maps

TDoA cross correlations

TDoA maps

TDoA cross corrlelations

Towards ionospheric ray-tracing

For the work on HF TDoA a realistic method for the signal delay is needed. Up to now, the great-circle distance divided by the speed of light is used which of course is incredibly naive. Nevertheless it seems to work, at least to some degree.

Rather than attempting a full-fledged ray-tracing simulation one can use the theorems of Breit and Tuve and Maryn's theorem for obtaining the signal propagation delay from virtual vertical height profiles, see, e.g, arXix:1104.2248 and here.

In order to evaluate this technique let us use the oblique ionograms measured by the University of Twente web SDR (thanks to PA3FWM for making these available! and for him and G3PLX for explanations):

The plots below show the time delay vs. UTC for two days in June at two different frequencies. Overlaid are time delays obtained by

• VOACAP: all propagation modes with probability>0.3 are shown,
• simulations explained above using electron density profiles obtained from the international reference ionosphere model IRI2016. 

(For this comparison the oblique ionograms have been corrected for a time offset of ~0.3ms whose origin is not yet clear)

All plots are generated using octave and this octave binding of the IRI2016 model.

As the IRI model is a climatological model (as is VOACAP), the agreement between model calculation and data is not expected to be perfect. Only the general features of these backscatter ionograms are reproduced, such as the 2-hop E-layer reflection for lower frequencies during mid-day but, e.g., not sporatic E-layer reflections in the late afternoon/evenings.

Note also that this simple method does not take into account magneto-ionic effects which become important for lower frequencies (and at local night-times).

Kalman filter position solution for the KiwiSDR

This is work in progress, updates can be found here on GitHub.

Using an extended Kalman filter for TDoA HF geo-location

In this post the precision of geo-location using TDoA on shortwave is explored using the data shown on this blog before.

The idea is to feed the time series of time differences into an extended Kalman filter (EKF) using two models for the propagation time from the transmitter to the receiver:

1) Simple ray-geometry for oblique propagation in the ionosphere:

• based on arXiv:1104.2248 which uses the Breit and Tuve + Martyn theorems to convert vertical to oblique incidence
• using vertical electron density profiles from the IRI2016 model as an input
• group refractive index: 1/sqrt(1-f_N²/f²), i.e., no magentoionic effects are taken into account
• when integrating over the group refractive index in the vertical direction, analytic integration of 1/sqrt(f(h)) is performed in each height interval in order to avoid the spurious numerical singularity at the reflection point
• spherical coordinates are used (r_E=6371km)

2) Alternatively, great-circle distances on the WGS84 ellipsoid are used:

• geographiclib adapted for octave

All receiver coordinates are assumed to be in WGS84, however in practice it is suspected that there are deviations from the true locations of up to 20 km, as the KiwiSDR positions are provided by the KiwiSDR owners and are not taken from the GPS position solutions used for time synchronization.

The plot below shows the output of the EKF

• implementation in octave following ADA285972
• state = [lat, lon] of the unknown position
• measurements = time differences between pairs of KiwiSDRs
• the measurements covariance matrix (constant) is build from the covariances of time differences (and is set to zero for time differences not sharing a common receiver)
• state covariance matrix = diag(0.01, 0.01)² deg² (constant)
• start covariance = diag(0.1, 0.1)² deg²
• there are about 60 measurements which are run 5 times sequentially through the EKF

Extended Kalman Filter (EKF) output; note that the range of the x(y) axis corresponds to approximately 17(67)km.

The simple ionosphere propagation model improves the match to the known position but there is still a remaining bias of about 30km North, 4km West. Clearly, more studies are needed in order to find out if this improvement is by chance or real.

De-chirping applied to a HF over the horizon radar signal (2)

This is a follow up to this blog post. Again the signals of the OTHR in Cyprus were analyzed using GPS time-stamped IQ samples from several KiwiSDRs.

In this case the OTHR signal was found between 13965 and 13985 kHz. The slope of the FMCW signal is μ=1MHz/s, and there are 50 sweeps per second. This results in a bandwidth of about 20kHz.

As is well known, the frequencies Δf of the spectrum of the de-chirped signal correspond to time delays τ=-Δf/μ in the case of a stationary target.

• for this one has to multiply the received signal with the original waveform
• tuning offsets w.r.t. center frequency of the OTHR signal correspond to a time delay of the original waveform
• when Δf is positive the delay corresponds to the frequency Δf-f_s (f_s is the sampling frequency), i.e. the ranges wrap around the x-axis.

Applying a 2nd Fourier transform to the time direction of time vs. Δf data one obtains the Doppler frequency f_d vs. Δf where f_d = v•λ/2 (for velocity v and wavelength λ). Here one has to be careful to adjust the phases in each bin to correct for the fact that the sampling times are not exactly aligned to multiples of 0.02 seconds.

Plots for 5 KiwiSDR are shown below. The splitting of the ionospheric reflection is most likely due to O- and X-mode propagation in the F layer.

13975 kHz 20180105T1114Z @CS5SEL; the band at f_d=0 is caused by an interference

13975 kHz 20180105T1114Z @DF0KL

13975 kHz 20180105T1114Z @G8JNJ

13975 kHz 20180105T1114Z @Izhvesk

13975 kHz 20180105T1114Z @Julisdalen

Thanks to all KiwiSDR owners who make their receivers available and do connect a GPS antenna.

TDoA measurements using GPS time-stamped IQ samples from KiwiSDRs (8)

Today I picked up a HF radar signal on 13500+-20 kHz. These are the time-differences between four KiwiSDRs:

TDoA 13490 kHz

This is most likely the Calypso CODAR radar system:

TDoA maps for 14390 kHz

Within the TDoA resolution the three sites in Ta'Sopu (Gozo), Ta'Barkat (Malta) and Pozzallo Harbour (Sicily) cannot be distinguished.

It is still puzzling for me that the TDoA maps seem to provide reasonable results, as for now great-circle distances are used, i.e., delays due to skywave propagation are not taken into account.