From brideout at haystack.mit.edu Fri Feb 6 15:40:33 2004 From: brideout at haystack.mit.edu (William Rideout) Date: Wed Jul 21 10:29:10 2004 Subject: [gps-developers] Benchmarking GPS processing techniques Message-ID: <4023FBC1.2000100@haystack.mit.edu> Anthea, Here's an update on the status of my development of a new GPS processing technique. This memo contains a background discussion of the issues in improving GPS data processing, some of which may be appropriate for the proposal. Description of the problem with the present technique: If you look at the tec values that go into one particular bin in our maps for a latitude and longitude where multiple receivers overlap, you will see that the distribtuion is not gaussian. In fact, it appears to have multiple peaks, associated with the different receivers that are contributing to the values. The average value is then is strong function of which receiver has the most measurements in that bin. This is clearly a source of noise. These multiple peaks are caused by imperfections in biases and the mapping function. For a bin with data from only one receiver, there is still a spread in vertical tec values due to spatial variations in the ionosphere within that bin's area, and due to the noise in the individual measurements. Benchmark definition The above problem can be defined with a very simple benchmark: I want the standard deviation of the tec values in a bin with multiple receivers to be as close as possible to that of the standard deviation of a bin with only one receiver. This isn't a complete benchmark, but its certainly a neccesary one. For example, its possible for the receiver biases to all be consistent using the difference technique described in Kevin Duh's memo, and also consistently off. This is due to the needed assumption that the receiver biases average to zero, a poor assumption when the number of receievers is small, and not even certain when the number is large. Hovever, with the new technique I should be solving for absolute receiver bias, so this benchmark should be a good one. My method for finding bins with large number of receivers was simply to look at bins with more than 400 points in a 20 minute period (2002 data). My method for finding bins with one receiver was simply to look at bins with between 50 and 100 points in a 20 minute period (2002 data). Description of old (0 tec receiever bias) technique This technique assumes that at some time during the time period the TEC goes to zero, and so the receiver bias is the difference between the lowest TEC and 0 TEC. If this assumption were true, there would typically be a floor in the TEC data; however, this is rarely the case. If the minimum TEC above a group of physically adjacent GPS receivers is uniform, then at least those receiver biases differences will be correct, which is all we need to optimize the above benchmark. If, however, there are variations in minimum TEC above physically adjacent GPS receivers, or if noise plays a role, then those receiver biases differences will not be consistent, worsening the benchmark. Description of elevation versus vertical TEC receiver bias technique This technique takes advantage of the fact that an incorrect bias causes graphs of distortions of the vertical TEC values taken at lower elevations. This is because incorrect receiver biases changes all line-of-sight TEC values by a constant amount. If the ionosphere is constant overhead, this error will be multiplied by the mapping function to cause systemically higher (or lower) values at low elevations. Even if the ionosphere is not constant overhead, on the average, this receiver bias error will cause low elevation vertical TEC values to be higher (or lower) than high elevation measurements. Receiver bias is found using this technique as follows: for each test receiver bias, that amount of TEC is added to all the line-of-sight TEC measurements during a given time period. My test has used two different time periods: the 4 hours around solar noon, and the four hours around solar midnight. These new line-of-sight TEC measurements are then converted to vertical TEC measurements via the mapping function. All data is binned in 1 degree of elevation bins, and those (at most) 90 points are fitted to a second degree polynomial. In the ideal case the result is a flat line. The best fit receiver bias is that which minimizes the sum of the first order term + 90 * the second order term. Results: These results cover three cases: 1. Data using the present technique, but before we fixed the error in satellite bias units. 2. Our present standard method (0 tec receiever bias). 3. The elevation versus vertical TEC receiver bias technique Case 1: ~5.8 TEC units Case 2: ~3.2 TEC units Case 3: ~3.2 TEC units In all cases, the standard deviation for bins with only one receiver is about 0.96 TEC. In theory, with perfect receiver bias correction and a perfect mapping method, this standard deviation should not change between the single receiver and multiple receiver case. Discussion: It's clear that fixing the units problem in satellite biases dramatically decreased the noise in our data. However, the elevation versus vertical TEC receiver bias technique does not seem to have any less error that the standard 0 tec receiever bias technique, so it will not dramatically improve our data. John Holt's approach of fitting for the ionosphere and the receiver bias together should reduce this benchmark down toward the 0.96 limit of a single receiver, and we should point this out in the proposal. In the meantime, I shifting my plans for a short term improvement toward the approach taken by Kevin Duh in his Matlab code, which is to look for receivers with overlapping measurements. However, I do not plan to make his assumption that the average receiver bias is 0. Instead, I will use the information provided by JPL on receiver biases for a subset of GPS receivers to get absolute bias levels. If no JPL data is available, I will apply my elevation versus vertical TEC receiver bias to get the average bias. In the limiting case of an isolated GPS receiver, I will use the elevation versus vertical TEC receiver bias itself. Since this will be isolated data, its noise will be less important. Bill -- Bill Rideout MIT Haystack Observatory Email: brideout@haystack.mit.edu Phone: 781 981-5624 From brideout at haystack.mit.edu Thu Feb 19 14:30:29 2004 From: brideout at haystack.mit.edu (William Rideout) Date: Wed Jul 21 10:29:11 2004 Subject: [gps-developers] Matlab mapping using CGM coordinates Message-ID: <40350ED5.2010004@haystack.mit.edu> John, Examples of polar and cartesian movies of GPS data for Nov.20, 2003 using corrected geomagnetic parameters are now on my web page. Please let me know if you have any comments or see any problems. If you want to run these scripts yourself, you have two choices. It's installed on hyperion, or you can download the GPS toolkit from my website, which contains all my Matlab scripts (along with python scripts and executables for processing data, which you can ignore). On hyperion, type: help make_gps_movie_cart or help make_gps_movie_polar to see usage information. Bill -- Bill Rideout MIT Haystack Observatory Email: brideout@haystack.mit.edu Phone: 781 981-5624