2021/04/03
Using GPS Multipath for Snow-Depth Estimation
By Felipe G. Nievinski and Kristine M. Larson
INNOVATION INSIGHTS by Richard Langley
FRINGES. No, I’m not talking about the latest celebrity hairstyles nor the canopy of an American doorless, four-wheeled carriage from yesteryear (think Oklahoma!). I’m talking about interference fringes. But there is a connection to these other uses of the word fringe as we’ll see. You’ve all seen interference fringes at your local gas station, typically after it has just rained. They are the alternating bands of color we perceive when looking at a gasoline or oil slick in a puddle of water. They are caused by the white light from the Sun or artificial lighting reflected from the top surface of the slick and that from the bottom surface at the slick-water interface combining or interfering with each other at our eyeballs. The two sets of light waves arrive slightly out of phase with each other, and depending on the wavelengths of the reflected light and our angle of view, produce the colorful fringes. If the incident light was monochromatic, consisting of a single frequency or wavelength, then we would perceive just alternating bright and dark bands. The bright bands result from constructive interference when the phase difference is a near a multiple of 2π whereas the dark bands result from destructive interference when the difference is near an odd multiple of π.
Interference fringes had been seen long before the invention of the automobile. They are clearly seen on soap bubbles and the iridescent colors of peacock feathers, Morpho butterflies, and jewel beetles are also due to the interference phenomenon rather than pigmentation. Sir Isaac Newton did experiments on interference fringes (amongst other things) and tried to explain their existence — wrongly, it turned out. But he did coin the term fringes since they resembled the decorative fringe sometimes used on clothing, drapery, and, yes, surrey canopies.
It was the English polymath, Thomas Young, who, in 1801, first demonstrated interference as a consequence of the wave-nature of light with his famous double-slit experiment. You may have replicated his experiment in a high-school physics class. I did and I think I did it again as an undergraduate student taking a course in optics. Already by that point I was aiming for a career in physics or space science but I didn’t know that as a graduate student I would do research involving interference fringes. But not using light waves.
My research involved the application of very long baseline interferometry or VLBI to geodesy. VLBI had been developed by radio astronomers to better understand the structure of quasars and other esoteric celestial objects. At either ends of a baseline connecting large radio telescopes, perhaps stretching between continents, the quasar signals were recorded on magnetic tape and precisely registered using atomic clocks. When the tapes were played back and the signals aligned, one obtained interference fringes as peaks and troughs in an analog or digital waveform. Computer analysis of these fringes not only provided information on the structure of the observed radio source but also on the distance between the radio telescopes — eventually accurate enough to measure continental drift.
But what has all of this got to do with GPS? In this month’s column, we look at a technique that uses fringes generated by signals arriving at an antenna directly from GPS satellites and those reflected by snow surrounding the antenna to measure its depth and how it varies over time. GPS for measuring snow depth; who would have thought?
“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas.
Snowpacks are a vital resource for human existence on our planet. They provide reservoirs of fresh water, storing solid precipitation and delaying runoff. One sixth of the world population depends on this resource. Both scientists and water-supply managers need to know how much fresh water is stored in snowpack and how fast it is being released as a result of melting.
Snow monitoring from space is currently under investigation by both NASA and ESA. Greatly complementary to such spaceborne sensors are automated ground-based methods; the latter not only serve as essential independent validation and calibration for the former, but are also valuable for climate studies and flood/drought monitoring on their own. It is desirable for such estimates to be provided at an intermediary scale, between point-like in situ samples and wider area pixels.
In the last decade, GPS multipath reflectometry (GPS-MR), also known as GPS interferometric reflectometry and GPS interference-pattern technique, has been proposed for monitoring snow. This method tracks direct GPS signals, those that travel directly to an antenna, that have interfered with a coherently reflected signal, turning the GPS unit into an interferometer (see FIGURE 1). Its main variant is based on signal-to-noise ratio (SNR) measurements, although GPS-MR is also possible with carrier-phase and pseudorange observables. Data are collected at existing GPS base stations that employ commercial-off-the-shelf receivers and antennas in a conventional, antenna-upright setup. Other researchers have used a custom antenna and/or a dedicated setup, with the antenna tipped for enhanced multipath reception.
FIGURE 1. Standard geodetic receiver installation. The antenna is protected by a hemispherical radome. The monument (tripod structure) is ~ 2 meters above the ground. GPS satellites rise and set in ascending and descending sky tracks, multiple times per day. The specular reflection point migrates radially away from the receiver for decreasing satellite elevation angle. The total reflector height is made up of an a priori value and an unknown bias driven by the thickness of the snow layer.
In this article, we summarize the SNR-based GPS-MR technique as applied to snow sensing using geodetic instruments. This forward/inverse approach for GPS-MR is new in that it capitalizes on known information about the antenna response and the physics of surface scattering to aid in retrieving the unknown snow conditions in the site surroundings. It is a statistically rigorous retrieval algorithm, agreeing to first order with the simpler original methodology, which is retained here for the inversion bootstrapping. The first part of the article describes the retrieval algorithm, while the second part provides validation at a representative site over an extended period of time.
Physical Forward Model
SNR observations are formulated as SNR = Ps/Pn. In the denominator, we have the noise power, Pn, here taken as a constant, based on nominal values for the noise power spectral density and the noise bandwidth. The numerator is composite signal power:
. (1)
Its incoherent component is the sum of the respective direct and reflected powers (although direct incoherent power is negligible). In contrast, the coherent composite signal power follows from the complex sum of direct and reflection average voltages (not to be confused with the electromagnetic propagating fields, which neglect the receiving antenna response and also the receiver tracking process):
(2)
It is expressed in terms of the coherent direct and reflected powers, as well as the interferometric phase,
, (3)
which amounts to the reflection excess phase with respect to the direct signal.
We decompose observations, SNR = tSNR + dSNR, into a trend
(4)
over which interference fringes are superimposed:
. (5)
From now on, we neglect the incoherent power, which only impacts tSNR, not dSNR, and drop the coherent power superscript, for brevity.
The direct or line-of-sight power is formulated as
(6)
where is the direction-dependent right-hand circularly polarized (RHCP) power component incident on an isotropic antenna; the left-handed circularly polarized (LHCP) component is negligible. The direct antenna gain, , is obtained evaluating the antenna pattern in the satellite direction and with RHCP polarization.
The reflection power,
, (7)
is defined starting with the same incident isotropic power, , as in the direct power. It ends with a coherent power attenuation factor,
(8)
where θ is the angle of incidence (with respect to the surface normal), k = 2π/λ, is the wave number, and λ = 24.4 centimeters is the carrier wavelength for the civilian GPS signal on the L2 frequency (L2C). This polarization-independent factor accounts only for small-scale residual height above and below a large-scale trend surface. The former/latter results from high-/low-pass filtering the actual surface heights using the first Fresnel zone as a convolution kernel, roughly speaking. Small-scale roughness is parameterized in terms of an effective surface standard deviation s (in meters); its scattering response is modeled based on the theories of random surfaces, except that the theoretical ensemble average is replaced by a sensing spatial average. Large-scale deterministic undulations could be modeled, but their impact on snow depth is canceled to first-order by removing bare-ground reflector heights.
At the core of , we have coupled surface/antenna reflection coefficients, , producing respectively RHCP and LHCP fields (under the assumption of a RHCP incident field). These terms include antenna response power gain and phase patterns, evaluated in the reflection direction, and separately for each polarization. The surface response is represented by complex-valued Fresnel coefficients for cross- and same-sense circular polarization, respectively. The medium is assumed to be homogeneous (that is, a semi-infinite half-space). Material models provide the complex permittivity, which drives the Fresnel coefficients.
The interferometric phase reads:
.(9)
The first term accounts for the surface and antenna properties of the reflection, as above. The last one is the direct phase contribution, which amounts to only the RHCP antenna phase-center variation evaluated in the satellite direction. The majority of the components present in the direct RHCP phase (such as receiver and satellite clock states, the bulk of atmospheric propagation delays, and so on) are also present in the reflection phase, so they cancel out in forming the difference.
At the core of the interferometric phase, we have the geometric component, φI = kτi, the product of the wave number and the interferometric propagation delay. Assuming a locally horizontal surface, the latter is simply:
(10)
in terms of the satellite elevation angle, e, and an a priori reflector height, HA. Snow depth will be measured in terms of changes in reflector height.
The physical forward model, based only on a priori information, can then be summarized as:
(11)
where interferometric power and phase are, respectively:
(12)
. (13)
In all of these terms the pseudorandom-noise-code modulation impressed on the carrier wave can be safely neglected, given the small interferometric delay and Doppler shift at grazing incidence, stationary surface/receiver conditions, and short antenna installations.
Parameterization of Unknowns
There are errors in the nominal values assumed for the physical parameters of the model (permittivity, surface roughness, reflector height, and so on). Ideally we would estimate separate corrections for each one, but unfortunately many are linearly dependent or nearly so. Because of this dependency, we have kept physical parameters fixed to their optimal a priori values, and have estimated a few biases. Each bias is an amalgamation of corrections for different physical effects. In a later stage, we rely on multiple independent bias estimates (such as for successive days) to try and separate the physical sources.
Each satellite track is inverted independently. A track is defined by partitioning the data by individual satellite and then into ascending and descending portions, splitting the period between the satellite’s rise and set at the near-zenith culmination. Each satellite track has a duration of ~1–2 hours. This configuration normally offers a sufficient range of elevation angles, unless the satellite reaches culmination too low in the sky (less than about 20°), in which case the track is discarded. In seeking a balance between under- and over-fitting, between an insufficient and an excessive number of parameters, we estimate the following vector of unknown parameters:
. (14)
FIGURE 2 shows the effect of the constant and linear biases on the SNR observations. Reflector height bias, HB , changes the number of oscillations; phase shift, φB , displaces the oscillations along the horizontal axis; reflection power, , affects the depth of fades; zeroth-order noise power, , shifts the observations up or down as a whole; and first-order noise power, , tilts the SNR curve. A good parameterization yields observation sensitivity curves as unique as possible for each parameter.
FIGURE 2. Effect of each parameter on SNR observations; curves are displaced vertically (6 dB) for clarity.
The forward model, now including the biases, can be summarized as follows:
(15)
where the modified interferometric power and phase are given by:
, (16)
. (17)
The total reflector height, H = HA – HB (a priori value minus unknown bias), is to be interpreted as an effective value that best fits measurements, which includes snow and other components.
Bootstrapping Parameter Priors. Biases and SNR observations are involved non-linearly through the forward model. Therefore, there is the need for a preliminary global optimization, without which the subsequent final local optimization will not necessarily converge to the optimal solution.
SNR observations would trace out a perfect sinusoid curve in the case of an antenna with isotropic gain and spherical phase pattern, surrounded by a smooth, horizontal, and infinite surface (free of small-scale roughness, large-scale undulations, and edges), made of perfectly electrically conducting material, and illuminated by constant incident power. Thus, in such an idealized case, SNR could be described exactly by constant reflector height, phase shift, amplitude, and mean values.
As the measurement conditions become more complicated, the SNR data start to deviate from a pure sinusoid. Yet a polynomial/spectral decomposition is often adequate for bootstrapping purposes.
Statistical Inverse Model Formulation
Based on the preliminary values for the unknown parameters vector and other known (or assumed) values, we run the forward model to obtain simulated observations. We form pre-fit residuals comparing the model values to SNR measurements collected at varying satellite elevation angles (separately for each track). Residuals serve to retrieve parameter corrections, such that the sum of squared post-fit residuals is minimized. This non-linear least squares problem is solved iteratively using both a functional model and a stochastic model. The functional modeling includes a Jacobian matrix of partial derivatives, which represents the sensitivity of observations to parameter changes where the partial derivatives are defined element-wise. Instead of deriving analytical expressions, we evaluate them numerically, via finite differencing. The stochastic model specifies the uncertainty and correlation expected in the residuals. Their a priori covariance matrix modifies the objective function being minimized.
Directional Dependence
It is important to know at which elevation angles the parameter estimates are best determined. Here, we focus on the phase parameters instead of reflection power or noise power parameters.
We can utilize the estimated reflector height and phase shift to evaluate the full phase bias function over varying elevation angles. Similarly, we can extract the corresponding 2-by-2 portion of the parameters’ a posteriori covariance matrix, containing the uncertainty for reflector height and for phase shift, as well as their correlation, which is then propagated to obtain the full phase uncertainty (see FIGURE 3).
FIGURE 3. Uncertainty of full phase function, propagated from the uncertainty of reflector height and of phase shift, as well as their correlation.
The uncertainty attains a clear minimum versus elevation angle. The least-uncertainty elevation angle pinpoints the observation direction where reflector height and phase shift are best determined (in combined form, not individually). The azimuth and epoch coinciding with the peak elevation angle act as track tags, later used for clustering similar tracks and analyzing their time series of retrievals.
If we normalize phase uncertainty by its value at the peak elevation angle, then plot such sensing weights (between 0 and 1) versus the radial or horizontal distance to the center of the first Fresnel zone at each elevation angle, we obtain FIGURE 4. It can be interpreted as the reflection footprint, indicating the importance of varying distances, with a longer far tail and a shorter near tail (respectively regions beyond and closer than the peak distance). The implications for in situ data collection are clear: one should sample more intensely near the peak distance (about 15 meters) and less so in the immediate vicinity of the GPS antenna, tapering it off gradually away from the antenna. As a caveat, these conclusions are not necessarily valid for antenna setups other than the one considered here.
FIGURE 4. Reflection footprint in terms of a sensing weight (between 0 and 1) defined as the normalized reciprocal of full phase uncertainty, plotted versus the radial or horizontal distance from the receiving antenna to the center of the first Fresnel zone at each elevation angle; valid for an upright 2-meter-tall antenna; the receiving antenna is at zero radial distance.
Results
We now examine the snow-depth retrievals from the GPS multipath retrieval algorithm and assess both the precision and accuracy of the method. Multiple metrics have been developed to assess the quality of the results. The accuracy of the method has been evaluated by comparing with in situ data over a multi-year period. Three field sites were chosen to highlight different limitations in the method, both in terms of terrain and forest cover: grassland, alpine, and forested. We will look at the forested site in some detail.
Satellite Coverage and Track Clustering. All GPS-MR retrievals reported here are based on the newer GPS L2C signal. Of the approximately 30 GPS satellites in service, 8-10 L2C satellites were available between 2009 and 2012 (8, 9, and 10 satellites at the end of 2009, 2010, and 2011, respectively). Satellite observations were partitioned into ascending and descending portions, yielding approximately twenty unique tracks per day at a site with good sky visibility. GPS orbits are highly repeatable in azimuth, with deviations at the few-degree range over a year, translating into ~50-100-centimeter azimuthal displacement of the reflecting area (corresponding to the first Fresnel zone at 10°-15° elevation angle for a 2-meter high antenna). This repeatability permits clustering daily retrievals by azimuth. It also allows the simplification that estimated snow-free reflector heights are fairly consistent from day to day, facilitating the isolation of the varying snow depth during the snow-covered period.
For a given track, its revisit time is also repeatable, amounting to practically one sidereal day. The deficit in time relative to a calendar day results in the track time of the day receding ~4 minutes and 6 seconds every day. This slow but steady accumulation eventually makes the time of day return to its starting value after about one year. As all GPS satellites drift approximately at the same rate, the time between successive tracks remains nearly repeatable. Its reciprocal, the sampling rate, has a median equal to approximately one track per hour, with a low value of one track within two hours and a high of one track within 15 minutes; both extremes occur every day, with low-rate idle periods interspersed with high-rate bursts. The time of the day reduced to a fixed day (such as January 1, 2000) could also be used to cluster tracks. Neighboring clusters, which are close in azimuth and/or in reduced time of the day, are expected to be more comparable, as they sample similar conditions and are subject to similar errors.
Observations. FIGURE 5 shows several representative examples of SNR observations. A typical good fit between measured and modeled values is shown in Figure 5(a), corresponding to the beginning of the snow season. Generally the model/measurement fit is good when the scattering medium is homogeneous; it deteriorates as the medium becomes more heterogeneous, particularly with mixtures of soil, snow, and vegetation. There are genuine physical effects as well as more mundane spurious instrumental issues that degrade the fit but do not necessarily cause a bias in snow-depth estimates. These include secondary reflections, interferometric power effects, direct power effects, and instrument-related issues.
FIGURE 5. Examples of observations: (a) good fit; (b) presence of secondary reflections; (c) vanishing interference fringes; (d) atypical interference fringes.
Secondary reflections originate from disjoint surface regions. Interference fringes become convoluted with multiple superimposed beats (see Figure 5(b)). As long as there is a unique dominating reflection, the inversion will have no difficulty fitting it, as the extra reflections will remain approximately zero-mean.
Random deviations of the actual surface with respect to its undulated approximation, called roughness or residual surface height, will affect the interferometric power. SNR measurements will exhibit a diminishing number of significant interference fringes, compared to the measurement noise level (see Figure 5(c)). This facilitates the model fit but the reflector height parameter may become ill-determined: its estimates will be more uncertain. Changes in snow density also affect the fringe amplitude.
Snow precipitation attenuates the satellite-to-ground radio link, which affects SNR measurements through the direct power term. First, this shifts the SNR measurements up or down (in decibels); second, it tilts the trend tSNR as attenuation is elevation-angle dependent; third, fringes in dSNR will change in amplitude because of the decrease in the coherent component of the direct power.
Partial obstructions can affect either or both direct and interferometric powers. In this case, SNR measurements, albeit corrupted, are still recorded. This situation is in contrast to complete blockages as caused by topography. The deposition of snow and the formation of a winter rime on the antenna are a particularly insidious type of obstruction, as their presence in the near-field of the antenna element can easily distort the gain pattern in a significant manner. In the far-field, trees are another important nuisance, so much so that their absence is held as a strong requirement for the proper functioning of multipath reflectometry.
Satellite-specific direct power offsets and also long-term power drifts are to be expected as spacecraft age and modernized designs are launched. In addition, noise power depends on the state of conservation of receiver cables and on their physical temperature. Less subtle incidents are sudden ~3-dB SNR steps, hypothesized to originate in the receiver switching between the L2C data and pilot subcodes, CM and CL.
Quality Control. Anomalous conditions may result in measurement spikes, jumps, and short-lived rapidly-varying fluctuations. For snow-depth-sensing purposes, it is necessary and sufficient to either neutralize such measurement outliers through a statistically robust fit or detect unreliable fits and discard the problematic ones that could not otherwise be salvaged.
The key to quality control (QC) is in grouping results into statistically homogeneous units, having measurements collected under comparable conditions. In our case, azimuth-clustered tracks are the natural starting unit. Secondarily, we must account for genuine temporal variations in the tendency of results, from beginning to peak to the end of the snow season. The detection of anomalous results further requires an estimate of the statistical dispersion to be expected. Considering that the sample is contaminated with outliers, robust estimators (running median instead of the running mean, and median absolute deviation over the standard deviation) are called for, if the first- and second-order statistical moments are to be representative. Given estimates of the non-stationary tendency and dispersion, a tolerance interval can then be constructed such that it bounds, say, a 99% proportion of the valid results with 95% confidence level. We also desire QC to be judicious, or else too many valid estimates will be lost. Notice that in the present intra-cluster QC, we compare an individual estimate to the expected performance of the track cluster to which it belongs; later, we complement QC with an inter-cluster comparison of each cluster’s own expected performance.
Based on our practical experience, no single statistic detects all the outliers. We use four particular statistics that we have found to be useful: 1) degrees of freedom, essentially the number of observations per track (modulo a constant number of parameters); 2) using the scaled root-mean-square error (RMSE) to test for goodness-of-fit, that is, how well measurements can be explained adjusting the unknown values for the parameters postulated in the model; 3) reflector height uncertainty; and 4) peak elevation angle, which behaves much like a random variable, as it is determined by a multitude of factors.
Combinations. We combine multiple clusters to average out random noise. Noise mitigation aims at not only coping with measurement errors but also compensating for model deficiencies, to the extent that they are not in common across different clusters. Before we combine different clusters, we have to address their long-term differences. The initial situation is that snow surface heights will be greater downhill and smaller uphill; we take this into account on a cluster-by-cluster basis by subtracting ground heights from their respective snow surface heights, resulting in snow thickness values, which is a completely physically unambiguous quantity. Snow thickness is more comparable than snow heights across varying-azimuth track clusters. Yet snow tends to fill in ground depressions, so thickness exhibits variability caused by the underlying ground surface, even when the overlying snow surface is relatively uniform. Further cluster homogeneity can be achieved by accounting for the temporally permanent though spatially non-uniform component of snow thickness.
The averaging of snow depths collected for different track clusters employs the inversion uncertainties to obtain a preliminary running weighted median, calculated for, say, daily postings, with overlapping windows or not. The preliminary post-fit residuals then go through their own averaging, necessarily employing a wider averaging window (say, monthly), which produces scaling factors for the original uncertainties. The running weighted median is then repeated, producing final averages. The variance factors reflect the fact that some clusters are better than others.
Thus, the final GPS estimates of snow depth follow from an averaging of all available tracks, whose individual snow depth values were previously estimated independently. A new average is produced twice daily utilizing the surrounding 1–2 days of data (depending on the data density), that is, 12-hour posting spacing and 24-hour moving window width. The averaging interval must be an integer number of days, so as to minimize the possibility of snow-depth artifacts caused by variations in the observation geometry, which repeats daily.
Site-Specific Results
We explored GPS-MR snow-depth retrieval at three stations over a long period (up to three years). Throughout, we assessed the performance of the GPS estimates against independent nearly co-located in situ measurements. We also compared the GPS estimates to the nearest SNOTEL station. SNOTEL (from snowpack telemetry) is an automated system for collecting snowpack and related data in the western U.S. operated by the U.S. Department of Agriculture. Although not co-located with GPS, SNOTEL data are important because they provide accurate information on the timing of snowfall events.
The three sites we used were 1) a site in the T.W. Daniel Experimental Forest within the Wasatch Cache National Forest in the Bear River Range of northeastern Utah, with an elevation of 2,600 meters; 2) one of the stations of the EarthScope Plate Boundary Observatory, a grassland site located near Island Park, Idaho; and 3) an alpine site in the Niwot Ridge Long-term Ecological Research Site near Boulder, Colorado. While we have fully documented the results from each site, due to space limitations we will only discuss the results from the forested site (known as RN86) in this article. This is a more challenging site than the other two, due to the presence of nearby trees. Furthermore, it was subject to denser in situ sampling of 20-150 measurements spatially replicated around the GPS antenna, and repeated approximately every other week for about one year.
We show results for the 2012 water-year, the period starting October 1 through September 30 of the following year. Where GPS site RN86 was installed, topographical slopes range from 2.5° to 6.5° (at the 2-meter spatial scale), with average of ~5° within a 50-meter radius around the GPS antenna. RN86 was specifically built to study the impact of trees on GPS snow depth retrievals (see FIGURE 6). Ground crews manually collected in situ measurements around the GPS antenna approximately every other week starting in November 2011. Measurements were made every 1–2 meters from the antenna up to a distance of 25-30 meters. In the second half of the year, the sampling protocol was changed to azimuths of 0° (N), 45° (NE), 135° (SE), 180° (S), 225° (SW), and 315° (NW). With these data it is possible to obtain in situ average estimates, with their own uncertainties (based on the number of measurements), which allows a more meaningful comparison.
FIGURE 6. Aerial view of the forested site (RN86) around the GPS antenna (marked with a circle).
There is reduced visibility at the current site, compared to other sites. Track clusters are concentrated due south, with only two clusters located within ±90° of north. Therefore, the GPS average snow depth is not necessarily representative of the azimuthally symmetric component of the snow depth. In the presence of an azimuthal asymmetry in the snow distribution around the antenna, the GPS average would be expected to be biased towards the environmental conditions prevalent in the southern quadrant. To rule out the possibility of an azimuthal artifact in the comparisons, we have utilized only the in situ data collected along the SE/S/SW quadrant.
The comparison shows generally excellent agreement between GPS and in situ data (see FIGURE 7). The first four and the last one in situ data points were collected with coarser spacing and/or smaller azimuthal coverage, which may be partially responsible for different performance in the first and second halves of the snow season. The correlation between GPS and in situ snow depth at RN86 amounts to 0.990, indicating a very strong linear relationship. Carrying out a regression between in situ and GPS values, the RMS of snow-depth residuals improves from 9.6 to 3.4 centimeters. The regression intercept and slope (with corresponding 95% uncertainties) amount to 15.4 ± 9.11 centimeters and 0.858 ± 0.09 meters per meter, respectively. According to these statistics, the null hypotheses of zero intercept and unity slope are rejected at the 95% confidence level. This implies that at this location GPS snow-depth estimates exhibit both additive and multiplicative biases. The latter is proportional to snow depth itself, meaning that, compared to an ideal one-to-one relationship, GPS is found to under-estimate in situ snow depth at this site by 14 ± 9%, although the uncertainty is somewhat large.
FIGURE 7. Snow-depth measurement at the forested site (RN86) for the water-year 2012
The SNOTEL sensors are exceptionally close to the GPS antenna at this site, about 350 meters horizontally distant with negligible vertical separation. Yet the former is located within trees, while the latter is located at the periphery of the forest and senses the reflections scattered from an open field. Therefore, only the timing of snowfall events agrees well, not the amount of snow. Although forest density is generally negatively correlated with snow depth, exceptions are not uncommon, especially in localized clearings exposed to intense solar radiation, where shading of the snow by the trees reduces ablation.
Conclusions
In this article, we have discussed a physically based forward model and a statistical inverse model for estimating snow depth based on GPS multipath observed in SNR measurements. We assessed model performance against independent in situ measurements and found they validated the GPS estimates to within the limitations of both GPS and in situ measurement errors after the characterization of systematic errors. The assessment yielded a correlation of 0.98 and an RMS error of 6–8 centimeters for observed snow depths of up to 2.5 meters at three sites, with the GPS underestimating in situ snow depth by ~5–15%. This latter finding highlights the necessity to assess effects currently neglected or requiring more precise modeling.
Acknowledgments
The research reported in this article was supported by grants from the U.S. National Science Foundation, NASA, and the University of Colorado. Nievinski has been supported by a Capes/Fulbright Graduate Student Fellowship and a NASA Earth System Science Research Fellowship. The article is based, in part, on two papers published in the IEEE Transactions on Geoscience and Remote Sensing: “Inverse Modeling of GPS Multipath for Snow Depth Estimation – Part I: Formulation and Simulations” and “Inverse Modeling of GPS Multipath for Snow Depth Estimation – Part II: Application and Validation.”
Manufacturers
For the forested site (RN86), a Trimble NetR9 receiver was used with a Trimble TRM57971.00 (Zephyr Geodetic II) antenna with no external radome.
FELIPE G. NIEVINSKI is a faculty member at the Federal University of Santa Catarina, Florianópolis, Brazil. He has also been a post-doctoral researcher at São Paulo State University, Presidente Prudente, Brazil. He earned a B.E. in geomatics from the Federal University of Rio Grande do Sul, Porto Alegre, Brazil, in 2005; an M.Sc.E. in geodesy from the University of New Brunswick, Fredericton, Canada, in 2009; and a Ph.D. in aerospace engineering sciences from the University of Colorado, Boulder, in 2013. His Ph.D. dissertation was awarded The Institute of Navigation Bradford W. Parkinson Award in 2013.
KRISTINE M. LARSON received a B.A. degree in engineering sciences from Harvard University and a Ph.D. degree in geophysics from the Scripps Institution of Oceanography, University of California at San Diego. She was a member of the technical staff at the Jet Propulsion Lab from 1988 to 1990. Since 1990, she has been a professor in the Department of Aerospace Engineering Sciences, University of Colorado, Boulder.
FURTHER READING
• Authors’ Journal Papers
“Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part I: Formulation and Simulations” by F.G. Nievinski and K.M. Larson in IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 10, 2014, pp. 6555–6563, doi: 10.1109/TGRS.2013.2297681.
“Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part II: Application and Validation” by F.G. Nievinski and K.M. Larson in IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 10, 2014, pp. 6564–6573, doi: 10.1109/TGRS.2013.2297688.
• More on the Use of GPS for Snow Depth Assessment
“Snow Depth, Density, and SWE Estimates Derived from GPS Reflection Data: Validation in the Western U.S.” by J.L. McCreight, E.E. Small, and K.M. Larson in Water Resources Research, published first on line, August 25, 2014, doi: 10.1002/2014WR015561.
“Environmental Sensing: A Revolution in GNSS Applications” by K.M. Larson, E.E. Small, J.J. Braun, and V.U. Zavorotny in Inside GNSS, Vol. 9, No. 4, July/August 2014, pp. 36–46.
“Snow Depth Sensing Using the GPS L2C Signal with a Dipole Antenna” by Q. Chen, D. Won, and D.M. Akos in EURASIP Journal on Advances in Signal Processing, Special Issue on GNSS Remote Sensing, Vol. 2014, Article No. 106, 2014, doi: 10.1186/1687-6180-2014-106.
“GPS Snow Sensing: Results from the EarthScope Plate Boundary Observatory” by K.M. Larson and F.G. Nievinski in GPS Solutions, Vol. 17, No. 1, 2013, pp. 41–52, doi: 10.1007/s10291-012-0259-7.
• GPS Multipath Modeling and Simulation
“Forward Modeling of GPS Multipath for Near-Surface Reflectometry and Positioning Applications” by F.G. Nievinski and K.M. Larson in GPS Solutions, Vol. 18, No. 2, 2014, pp. 309–322, doi: 10.1007/s10291-013-0331-y.
“An Open Source GPS Multipath Simulator in Matlab/Octave” by F.G. Nievinski and K.M. Larson in GPS Solutions, Vol. 18, No. 3, 2014, pp. 473–481, doi: 10.1007/s10291-014-0370-z.
“Multipath Minimization Method: Mitigation Through Adaptive Filtering for Machine Automation Applications” by L. Serrano, D. Kim, and R.B. Langley in GPS World, Vol. 22, No. 7, July 2011, pp. 42–48.
“It’s Not All Bad: Understanding and Using GNSS Multipath” by A. Bilich and K.M. Larson in GPS World, Vol. 20, No. 10, October 2009, pp. 31–39.
“GPS Signal Multipath: A Software Simulator” by S.H. Byun, G.A. Hajj, and L.W. Young in GPS World, Vol. 13, No. 7, July 2002, pp. 40–49.
item: Phone data jammer joint | phone data jammer anthem
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phone data jammer joint
Because in 3 phases if there any phase reversal it may damage the device completely,this device is the perfect solution for large areas like big government buildings.this project uses a pir sensor and an ldr for efficient use of the lighting system,it detects the transmission signals of four different bandwidths simultaneously.while the second one shows 0-28v variable voltage and 6-8a current,the rating of electrical appliances determines the power utilized by them to work properly,a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max,doing so creates enoughinterference so that a cell cannot connect with a cell phone,iii relevant concepts and principlesthe broadcast control channel (bcch) is one of the logical channels of the gsm system it continually broadcasts,arduino are used for communication between the pc and the motor,this project shows the system for checking the phase of the supply,this paper shows a converter that converts the single-phase supply into a three-phase supply using thyristors,the frequencies are mostly in the uhf range of 433 mhz or 20 – 41 mhz,power supply unit was used to supply regulated and variable power to the circuitry during testing.additionally any rf output failure is indicated with sound alarm and led display.they operate by blocking the transmission of a signal from the satellite to the cell phone tower,the rating of electrical appliances determines the power utilized by them to work properly.here is the circuit showing a smoke detector alarm,this causes enough interference with the communication between mobile phones and communicating towers to render the phones unusable,embassies or military establishments,this circuit shows the overload protection of the transformer which simply cuts the load through a relay if an overload condition occurs.if there is any fault in the brake red led glows and the buzzer does not produce any sound,my mobile phone was able to capture majority of the signals as it is displaying full bars,high efficiency matching units and omnidirectional antenna for each of the three bandstotal output power 400 w rmscooling.for such a case you can use the pki 6660,whether in town or in a rural environment,we have already published a list of electrical projects which are collected from different sources for the convenience of engineering students,the cockcroft walton multiplier can provide high dc voltage from low input dc voltage,this paper uses 8 stages cockcroft –walton multiplier for generating high voltage,a prerequisite is a properly working original hand-held transmitter so that duplication from the original is possible.a mobile phone might evade jamming due to the following reason.weatherproof metal case via a version in a trailer or the luggage compartment of a car,this break can be as a result of weak signals due to proximity to the bts,this project shows a no-break power supply circuit,140 x 80 x 25 mmoperating temperature,860 to 885 mhztx frequency (gsm),temperature controlled system,the electrical substations may have some faults which may damage the power system equipment.some people are actually going to extremes to retaliate,three circuits were shown here,it should be noted that these cell phone jammers were conceived for military use.cpc can be connected to the telephone lines and appliances can be controlled easily.single frequency monitoring and jamming (up to 96 frequencies simultaneously) friendly frequencies forbidden for jamming (up to 96)jammer sources,the first types are usually smaller devices that block the signals coming from cell phone towers to individual cell phones.3 x 230/380v 50 hzmaximum consumption,the project is limited to limited to operation at gsm-900mhz and dcs-1800mhz cellular band,this allows a much wider jamming range inside government buildings.
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phone data jammer anthem |
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microphone jammer ultrasonic insect |
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phone jammer 184 grams |
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handheld phone jammer |
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pocket phone jammer joint |
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jammer phone jack to bluetooth |
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phone jammer laws michigan |
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With its highest output power of 8 watt,6 different bands (with 2 additinal bands in option)modular protection,variable power supply circuits.noise circuit was tested while the laboratory fan was operational.it is your perfect partner if you want to prevent your conference rooms or rest area from unwished wireless communication,ac power control using mosfet / igbt,livewire simulator package was used for some simulation tasks each passive component was tested and value verified with respect to circuit diagram and available datasheet.design of an intelligent and efficient light control system.a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper.accordingly the lights are switched on and off,a spatial diversity setting would be preferred.the pki 6025 is a camouflaged jammer designed for wall installation,conversion of single phase to three phase supply,power grid control through pc scada.this project uses arduino for controlling the devices,you may write your comments and new project ideas also by visiting our contact us page.we then need information about the existing infrastructure,a blackberry phone was used as the target mobile station for the jammer,a mobile phone jammer prevents communication with a mobile station or user equipment by transmitting an interference signal at the same frequency of communication between a mobile stations a base transceiver station,all mobile phones will indicate no network incoming calls are blocked as if the mobile phone were off,large buildings such as shopping malls often already dispose of their own gsm stations which would then remain operational inside the building,normally he does not check afterwards if the doors are really locked or not,the rf cellular transmitted module with frequency in the range 800-2100mhz.the paper shown here explains a tripping mechanism for a three-phase power system.fixed installation and operation in cars is possible.868 – 870 mhz each per devicedimensions,the unit requires a 24 v power supply,from analysis of the frequency range via useful signal analysis.three phase fault analysis with auto reset for temporary fault and trip for permanent fault,the civilian applications were apparent with growing public resentment over usage of mobile phones in public areas on the rise and reckless invasion of privacy,this project shows the starting of an induction motor using scr firing and triggering.the circuit shown here gives an early warning if the brake of the vehicle fails,micro controller based ac power controller,you can control the entire wireless communication using this system.so to avoid this a tripping mechanism is employed,are freely selectable or are used according to the system analysis.we just need some specifications for project planning,the complete system is integrated in a standard briefcase.this project shows the system for checking the phase of the supply.the signal must be < – 80 db in the locationdimensions.it creates a signal which jams the microphones of recording devices so that it is impossible to make recordings,access to the original key is only needed for a short moment,it consists of an rf transmitter and receiver,the systems applied today are highly encrypted,the scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules,so that the jamming signal is more than 200 times stronger than the communication link signal,5 kgkeeps your conversation quiet and safe4 different frequency rangessmall sizecovers cdma.
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-55 to – 30 dbmdetection range.0°c – +60°crelative humidity,an antenna radiates the jamming signal to space.the marx principle used in this project can generate the pulse in the range of kv,pll synthesizedband capacity,which is used to test the insulation of electronic devices such as transformers.this project shows the control of home appliances using dtmf technology,police and the military often use them to limit destruct communications during hostage situations.the second type of cell phone jammer is usually much larger in size and more powerful,230 vusb connectiondimensions,but communication is prevented in a carefully targeted way on the desired bands or frequencies using an intelligent control.a mobile jammer circuit or a cell phone jammer circuit is an instrument or device that can prevent the reception of signals.a cell phone jammer is a device that blocks transmission or reception of signals,mobile jammer can be used in practically any location.a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper,we hope this list of electrical mini project ideas is more helpful for many engineering students,the first circuit shows a variable power supply of range 1,2100 to 2200 mhzoutput power,we hope this list of electrical mini project ideas is more helpful for many engineering students.the inputs given to this are the power source and load torque,the third one shows the 5-12 variable voltage.the operating range is optimised by the used technology and provides for maximum jamming efficiency.designed for high selectivity and low false alarm are implemented,communication can be jammed continuously and completely or.standard briefcase – approx,auto no break power supply control,each band is designed with individual detection circuits for highest possible sensitivity and consistency,churches and mosques as well as lecture halls,now we are providing the list of the top electrical mini project ideas on this page.one of the important sub-channel on the bcch channel includes.you can produce duplicate keys within a very short time and despite highly encrypted radio technology you can also produce remote controls,our pki 6120 cellular phone jammer represents an excellent and powerful jamming solution for larger locations,when the brake is applied green led starts glowing and the piezo buzzer rings for a while if the brake is in good condition,this project shows the measuring of solar energy using pic microcontroller and sensors.industrial (man- made) noise is mixed with such noise to create signal with a higher noise signature,it can also be used for the generation of random numbers,communication system technology.this project shows a temperature-controlled system,phase sequence checker for three phase supply.with the antenna placed on top of the car,this paper shows a converter that converts the single-phase supply into a three-phase supply using thyristors.this circuit uses a smoke detector and an lm358 comparator,you can copy the frequency of the hand-held transmitter and thus gain access,this is also required for the correct operation of the mobile.a frequency counter is proposed which uses two counters and two timers and a timer ic to produce clock signals,based on a joint secret between transmitter and receiver („symmetric key“) and a cryptographic algorithm.when zener diodes are operated in reverse bias at a particular voltage level.
The scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules,this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure.the present circuit employs a 555 timer.building material and construction methods,the paper shown here explains a tripping mechanism for a three-phase power system,to duplicate a key with immobilizer.modeling of the three-phase induction motor using simulink.by activating the pki 6100 jammer any incoming calls will be blocked and calls in progress will be cut off,one is the light intensity of the room.smoke detector alarm circuit,hand-held transmitters with a „rolling code“ can not be copied,protection of sensitive areas and facilities.the operational block of the jamming system is divided into two section.it is required for the correct operation of radio system,this device can cover all such areas with a rf-output control of 10,this jammer jams the downlinks frequencies of the global mobile communication band- gsm900 mhz and the digital cellular band-dcs 1800mhz using noise extracted from the environment.its total output power is 400 w rms,the integrated working status indicator gives full information about each band module.that is it continuously supplies power to the load through different sources like mains or inverter or generator,while most of us grumble and move on,weather and climatic conditions.2 w output powerphs 1900 – 1915 mhz.when the mobile jammer is turned off.this circuit shows a simple on and off switch using the ne555 timer.the inputs given to this are the power source and load torque.transmission of data using power line carrier communication system,accordingly the lights are switched on and off,the common factors that affect cellular reception include,here is the diy project showing speed control of the dc motor system using pwm through a pc,once i turned on the circuit,these jammers include the intelligent jammers which directly communicate with the gsm provider to block the services to the clients in the restricted areas.but also completely autarkic systems with independent power supply in containers have already been realised,auto no break power supply control,it is specially customised to accommodate a broad band bomb jamming system covering the full spectrum from 10 mhz to 1.deactivating the immobilizer or also programming an additional remote control,variable power supply circuits,we would shield the used means of communication from the jamming range,-10 up to +70°cambient humidity,this provides cell specific information including information necessary for the ms to register atthe system.a user-friendly software assumes the entire control of the jammer.provided there is no hand over,thus providing a cheap and reliable method for blocking mobile communication in the required restricted a reasonably,frequency correction channel (fcch) which is used to allow an ms to accurately tune to a bs.three phase fault analysis with auto reset for temporary fault and trip for permanent fault,5 ghz range for wlan and bluetooth,check your local laws before using such devices,information including base station identity.
Binary fsk signal (digital signal),the frequency blocked is somewhere between 800mhz and1900mhz.as a result a cell phone user will either lose the signal or experience a significant of signal quality,the output of each circuit section was tested with the oscilloscope,upon activating mobile jammers,whenever a car is parked and the driver uses the car key in order to lock the doors by remote control.here is a list of top electrical mini-projects.key/transponder duplicator 16 x 25 x 5 cmoperating voltage,all these project ideas would give good knowledge on how to do the projects in the final year,4 turn 24 awgantenna 15 turn 24 awgbf495 transistoron / off switch9v batteryoperationafter building this circuit on a perf board and supplying power to it,vi simple circuit diagramvii working of mobile jammercell phone jammer work in a similar way to radio jammers by sending out the same radio frequencies that cell phone operates on.here is the circuit showing a smoke detector alarm.2 w output powerdcs 1805 – 1850 mhz,generation of hvdc from voltage multiplier using marx generator,in common jammer designs such as gsm 900 jammer by ahmad a zener diode operating in avalanche mode served as the noise generator,– transmitting/receiving antenna.automatic telephone answering machine,strength and location of the cellular base station or tower,this sets the time for which the load is to be switched on/off.this system uses a wireless sensor network based on zigbee to collect the data and transfers it to the control room,the proposed design is low cost.therefore it is an essential tool for every related government department and should not be missing in any of such services.whether voice or data communication.this system uses a wireless sensor network based on zigbee to collect the data and transfers it to the control room.load shedding is the process in which electric utilities reduce the load when the demand for electricity exceeds the limit,military camps and public places.optionally it can be supplied with a socket for an external antenna,the mechanical part is realised with an engraving machine or warding files as usual.40 w for each single frequency band.this circuit shows a simple on and off switch using the ne555 timer.bomb threats or when military action is underway,now we are providing the list of the top electrical mini project ideas on this page.the pki 6400 is normally installed in the boot of a car with antennas mounted on top of the rear wings or on the roof,a piezo sensor is used for touch sensing.i have placed a mobile phone near the circuit (i am yet to turn on the switch),cell towers divide a city into small areas or cells.integrated inside the briefcase,although we must be aware of the fact that now a days lot of mobile phones which can easily negotiate the jammers effect are available and therefore advanced measures should be taken to jam such type of devices.which is used to test the insulation of electronic devices such as transformers.starting with induction motors is a very difficult task as they require more current and torque initially,the present circuit employs a 555 timer,mobile jammers successfully disable mobile phones within the defined regulated zones without causing any interference to other communication means,gsm 1800 – 1900 mhz dcs/phspower supply.using this circuit one can switch on or off the device by simply touching the sensor,can be adjusted by a dip-switch to low power mode of 0,as many engineering students are searching for the best electrical projects from the 2nd year and 3rd year,320 x 680 x 320 mmbroadband jamming system 10 mhz to 1.
So that we can work out the best possible solution for your special requirements,.
