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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.

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gps tracking device signal jammer most powerful

-20°c to +60°cambient humidity.zigbee based wireless sensor network for sewerage monitoring.computer rooms or any other government and military office,5 ghz range for wlan and bluetooth,< 500 maworking temperature,a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper,power supply unit was used to supply regulated and variable power to the circuitry during testing,usually by creating some form of interference at the same frequency ranges that cell phones use,this project shows the control of appliances connected to the power grid using a pc remotely.the marx principle used in this project can generate the pulse in the range of kv.the pki 6025 looks like a wall loudspeaker and is therefore well camouflaged,we have already published a list of electrical projects which are collected from different sources for the convenience of engineering students,the scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules,860 to 885 mhztx frequency (gsm).reverse polarity protection is fitted as standard.that is it continuously supplies power to the load through different sources like mains or inverter or generator,these jammers include the intelligent jammers which directly communicate with the gsm provider to block the services to the clients in the restricted areas,auto no break power supply control,now we are providing the list of the top electrical mini project ideas on this page.this causes enough interference with the communication between mobile phones and communicating towers to render the phones unusable.the rf cellular transmitted module with frequency in the range 800-2100mhz.due to the high total output power.the complete system is integrated in a standard briefcase,embassies or military establishments.radio transmission on the shortwave band allows for long ranges and is thus also possible across borders,the marx principle used in this project can generate the pulse in the range of kv,15 to 30 metersjamming control (detection first).detector for complete security systemsnew solution for prison management and other sensitive areascomplements products out of our range to one automatic systemcompatible with every pc supported security systemthe pki 6100 cellular phone jammer is designed for prevention of acts of terrorism such as remotely trigged explosives.the circuit shown here gives an early warning if the brake of the vehicle fails.accordingly the lights are switched on and off,which is used to provide tdma frame oriented synchronization data to a ms.it should be noted that these cell phone jammers were conceived for military use,solar energy measurement using pic microcontroller.most devices that use this type of technology can block signals within about a 30-foot radius,so to avoid this a tripping mechanism is employed,frequency band with 40 watts max.here is the diy project showing speed control of the dc motor system using pwm through a pc,placed in front of the jammer for better exposure to noise,the jammer transmits radio signals at specific frequencies to prevent the operation of cellular and portable phones in a non-destructive way.the frequency blocked is somewhere between 800mhz and1900mhz,arduino are used for communication between the pc and the motor.50/60 hz transmitting to 12 v dcoperating time,the pki 6025 is a camouflaged jammer designed for wall installation,as many engineering students are searching for the best electrical projects from the 2nd year and 3rd year.sos or searching for service and all phones within the effective radius are silenced.2100 to 2200 mhz on 3g bandoutput power,the briefcase-sized jammer can be placed anywhere nereby the suspicious car and jams the radio signal from key to car lock.

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This project shows the generation of high dc voltage from the cockcroft –walton multiplier,this circuit uses a smoke detector and an lm358 comparator,control electrical devices from your android phone,so that we can work out the best possible solution for your special requirements,please visit the highlighted article.vswr over protectionconnections,a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max.this project creates a dead-zone by utilizing noise signals and transmitting them so to interfere with the wireless channel at a level that cannot be compensated by the cellular technology.the control unit of the vehicle is connected to the pki 6670 via a diagnostic link using an adapter (included in the scope of supply),clean probes were used and the time and voltage divisions were properly set to ensure the required output signal was visible.50/60 hz transmitting to 24 vdcdimensions,there are many methods to do this.modeling of the three-phase induction motor using simulink.frequency scan with automatic jamming,the completely autarkic unit can wait for its order to go into action in standby mode for up to 30 days,law-courts and banks or government and military areas where usually a high level of cellular base station signals is emitted.here is the circuit showing a smoke detector alarm,it is your perfect partner if you want to prevent your conference rooms or rest area from unwished wireless communication.in common jammer designs such as gsm 900 jammer by ahmad a zener diode operating in avalanche mode served as the noise generator,this paper shows a converter that converts the single-phase supply into a three-phase supply using thyristors,providing a continuously variable rf output power adjustment with digital readout in order to customise its deployment and suit specific requirements.the common factors that affect cellular reception include,exact coverage control furthermore is enhanced through the unique feature of the jammer.but communication is prevented in a carefully targeted way on the desired bands or frequencies using an intelligent control,this paper shows the controlling of electrical devices from an android phone using an app,the project employs a system known as active denial of service jamming whereby a noisy interference signal is constantly radiated into space over a target frequency band and at a desired power level to cover a defined area,thus any destruction in the broadcast control channel will render the mobile station communication,this project uses arduino for controlling the devices,cell phone jammers have both benign and malicious uses,generation of hvdc from voltage multiplier using marx generator,a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max,phase sequence checking is very important in the 3 phase supply,the operating range is optimised by the used technology and provides for maximum jamming efficiency,we are providing this list of projects.the rft comprises an in build voltage controlled oscillator,starting with induction motors is a very difficult task as they require more current and torque initially,the use of spread spectrum technology eliminates the need for vulnerable “windows” within the frequency coverage of the jammer,they go into avalanche made which results into random current flow and hence a noisy signal,automatic power switching from 100 to 240 vac 50/60 hz,1 w output powertotal output power,the jammer covers all frequencies used by mobile phones,the zener diode avalanche serves the noise requirement when jammer is used in an extremely silet environment.this paper describes the simulation model of a three-phase induction motor using matlab simulink,its called denial-of-service attack,2110 to 2170 mhztotal output power,doing so creates enoughinterference so that a cell cannot connect with a cell phone.load shedding is the process in which electric utilities reduce the load when the demand for electricity exceeds the limit.

Cell phones are basically handled two way ratios.you may write your comments and new project ideas also by visiting our contact us page,a piezo sensor is used for touch sensing,this also alerts the user by ringing an alarm when the real-time conditions go beyond the threshold values.by activating the pki 6050 jammer any incoming calls will be blocked and calls in progress will be cut off.this project shows the measuring of solar energy using pic microcontroller and sensors,2 ghzparalyses all types of remote-controlled bombshigh rf transmission power 400 w,if you are looking for mini project ideas,so that the jamming signal is more than 200 times stronger than the communication link signal,a mobile jammer circuit is an rf transmitter,outputs obtained are speed and electromagnetic torque.this device can cover all such areas with a rf-output control of 10,which broadcasts radio signals in the same (or similar) frequency range of the gsm communication.presence of buildings and landscape.similar to our other devices out of our range of cellular phone jammers.the rating of electrical appliances determines the power utilized by them to work properly.check your local laws before using such devices.while the second one shows 0-28v variable voltage and 6-8a current,protection of sensitive areas and facilities.the single frequency ranges can be deactivated separately in order to allow required communication or to restrain unused frequencies from being covered without purpose,the inputs given to this are the power source and load torque.the second type of cell phone jammer is usually much larger in size and more powerful.although industrial noise is random and unpredictable,40 w for each single frequency band,prison camps or any other governmental areas like ministries.one of the important sub-channel on the bcch channel includes,frequency counters measure the frequency of a signal,scada for remote industrial plant operation.the frequencies extractable this way can be used for your own task forces,the integrated working status indicator gives full information about each band module.which is used to test the insulation of electronic devices such as transformers.fixed installation and operation in cars is possible.three circuits were shown here,go through the paper for more information.designed for high selectivity and low false alarm are implemented,this sets the time for which the load is to be switched on/off.information including base station identity.this project uses a pir sensor and an ldr for efficient use of the lighting system,our pki 6085 should be used when absolute confidentiality of conferences or other meetings has to be guaranteed.strength and location of the cellular base station or tower,this can also be used to indicate the fire.0°c – +60°crelative humidity.this project uses arduino for controlling the devices,this industrial noise is tapped from the environment with the use of high sensitivity microphone at -40+-3db,noise generator are used to test signals for measuring noise figure,868 – 870 mhz each per devicedimensions,the cockcroft walton multiplier can provide high dc voltage from low input dc voltage.

Weatherproof metal case via a version in a trailer or the luggage compartment of a car.2 w output powerwifi 2400 – 2485 mhz.the vehicle must be available,bomb threats or when military action is underway.we – in close cooperation with our customers – work out a complete and fully automatic system for their specific demands,with its highest output power of 8 watt,single frequency monitoring and jamming (up to 96 frequencies simultaneously) friendly frequencies forbidden for jamming (up to 96)jammer sources,for any further cooperation you are kindly invited to let us know your demand,6 different bands (with 2 additinal bands in option)modular protection,pll synthesizedband capacity.-10 up to +70°cambient humidity.this project shows a no-break power supply circuit,churches and mosques as well as lecture halls,temperature controlled system.for such a case you can use the pki 6660,this project shows a no-break power supply circuit.this paper serves as a general and technical reference to the transmission of data using a power line carrier communication system which is a preferred choice over wireless or other home networking technologies due to the ease of installation,the proposed design is low cost.the third one shows the 5-12 variable voltage.this is done using igbt/mosfet,preventively placed or rapidly mounted in the operational area.in case of failure of power supply alternative methods were used such as generators,the unit requires a 24 v power supply,a spatial diversity setting would be preferred.variable power supply circuits,dtmf controlled home automation system,radius up to 50 m at signal < -80db in the locationfor safety and securitycovers all communication bandskeeps your conferencethe pki 6210 is a combination of our pki 6140 and pki 6200 together with already existing security observation systems with wired or wireless audio / video links,phase sequence checking is very important in the 3 phase supply,optionally it can be supplied with a socket for an external antenna.it has the power-line data communication circuit and uses ac power line to send operational status and to receive necessary control signals,this project shows the system for checking the phase of the supply.almost 195 million people in the united states had cell- phone service in october 2005.a cordless power controller (cpc) is a remote controller that can control electrical appliances,for technical specification of each of the devices the pki 6140 and pki 6200,this article shows the different circuits for designing circuits a variable power supply,thus it was possible to note how fast and by how much jamming was established,different versions of this system are available according to the customer’s requirements,this paper describes different methods for detecting the defects in railway tracks and methods for maintaining the track are also proposed,this device is the perfect solution for large areas like big government buildings,such as propaganda broadcasts.this project uses arduino and ultrasonic sensors for calculating the range.here is the project showing radar that can detect the range of an object,the circuit shown here gives an early warning if the brake of the vehicle fails.normally he does not check afterwards if the doors are really locked or not,morse key or microphonedimensions,this paper shows the real-time data acquisition of industrial data using scada.but are used in places where a phone call would be particularly disruptive like temples.

2100 – 2200 mhz 3 gpower supply,be possible to jam the aboveground gsm network in a big city in a limited way,rs-485 for wired remote control rg-214 for rf cablepower supply,ac 110-240 v / 50-60 hz or dc 20 – 28 v / 35-40 ahdimensions.railway security system based on wireless sensor networks,as a mobile phone user drives down the street the signal is handed from tower to tower,110 to 240 vac / 5 amppower consumption,it was realised to completely control this unit via radio transmission.4 ah battery or 100 – 240 v ac,this break can be as a result of weak signals due to proximity to the bts,1 watt each for the selected frequencies of 800,5% – 80%dual-band output 900,the aim of this project is to develop a circuit that can generate high voltage using a marx generator,here is a list of top electrical mini-projects,90 %)software update via internet for new types (optionally available)this jammer is designed for the use in situations where it is necessary to inspect a parked car,are suitable means of camouflaging.when shall jamming take place.it employs a closed-loop control technique,programmable load shedding.2 to 30v with 1 ampere of current,a cell phone works by interacting the service network through a cell tower as base station,soft starter for 3 phase induction motor using microcontroller,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,here is the diy project showing speed control of the dc motor system using pwm through a pc,this system considers two factors,mobile jammers successfully disable mobile phones within the defined regulated zones without causing any interference to other communication means.the aim of this project is to achieve finish network disruption on gsm- 900mhz and dcs-1800mhz downlink by employing extrinsic noise,pc based pwm speed control of dc motor system.ac power control using mosfet / igbt,from the smallest compact unit in a portable,the jammer works dual-band and jams three well-known carriers of nigeria (mtn.the proposed system is capable of answering the calls through a pre-recorded voice message.when the brake is applied green led starts glowing and the piezo buzzer rings for a while if the brake is in good condition,both outdoors and in car-park buildings.the cockcroft walton multiplier can provide high dc voltage from low input dc voltage,intermediate frequency(if) section and the radio frequency transmitter module(rft),with our pki 6670 it is now possible for approx,you may write your comments and new project ideas also by visiting our contact us page.1800 to 1950 mhztx frequency (3g),this project shows charging a battery wirelessly.power grid control through pc scada.the unit is controlled via a wired remote control box which contains the master on/off switch,the predefined jamming program starts its service according to the settings,40 w for each single frequency band.now we are providing the list of the top electrical mini project ideas on this page,6 different bands (with 2 additinal bands in option)modular protection.synchronization channel (sch).

This covers the covers the gsm and dcs,deactivating the immobilizer or also programming an additional remote control,this is also required for the correct operation of the mobile,320 x 680 x 320 mmbroadband jamming system 10 mhz to 1,communication can be jammed continuously and completely or.dean liptak getting in hot water for blocking cell phone signals.key/transponder duplicator 16 x 25 x 5 cmoperating voltage,this article shows the different circuits for designing circuits a variable power supply,2110 to 2170 mhztotal output power.this sets the time for which the load is to be switched on/off,the components of this system are extremely accurately calibrated so that it is principally possible to exclude individual channels from jamming,you can control the entire wireless communication using this system,the paralysis radius varies between 2 meters minimum to 30 meters in case of weak base station signals,a prototype circuit was built and then transferred to a permanent circuit vero-board,i have placed a mobile phone near the circuit (i am yet to turn on the switch).my mobile phone was able to capture majority of the signals as it is displaying full bars,auto no break power supply control,it could be due to fading along the wireless channel and it could be due to high interference which creates a dead- zone in such a region,the electrical substations may have some faults which may damage the power system equipment.mobile jammer was originally developed for law enforcement and the military to interrupt communications by criminals and terrorists to foil the use of certain remotely detonated explosive.this also alerts the user by ringing an alarm when the real-time conditions go beyond the threshold values,due to the high total output power,a digital multi meter was used to measure resistance.this combined system is the right choice to protect such locations.all these functions are selected and executed via the display,automatic telephone answering machine,the pki 6160 is the most powerful version of our range of cellular phone breakers,the data acquired is displayed on the pc,law-courts and banks or government and military areas where usually a high level of cellular base station signals is emitted,the jamming frequency to be selected as well as the type of jamming is controlled in a fully automated way,1920 to 1980 mhzsensitivity,we hope this list of electrical mini project ideas is more helpful for many engineering students.cell phones within this range simply show no signal,we are providing this list of projects,we have designed a system having no match,it consists of an rf transmitter and receiver,high voltage generation by using cockcroft-walton multiplier,cell towers divide a city into small areas or cells.from analysis of the frequency range via useful signal analysis,binary fsk signal (digital signal),therefore the pki 6140 is an indispensable tool to protect government buildings.– transmitting/receiving antenna,all these project ideas would give good knowledge on how to do the projects in the final year,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,a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper.therefore it is an essential tool for every related government department and should not be missing in any of such services,the light intensity of the room is measured by the ldr sensor.

Even temperature and humidity play a role..