\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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It reflects new engineering and building developments, the most current design methods, and the latest industry standards and policies. It provides a comprehensive overview of the significant characteristics for bridge engineering. It highlights the recent advancements, requirements, improvements, and details of the latest techniques in the global market. It contains a collection of the latest research developments on the bridge engineering. It comprehensively covers the basic theory and practice in sufficient depth to provide a solid grounding to bridge engineers. It helps readers to maximize effectiveness in all facets of bridge engineering. This professional book as a credible source and a valuable reference can be very applicable and useful for all professors, researchers, engineers, practicing professionals, trainee practitioners, students and others who are interested in the bridge projects.",isbn:"978-1-78923-105-2",printIsbn:"978-1-78923-104-5",pdfIsbn:"978-1-83881-451-9",doi:"10.5772/intechopen.70024",price:119,priceEur:129,priceUsd:155,slug:"bridge-engineering",numberOfPages:150,isOpenForSubmission:!1,hash:"1d5fcf0ef5708024ef95eb8b3d7310be",bookSignature:"Hamid Yaghoubi",publishedDate:"May 23rd 2018",coverURL:"https://cdn.intechopen.com/books/images_new/6395.jpg",keywords:null,numberOfDownloads:14036,numberOfWosCitations:0,numberOfCrossrefCitations:2,numberOfDimensionsCitations:2,numberOfTotalCitations:4,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"June 8th 2017",dateEndSecondStepPublish:"June 29th 2017",dateEndThirdStepPublish:"September 25th 2017",dateEndFourthStepPublish:"December 24th 2017",dateEndFifthStepPublish:"February 22nd 2018",remainingDaysToSecondStep:"4 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"103965",title:"Dr.",name:"Hamid",middleName:null,surname:"Yaghoubi",slug:"hamid-yaghoubi",fullName:"Hamid Yaghoubi",profilePictureURL:"https://mts.intechopen.com/storage/users/103965/images/system/103965.jpeg",biography:"Dr. Hamid Yaghoubi is the director of Iran Maglev Technology (IMT). He became the Iran top researcher in 2010. In this regard, he was awarded by the Iranian president; the Iranian Minister of Science, Research and Technology; and the Iranian Minister of Information and Communication Technology. He became the 2011 and 2012 Outstanding Reviewer for the Journal of Transportation Engineering (JTE), American Society of Civil Engineers (ASCE), USA. One of his journal papers became the 2011 Top Download Paper for JTE. He received the ICCTP2011 Award for the 11th International Conference of Chinese Transportation Professionals (ICCTP2011), ASCE. He is an assistant chief editor and an editorial board member for some journals. He has been a reviewer for the majority of journals, books and conferences. He has also been an editor for some books. 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Organochlorines (OCs) are organic molecules with chlorine in their structure. There are known a large number of organochlorine compounds. A large amount of chlorinated organic compounds are produced for industrial, agricultural, pharmaceutical, household purposes, etc. In many studies, the main focus is on OC which has been evaluated as environmental contaminants with toxic effects on humans. Different types of organochlorine have been produced throughout the world. Some of the most popular classes are organochlorine pesticides (OCPs), polychlorinated biphenyls (PCBs), dioxins, chlorobenzenes, chlorophenols, chlorinated alkanes, etc. Organochlorine compounds usually have a large molecular mass. They are very stable. Generally, they are molecules of moderate polarity (low solubility in water). This makes OC easily soluble in fats. They were found in almost all environments: air, water, soil, sediments, and biota samples. They can spread out easily in different geographic altitudes and latitudes. Volatile and semi-volatile OCs have the ability to spread far away from the place where they were used. Some studies have reported some organochlorines in the North Pole at the same levels as the areas where they were produced or applied. They have the ability to bioaccumulate easily in biota. Passing through the food chain levels, they increase their concentrations (biomagnifying). Contaminated foods with OCs and exposures to them are their main ways to arrive in the human body. Generally, they display their effects after a relatively long period of exposure. This is the main reason why they are produced and used for a long time before their production and use were banned. The most important health effects that organochlorines can cause are mutagenic, endocrine-disruptor, carcinogenic and central nervous or peripheral disorders. After identification of the consequences for many organochlorines, their production and use in many countries were banned but unfortunately their effects were shown for many other years.
Organochlorine pesticides were used widely for agricultural purposes after the Second World War. The insecticidal properties of DDT were discovered firstly. After that many other OCPs were synthesized and used. Many tons of DDT, aldrin, heptachlor, lindane, hexachlorobenzene, toxaphene, and many other pesticides with chlorine in their molecules were produced and used all over the world for many years. They affected significantly the growth of agricultural products around 1960, bringing what was called the “Green Revolution.” Their use was very effective especially in countries that suffered from many diseases spread by insects such as malaria. In early 1970s, their toxic effects were verified firstly in birds and fishes. After that, OCPs were banned in the USA and Europe. OCPs and their degradation products are found in many ecosystems until now because of their persistence and their bioaccumulation ability. The presence of OCPs was reported in many environmental and food studies. Water irrigation and rainfall landslides make them possible to pass over surface and underground waters. So, they can spread far away from areas where they have been applied. Bioaccumulation processes make their presence possible in all food chain [1, 2].
PCBs were produced from 1930 to 1977. PCB mixtures were prepared from chlorination of biphenyls in the presence of various catalysts. There are 209 different congeners depending on the number of chlorine atoms and their positions in the molecule. Usually they were used as mixtures (aroclor, kanechlor, etc.). These mixtures are classified and used according to the percentage of chlorine. They were widely used as insulating and hydraulic fluids in numerous industrial processes. They were banned in 1980 because of the possible risks to human health and the environment. Higher toxicity presents non- and mono-ortho-substituted congeners because of their planarity. They are called dioxin-like congeners of PCBs, classified as endocrine disruptor and possible carcinogen to humans [3, 4]. Many accidents have occurred around the world due to the use of PCB: Kyushu, Japan (1968); Hudson River, USA (1977); Brescia, Italy (1999); etc. These accidents and laboratory in vivo/in vitro data verified their toxic ability to humans [5, 6, 7, 8].
Polychlorinated dibenzo-p-dioxin (PCDDs) and polychlorinated dibenzofurans (PCDFs) are highly toxic, the most dangerous being 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Testing study on toxicity of the TCDD is used as a mechanism and reference value for other dioxins [9, 10, 11]. PCDD/Fs and PCB dioxin-like were verified in different experiments to have the same mechanism of toxicity via the aryl hydrocarbon receptor (AHR). Dioxins can produced in higher temperature as secondary products, e.g. by increate of urban wastes or many industrial processes. Dioxins have no common use. PCDD/F even in low levels can cause serious problems to humans and other organisms because of their high toxicity [12, 13]. Various studies have clarified the implications of their presence at ultra-trace levels like that in Seveso, Italy (1976), Belgian PCB/dioxin incident (1999), etc [14, 15].
Derivatives with chlorine of benzene, phenol, aniline, nitrobenzene, benzoic acid, phenyl acetic acid, and many other similar compounds are usually produced as raw materials for many syntheses in the pharmaceutical industry, plastic production, pesticide production, and many other synthetic compounds. Some of them were used as pesticides, for example, tecnazene (tetrachloronitrobenzene), Kvintozen (pentachloraniline), etc. Chlorinated derivatives can be impure in many synthetic products. They can be obtained by degradation processes of large chlorinated molecules. They were reported as part of the metabolism of large chlorine molecules in different organisms. Most of them are harmful to the environment and living organisms. Their toxicity is different depending on the number and position of chlorine in the molecules.
Many studies have shown that chlorine compounds have harmful health effects not only for exposed persons but also for the entire population, it was necessary to regulate the equivalence of international legislation on limitations on the production and use of toxic substances. So several agreements were reached, but the most important is the Stockholm Convention (2001) on Persistent Organic Pollutants (POPs). This convention, adopted by most countries, aimed at the elimination or reduction and use of many OCs including OCPs, PCBs, and dioxins. It provided several phases and guidelines for the immediate prohibition of use, production, and reduction of those substances called POPs. Although in most countries this convention became effective soon, OC presence was reported in certain areas as a result of waste disposal, equipment accidents, or their use under false trademark. Their high persistence is an important factor. Control of the OC should be continuous in environmental and food samples due to their wide spread.
Although they have been banned many years ago, levels of OC were reported frequently in different studies. They are widespread in both applied environments and in areas far away from their application sites. This is due to high stability, high bioaccumulation capacity, biomagnification, and the ability to spread out of the application site. Generally, these compounds are difficult to degrade. In the soil or sediment environment, the speed of degradation is much smaller. Different degradation mechanisms are known, such as photochemical degradation, thermal degradation, biological degradation, and chemical degradation [7]. Their degradation products are derivatives which in most cases also contain chlorine and exhibit certain toxicity. The study of degradation mechanisms will affect the speeding up of their elimination processes under practical conditions.
The levels of chlorine compounds in both environmental and food samples were found in very low (trace or ultra-trace) levels from ppm to ppt. For their qualitative and quantitative determination, it is necessary to use different techniques of extraction such as Soxhlet, ultrasonic extraction, SPE, ASE, etc. The samples of clean-up procedures generally were realized in SPE columns with adsorbents that have different polarities. Analytical determinations of organochlorines were recommended to be achieved by gas chromatography techniques especially coupled with mass spectrometry (GC/MS). GC/MS/MS and LC/MS/MS are recommended in many methods for OC analysis in environmental and food samples [16, 17]. In many standard methods (EN, ASTM, etc.), techniques of simultaneous determination of organochlorine compounds for the same type or different types due to their similarity are described.
This compact book has some data on organochlorine compounds and their degradation products. Clarification of degradation processes for OC is important for polluted ecosystems. Reviews on legislations for organochlorine compounds especially on persistent and toxic OC were shown also in this book. Analytical procedures (extraction techniques, clean-up procedures, equipment, etc.) and experimental data for OC analysis are mentioned briefly on book chapters.
Chapter I, “Service Sector-Based Dioxin and Furan Emissions and Management Techniques,” describes PCDD/F as one of the important classes of organochlorine contaminants. This chapter presents the importance of study dioxins because they cause people’s health problems. Through various studies that authors have used, this review is focused mainly on emission sources and monitoring of these contaminants in some countries in order to conclude to the situation in Ethiopia. PCDD/Fs are part of the POPs because of their persistence and toxicity. Also, in this chapter, are given data on other chlorinated compounds, classified as POPs, such as organochlorine pesticides, PCB, PBB, etc. The connection between PCDD/F and other POPs could have been clearly demonstrated.
Chapter II, “Mechanistic Considerations on the Hydrodechlorination Process of Polychloroarenes,” is a review of different hydrodechlorination mechanisms for organochlorine pollutants such as PCDD/F and PCB. These pollutants are persistent for many years because of their structure. Their presence could be for many years not only in environment but also in food chain because of bioaccumulation processes. Authors have considered different studies of hydrodechlorination mechanisms based on different redox mechanisms. These mechanisms of hydrodechlorination are important processes because degradation products usually are organic compounds with lower toxicity. Understanding these reaction mechanisms can lead to their efficient use in practice. The use of these reactions in incinerator filters and contaminated areas can bring a reduction of PCDD/PCDF and PCB pollution.
Chapter III, “Application of Heterogeneous Catalysts in Dechlorination of Chlorophenols,” is a review on heterogeneous catalysts for dechlorination of chlorophenols. These compounds are widely distributed especially in waste and surface waters because of household products, urban wastes and other chlorinated compounds such as pesticides. Heterogeneous catalyst can replace the homogeneous catalyst to solve the catalyst recycling problem, especially for the precious metal catalysts. The heterogeneous catalyst costs are more reduced than homogeneous catalyst. Dechlorination of chlorophenols using heterogeneous catalyst could be useful for dechlorination of other chlorinated compounds.
At present, five constellations of GNSS satellites are involved in the formation of observational data, which serve as a source for many applications related to navigation, geodesy, geodynamics, and in the performance of solving of many fundamental problems. These are American Global Positioning System (GPS), Russian Global Navigation Satellite System (GLONASS), European Galileo, Chinese BeiDou, and Japanese Quasi-Zenith Satellite System (QZSS). The satellites of each of the operating systems transmit signals, as a rule, on two L-band carriers, which are received by GNSS receivers. A large number of stations equipped with GNSS receivers and located around the World are part of the International GNSS Service (IGS) network. These stations generate observation data files and transmit them to international databases in real time [1, 2], after which these data become available for use by many institutions and laboratories over the World. When solving applications, the measurement data go through various processing steps. Significant element of the data processing is the detection of rough measurements and removal them from the further processing. Despite the fact that many of the laboratories use a high-end application of the software regarding accuracy, reliability, and robustness, the presence of rough measurements in the observational data excludes the possibility of obtaining an accurate final result. In order to obtain results of unprecedented accuracy, the measurement data must be cleared of coarse measurements or outliers. It should be noted that the concept of outliers is key in the measurement processing theory [3], and there is no general definition for it. In order to distinguish outliers from the rest of the measured data, in some cases, the deviation of the data series values from some average value of the data is considered. If the deviation from the average is exceeded by a predetermined threshold value, the measured value is considered as an outlier. Such an approach has a significant disadvantage that the exact mean is generally unknown, and the estimate obtained by averaging a series may be very inaccurate due to outliers. Existing iterative procedures are also based on the idea of calculating deviation from the average and often result in the unjustified rejection of many observations. Reducing the data involved in processing may, in turn, result in a loss of accuracy of the final result.
This chapter describes the outliers cleaning algorithm for GNSS data. The proposed algorithms are based on the search for the so-called optimal solution with the minimum amount of invalidly rejected data. The algorithm for accelerated detection of outliers in a large amount of measurements has been developed, as well as an algorithm for detecting outliers in data containing an unknown trend. In conclusion, the algorithm of jump detection in the Melbourne-Wübbena combination [3, 4, 5], including the developed procedure of cleaning data from outliers, is considered.
In Section 2, the problem of searching for the so-called optimal solution is formulated. Section 3 provides a search algorithm, with a common number of arithmetic operations not exceeding ∼N2. Section 4 presents the test results for actual measurements in global navigational satellite systems at two carrier frequencies. The searching of outliers was performed in the Melbourne-Wübbena combination. In Section 5, the assertions that are the mathematical prerequisites for justifying a fast outlier search algorithm are proved. In Section 6, the fast outlier detection algorithm with the number of arithmetic operations of Nlog2N is proposed. Section 7 describes the case of data with unknown trend. Iterative procedure of outlier search is proposed based on the finding of suitable trend approximation in polynomials class. The idea of excluding coarse measurements is based on finding a so-called minimizing set of measurement data of a given length. This distinguishes the proposed algorithm from known similar procedures in which outliers are detected by exceeding a preset threshold. The test results with simulated data are given. Sections 8 and 9 discuss the problem of detecting jumps in the Melbourne-Wübbena combination. An algorithm is proposed that includes the outlier cleaning procedure based on the search for the optimal solution. Section 10 shows the numerical calculations with real data for algorithms presented in Sections 3–9. Section 11 concludes the chapter.
Often, measurements
where
Detection of outliers in data series expressed in Eq. (1) with unknown trend is uncertain since the concept of measurement or outliers itself is uncertain. In many cases, however, the trend function is known a priori.
For example, many data processing programs often use different linear combinations formed of code and phase measurement data to eliminate unknown parameters. One such combination is the Melbourne-Wübbena combination composed of both, carrier phase and code observables as described by Melbourne [4] and Wübbena [5]. This combination eliminates the effect of the ionosphere, the geometry, the clocks, and the troposphere [3], and it is often used to detect loss of carrier phase capture in the preprocessing stages. The Melbourne-Wübbena combination generated for a specific satellite-receiver pair can be presented in the form of the sum of three terms [6]. One of the terms includes the integer wide-lane ambiguity for the two carrier frequencies [3]; the second component accounts for the satellite and receiver instrumental delays; and the third component is the measurement noise, including carrier phase and code multipath. Thus, during a time interval where the integer wide-lane ambiguity does not change, the Melbourne-Wübbena combination can be written as formula (1) with
Another example is satellite clock correction values derived from navigation message data, which can also be represented as in Eq. (1) with
with an unknown constant z, which we cannot be determined in advance, because the random value
In Sections 2–6, we consider the case where the trend is known a priori, that is, the data can be presented as Eq. (2). A problem with an unknown trend will be discussed in Section 7. In principle, the outlier detection procedure described below is not affected by the measurement format expressed in Eq. (1) or (2); it can be applied to any set of data measurements
The preliminary processing task includes rejection of rough measurements or outliers from data series (2). In other words, it is necessary to find a set
where
The values
1. First, we will require that the length of the set sought be the maximum, that is, the number of measurements deemed to be coarse is the minimum:
Note that for the predetermined values
2. From all possible sets that satisfy conditions expressed in Eqs. (3)–(5) and (6), we will select the one for which the variable
Let us define
Definition 1. For a given sequence of values
satisfying conditions in Eqs. (3)–(7), we refer to as the optimal solution of the problem expressed in Eqs. (3)–(7). The corresponding SD value is denoted by
Thus, the problem consists in the creation of a search algorithm for the optimal solution of the problem shown in Eqs. (3)–(7).
In a practical situation, the precise value z, given conditions in Eqs. (3) and (4), is not known. We will estimate the values using the following formula:
Note that the value z depends on the required solution, which will complicate its search.
Usually, iterative methods are used to find a solution to problem expressed in Eqs. (3)–(5). For example, the algorithm implemented in the observation data smoothing program (see [3]) is designed to find a set Y satisfying the conditions given by Eqs. (3)–(5). The proposed step-by-step algorithm is based on iterations (the index number of iteration is designated by the upper index in parentheses):
Step 1: Initialization:
Step 2: Checking the length of the set
Step 3: Calculation of the values
Step 4: Checking the fulfillment of the inequality
Step 5: Definition of
In order to prevent an infinite loop of iterations, a required verification is carried out:
If this inequality is not satisfied, then the following is assumed:
Step 6: Definition of a new set
Step 7: Increasing k by 1: k++. Transition to Step 2.
Note that the optimal solution cannot be found in such a manner, as confirmed by numerical calculations (see Section 4).
Let us formulate a statement that is the key to the creation of an effective search algorithm for the optimal solution (Eqs. (3)–(7)).
Assertion 1. Let the set
then the interval
Proof. In fact, let us assume the opposite: Let
In the first case, Case (a), we replace the value
Further, note that if
Note that due to the formulated Assertion 1, if
Thus, the optimal solution should be sought in the ascending sequence
Hence, instead of searching for all possible sets of various length, numbering
Let
We rewrite conditions given by Eqs. (3) and (4) in the new designations:
Note that the two last inequalities directly follow from Eq. (4), monotony of yj, and obvious inequalities:
Remark. In the conditions expressed in Eqs. (15) and (16), L means the length of the set under checking, and k is the index of the smallest number included in the set. Although “k” and “L” are also encountered as indexes in the sets we use below for monotonically increasing sequences, we hope nevertheless that this will not lead to confusion.
The following recursive relationships are available, making it possible to find
The values of the fractions may be computed in advance as elements of a one-dimensional array. Analogously, the following formulas can make it possible to express
The algorithm described below is based on the search for all possible pairs (k, L), where L denotes the length of the set to be checked and k is the index of the smallest of the values included in the set. At that, k and L must satisfy conditions Eqs. (11) and (12). The set
We organize this search according to the algorithm described below, at each step of which we check the validation of Eqs. (15) and (16) for all possible sets of a certain length. We start the examine process with Step 1, where we check the set of maximum length N. Further, with each next step, we will reduce the length of the sets to be checked by 1.
Step 1: We consider the set of length N. There is only one such set:
Step 2: We consider the sets of length N − 1. There are two sets of length N − 1.
We test each of these sets for compliance with the conditions specified by Eqs. (15) and (16). If none of them satisfies conditions (15) and (16), then we transit to the next step. Otherwise, the following options are available:
Option 1: if only one set from them is found that satisfies conditions (15) and (16), then it will also be the solution of the stated problem; the search process stops here, where
Option 2: if both sets simultaneously satisfy conditions (15) and (16), we will select the set corresponding to the smallest of two values
Step N − L + 1: We consider the sets of length L. If L < MINOBS, then the search process stops, and a solution is not found. For L ≥ MINOBS, we examine N − L + 1 sets of length L:
We check each of these sets for fulfillment of conditions (15) and (16). If any of them does not satisfy these conditions, then we transit to the next step where we consider the sets of length (L − 1). Otherwise, two options are possible:
Option 1: if only one set from (23) is found that satisfies the conditions of (15) and (16), then it will also be the solution of the stated problem with
Option 2: if several sets simultaneously satisfy conditions (15) and (16), we chose the set for which the value
In order to calculate the values
Scheme of calculations when finding the optimal solution.
In accordance with the proposed arrangement, we calculate the values
In the above number of computations, the computational costs of verifying the satisfaction of inequalities (15) and (16) are also considered, which comprise from 0 to 2 arithmetic operations.
We test the algorithms discussed above on the real data obtained by the ONSA station that is a part of the IGS network [2]. These data are included in the distribution kit of the installation software package [3] and available for usage. We consider measurement data received from global positioning system (GPS) satellite with system number PRN = 12 for 2010, day 207 to check the efficiency of the proposed algorithm described in Section 3. Figure 2 plots the values of the Melbourne-Wübbena combination over a time interval of 89.5 min (N = 180). The index numbers j of time epochs counting from the beginning of a 24-h period with a 30-second interval are plotted on the horizontal axis. The values
Melbourne-Wübbena combination for ONSA station (GPS satellite, PRN = 12 for 2010, day 207).
(a) Deviations of values of the Melbourne-Wübbena combination from the mean value after data cleaning from outliers using the algorithm described in Section 2. (b) Deviations of values of the Melbourne-Wübbena combination from the mean value after data cleaning from outliers using the developed algorithm (see Section 3).
We also provide similar results for data obtained by TLSE station, which is also included in the IGS network. We consider measurement data from GLONASS, Russia satellite with system number PRN = 1 for 2010, day 207. Figure 4 shows the values of the Melbourne-Wübbena combination over a time interval of 65.5 min (N = 132). Figure 5 plots the values of deviations from the mean value of the data cleared of outliers using the algorithms described in Sections 2 and 3, respectively. Parameters
Melbourne-Wübbena combination for TLSE station (GLONASS satellite, PRN = 1 for 2010, day 207).
(a) Deviations of values of the Melbourne-Wübbena combination from the mean value after data cleaning from outliers using the algorithm described in Section 2. (b) Deviations of values of the Melbourne-Wübbena combination from the mean value after data cleaning from outliers using the developed algorithm (see Section 3).
Note that the number of arithmetic operations required to find the optimal solution according to the algorithm described in Section 3 depends on the
The necessary preparations are given in this section. Note that in this and the next sections we are dealing with the sequence
Assertion 2. Let
Proof. From the monotonicity of the sequence
One of two cases is possible:
Suppose, for example, the case (a) holds. Let us show that in this case
At first, we will show that:
Truly, inequalities:
and the above inequality derived in Case (a) implies:
These inequalities, in turn, imply Eq. (28). Next let us prove (27). This inequality is expanded as follows:
Substituting here of the expression (17) in place of
Transform the right-hand side of this inequality:
Here we take into account the equality:
Substituting this expression in Eq. (31), we get inequality
that is true due to Eq. (28). Thus, Eq. (27) is proved for case (a). Analogously, case (b) is considered.
We introduce the notation:
Assertion 3. The following inequalities hold:
That is, the sequence
Proof. Assertion 2 and definition of
Since k is chosen arbitrarily, then for all L = MINOBS, …, N − 1 the following inequalities hold:
which proves Assertion 3.
Assertion 3 implies the following corollary.
Corollary 1. If the inequality
holds for some
Proof. Let us assume that L ≥
In particular, we have come to the next important result. If, for example, the inequalities
In the above-described procedure for solving problem (3)–(7), it takes ∼
This will require approximately ∼N arithmetic operations. If none of these conditions are fulfilled, the solution search must stop because the solution does not exist. As a result, only ∼N arithmetic operations are required to ensure that there is no solution.
The above proposed search procedure consists in the calculating values of
First of all, note one property that is the key to the construction of a fast outlier search algorithm. Note that if the inequality (15) holds for some set of length L + 1, then there exists a set of length L for which the inequality (15) is valid too. Truly, let assume for some k the inequality
From this, it follows that
This means that at least one of these sets
However, this property is not true when checking the conditions expressed in Eq. (16). In other words, if these conditions are fulfilled for any set of length L + 1, it might happen that none of the sets of length L may satisfy them. This fact is a significant obstacle to increasing the rate of outlier detection that is necessary when processing a large amount of data with a large number of rough measurements. To overcome this obstacle, we will make the condition expressed in Eq. (16) weaker.
First of all, note that if for some set
Consider a problem with condition expressed in Eq. (36) instead of conditions expressed in Eq. (16).
Remark. Recall that in this condition L means the length of the set under checking, and k is the index of the smallest number included in the set. Although “k” and “L” are also encountered as indexes in the sets we use hereinafter, we hope nevertheless that this will not lead to confusion.
It is easily seen that condition expressed in Eq. (36) for an arbitrary set
Thus, we have established the validity of the following assertion.
Assertion 4. If the set yk…yk+Lof length L + 1 satisfies conditions (15) and (36), then at least one of the two sets
Based on this statement, we can formulate the following:
Assertion 5. Solution for the problem (15) + (36) can be found for ∼
Proof. Let us consider the sequence of steps.
Step 0: Consider the segment
Step 1: Step 1 is the same as Step k described below for k = 1
…
Step k: On the kth step, where (k ≥ 1), we consider a segment
Three possible cases for the proposed search. In case (a) we go to the right-hand side range (range for length of sets) to find a solution, in case (c) we go to the left-hand side range to find a solution, in case (b) we look for a solution with length L = NMidk−1 and the search ends.
The search process will continue until either case (b) or until the length of the segment
The need to process GNSS measurements including a trend on which noise and outliers are superimposed arises at different processing stages of the application process. As already stated above, satellite clock corrections contain a linear trend. In some cases, it may not be known, and then, one has to search for it, for example, by the least square method. The presence of outliers in the measurement data is a significant obstacle to accurate determination of drift and offset parameters of satellite clocks. Other examples are linear combinations of code and phase data on two carriers [3]. To obtain high accuracy results, it is necessary to detect outliers against an unknown trend and remove them from further processing. This is the subject of this section.
Consider the problem of outlier detecting in data presented in the form of Eq. (1), recall that:
The procedure described above for finding the optimal solution in an ordered series of numbers may not produce an adequate result if applied to data containing an unknown trend. For example, there may be no solution, and all data will be defined as outliers. In order to detect outliers in a series of numbers with a trend using the algorithm described above, it is necessary to find a suitable approximation of an unknown function
where n is the polynomial degree, and
Thus, the problem consists in the creation of an algorithm for searching the trend in the class of power polynomial and detecting outliers in specified data series
Before we turn to the trend search algorithm construction, we will define the so-called minimizing set of given length L, which plays an essential role in the trend search. In addition, in Section 7.3, we will describe a search algorithm for such set based on the recurrent formulas (17)–(19) and (20)–(22).
Let
Definition 2. Given L for a specified sequence of values
at which the minimum value of
According to this definition, we have
Minimum in Eq. (41) is searched by all kinds of sets of length L composed of numbers of series
Note that the numbers
Next, we will formulate and prove a statement similar to Assertion 1, which will allow us, when searching for a minimizing set, to proceed from the original series to its ordered permutation.
Assertion 6. Let
then the interval
Proof. Let us assume the opposite: Let
a.
b.
In the first case, Case (a), we replace the value
Suppose Case (a). For brevity, we will write below z instead of
and
We want to show that
Modify
After simplification with taking into account Eq. (45), we get from here:
From (42), it follows (recall that we write z instead of
Assertion 6 is much like Assertion 1, which made it possible to go from an arbitrary numerical series to an ordered one for the optimal solution search (see Section 3). Similarly, Assertion 6 makes it possible to go to an ordered number series to find the minimizing set of numbers of a given length. In our case, considerations similar to those presented in Section 3 may be made when searching for a minimizing set. Namely, if
Note that due to Assertion 6, if
Thus, in order to find a minimizing set of length L, it is sufficient for us to check N − L + 1 sets
and choose from them the one that has minimal SD value. In the minimizing set searching procedure, we use the appropriate designations
The calculation of
At first, we carry out the transitions in the direction of the vertical arrows (see diagram in Figure 7) and calculate sequential values
Scheme of calculations when finding the minimizing set of length L.
In order to correctly detect outliers in measurement data that include an unknown trend, it is necessary to find and remove trend from the original data. The problem in determining of unknown trend is to find a suitable profile for the measurement data by adjusting the fitting parameters. This implies, in turn, the needs to select from the specified series
We describe herein a strategy for finding an unknown trend and detecting outliers. This strategy assumes that the number of outliers in the series presented by Eq. (1) does not exceed a certain value
Below L is supposed to be fixed and associated with the number of the reference values of the series (1) used for fitting, and L ≤ N −
Let us consider the following algorithm. It contains internal iterations, which we will denote with the upper index “s” in parentheses.
Step 0: n = 0. We set some L, satisfying the condition L ≤ N −
Step 1: n++; s = 0;
Step 2: s++. We fit polynomial to the data set and find fitting coefficients
Step 3: Consider the values
Using the algorithm described in Section 7.3, we find from the numbers
We transit to Step 2 and do so until the convergence of the
Step 4: Searching the optimal solution for data set
We find the optimal solution for values
We do this until we find a solution or until n reaches some preset value Nmax (e.g., 10). In this case, probably, we may need to select a different functional class to search for a trend.
Example. Let us consider the data simulated in accordance with formula:
Data simulated using: yj = 10j+10+2randomj and fourth degree polynomial after the first iteration.
Simulated data and fourth degree polynomial after the eighth iteration.
The differences ŷj=yj−P4,ja→, approximation of unknown trend with fourth degree polynomial.
This section explains the convergence of the iterations described in the trend search algorithm (see previous section).
Assertion 7. The SD sequence
and therefore converged.
Proof. We start our consideration with Step 3 and sth iteration, s = 1, 2, … In Step 3, for the sequence
Transform the expression on the right side of Eq. (56). Substitution here instead of
Using the
Here we introduce the designation
We transit to Step 2; s is incremented by 1. We find a vector
Thus,
From the definition of the extremum of functional, it follows:
Taking into account Eq. (58), we have:
The extremum condition (one of n + 1) of functional
From here, we derive:
Taking into account the designation for
Consider the set
and
Thus,
We transit to Step 3. In this step, for sequence
Finally, from Eqs. (61) and (63) and the last inequality (64), we get
that is,
In this and the following section, we describe cycle slip repair algorithm for observers represented in the form of Melbourne-Wübbena combination, which is often used in modern GNSS measurement data processing programs. Loss by the receiver of the carrier phase capture results in jumps in the code and phase measurement data. In the absence of jumps, as we already discussed in Section 2, the values of the combination consist of measurement noise superimposed on an unknown constant value dependent on a specified satellite-receiver pair.
In case of temporary loss of carrier phase capture by the receiver, jumps occur in a series of values representing the Melbourne-Wübbena combination. The procedure of detecting jumps and eliminating them from the values of the combination, called cycle slip repair, is one of the most important steps of preprocessing GNSS data. The main difficulty in detecting jumps is that neither the exact size of jumps nor their epochs are known. A number of algorithms, descriptions of which can be found, for example, in Refs. [3, 6, 8] are proposed for the detection of jumps. Although differing in detail, they are based on a common idea, that is, comparison of the SDs of the time series of measurement data obtained from one of the bounds of the time interval to an arbitrary moment, an epoch. If the differences of the SDs corresponding to two adjacent epochs exceed a predetermined threshold value, then a jump is declared in one of these two epochs. A drawback of similar algorithms is the frequent false detection of jumps during epochs containing rough measurements (outliers) since the values of outliers can exceed the sizes of a jump itself. On the other hand, an attempt to increase the threshold value leads to the opposite effect, an inability to recognize jumps that are small in magnitude.
Below, we propose a robust cycle slip repair algorithm that allows, more reliably than similar known algorithms, to detect jumps and determine their sizes. The proposed algorithm is based on search for so-called clusters consisting of epochs, in which the values of the combination are grouped about corresponding predefined values. Besides, this algorithm implements the above-described method of cleaning data from outliers based on the search for the optimal solution. This method, combined with Springer’s algorithm used in Ref. [3], allows for the reliable determination of multiple (cascade) jumps in the Melbourne-Wübbena combination.
The Melbourne-Wübbena combination
where
where
Let us present the proposed algorithm as the following sequence of steps.
Step 0: We introduce parameter
Arrange the array
Step 1: On this step, we are looking for the maximum density of array values
Step 2: Let
Searching for the maximum of the density of values of the array Yj.
Step 3: Cluster searching. The values
Definition 3. We designate as an
all points of the segment [k, l] are marked by the same value:
at the points j= k, l of the left and right boundaries of the segment, this inequality is satisfied:
the amount of points at which (69) is satisfied is no less than the present value of MINOBS;
the number of consecutive points in which (69) is not satisfied does not exceed the predefined value MAXGAP (e.g., 5);
the value of k cannot be reduced while maintaining the requirements of a–d; and
the value of l cannot be incremented while maintaining the requirements of a–d.
This definition illustrates in Figure 12.
Epochs with indexes k≤j≤l form mΔ cluster.
It is understood that for specified values of m and Δ, there might be one, several, or no (m, Δ) clusters. Searching for clusters is performed by sequential checking of the satisfaction of inequality (69) for all j = 1, …, N for which flagj = 0. Note that inequality (69) is satisfied for at least
and since the arrays
are fulfilled for
If cluster was found, then we mark all points of it as 1, and then, we repeat the cluster search procedure. If even just one cluster has been found at this step, we transfer to Step 1. If not even one cluster has been found, then the search for clusters is complete and we transfer to Step 4.
Step 4: If even just one cluster has been found, we transfer to Step 5, and otherwise: (a) all points of the segment
Step 5: Search for individual jumps in clusters. Let us assume that n ≥ 1 clusters have been found:
In each of the clusters that are found, outliers and 1-size jumps are possible. This follows immediately from the inequalities in (69) and the preestablished value
Substep 5.1: In detecting a 1-size jump in a cluster, we use modified Springer algorithm (see Refs. [9, 10]) combined with the proposed in Section 3 algorithm that executes a search for the optimal solution with a minimum quantity of defective data.
Substep 5.2: We find all epochs
Substep 5.3: We repair the data by the value of each found jump, using the formula
where
Substep 5.4: We rename:
Step 6: Marking of points outside clusters. All points outside of the found clusters (if any) are marked as outliers.
Step 7: Ordering of clusters. We renumber the clusters so that they are placed left to right on the time axis. For the ordered set of clusters [kp, lp], p = 1, …, n, the conditions 1 ≤ k1 < l1 < k2 < l2 < … < kn < ln ≤ N are satisfied.
Step 8: Data screening within clusters and improving the mean values of
Substep 8.1: In accordance with the algorithm proposed in Section 3, we perform screening from outliers in each of the n clusters.
Substep 8.2: For each of the clusters cleaned of outliers, we determine the modified mean values
Step 9: Jumps between clusters. It follows from the description presented above that the remaining jumps in the data
Step 10: Repair data. We delete the jumps between clusters using formula analogous to (72):
where
We rename:
We present here the results of testing the proposed algorithm using real data obtained by the JOZ2 station, which is part of the IGS network [2]. These data are included in the distribution set of the installation software package [3]. Testing was carried out for data obtained from GPS satellite with number PRN = 13 for 2010, day 207. Figure 13 shows the Melbourne-Wübbena combination values in the 107 min time interval (N = 215). The number j of time epochs counted from the beginning of 24-h day with interval of 30 seconds is plotted along the horizontal axis. The combination values
Values of the Melbourne-Wübbena combination for the JOZ2 station (PRN = 13 for 2010, day of year = 207).
Figure 14a and b presents the values of the deviations from the mean value z of data after cycle slip repair procedure, by using the algorithm applied in Ref. [3] (see Figure 14a) and the proposed algorithm (Figure 14b). The values
(a) Deviations of the values of the Melbourne-Wübbena combination from the mean after detection and elimination of jumps from the data using the algorithm from Ref. [3]. (b) Deviations of the values of the Melbourne-Wübbena combination from the mean after detection and elimination of jumps from the data using the proposed algorithm in Section 9.
This chapter presents several effective and stable algorithms for processing data received from GNSS receivers. These data form the basis of almost all engineering applications in the field of computational geo-dynamics and navigation and cadastral survey and in numerous fundamental research works as well. The accuracy of the results obtained is significantly influenced by the quality of the data used in the calculations. In particular, the presence of rough measurements (outliers) in the observation data can significantly reduce the accuracy of the calculations carried out. One of the tasks at the preliminary stage of data processing is reliable detection and removal of rough measurements from the series of measured data with minimum amount of rejected data. The so-called optimal solution, introduced in the chapter, made it possible to detect and eliminate outliers from observed data minimizing the number of rejected measurements. In addition, it is assumed that the data may contain a trend as an unknown function of time. The strategy for determining of the trend is depending on the physical process in question under an assumption that the trend is a continuous function of time. The efficiency of the search is definitely influenced by the choice of the function class from which the trend is searched. In this chapter, we considered the class of power polynomials, but in some cases, this choice may not lead to the expected result. It may require, for example, a class of trigonometric functions to find a suitable trend. The automatic search for the best functional class, together with the strategy of effectively finding an unknown trend, against the background of random noise and outliers, is a complex task for future research.
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