The Implementation of Precise Point Positioning (PPP): A Comprehensive Review.

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP's implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP's error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

Correction: Elsheikh et al. Low-Cost Real-Time PPP/INS Integration for Automated Land Vehicles. Sensors 2019, 19, 4896.

The authors wish to make the following corrections in the original paper [...].

GPS Swept Anti-Jamming Technique Based on Fast Orthogonal Search (FOS).

Recently, there has been growing demand for GPS-based reliable positioning, with the broadening of a range of new applications that mainly rely on GPS. GPS receivers have, recently, been attractive targets for jamming. GPS signals are received below the noise floor. Thus, they are vulnerable to interference and jamming. A jamming signal can potentially decrease the SNR, which results in disruption of GPS-based services. This paper aims to propose a reliable and accurate, swept anti-jamming technique based on high-resolution spectral analysis, utilizing the FOS method to provide an accurate spectral estimation of the GPS swept jamming signal. resulting in suppressing the jamming signal efficiently at the signal processing stages in the GPS receiver. Experiments in this research are conducted using the SpirentTM GSS6700 simulation system to create a fully controlled environment to test and validate the developed method's performance. The results demonstrated the proposed method's capabilities to detect, estimate, and adequately suppress the GPS swept jamming signals. After the proposed anti-jamming module was employed, the software receiver was able to provide a continuous positioning solution during the presence of jamming within a 10 m positioning accuracy.

Direction of Arrival Estimation of GPS Narrowband Jammers Using High-Resolution Techniques.

GPS jamming is a considerable threat to applications that rely on GPS position, velocity, and time. Jamming detection is the first step in the mitigation process. The direction of arrival (DOA) estimation of jamming signals is affected by resolution. In the presence of multiple jamming sources whose spatial separation is very narrow, an incorrect number of jammers can be detected. Consequently, mitigation will be affected. The ultimate objective of this research is to enhance GPS receivers' anti-jamming abilities. This research proposes an enhancement to the anti-jamming detection ability of GPS receivers that are equipped with a uniform linear array (ULA) and uniform circular array (UCA). The proposed array processing method utilizes fast orthogonal search (FOS) to target the accurate detection of the DOA of both single and multiple in-band CW jammers. Its performance is compared to the classical method and MUSIC. GPS signals obtained from a Spirent GSS6700 simulator and CW jamming signals were used. The proposed method produces a threefold advantage, higher accuracy DOA estimates, amplitudes, and a correct number of jammers. Therefore, the anti-jamming process can be significantly improved by limiting the erroneous spatial attenuation of GPS signals arriving from an angle close to the jammer.

Low-Cost Real-Time PPP/INS Integration for Automated Land Vehicles.

The last decade has witnessed a growing demand for precise positioning in many applications including car navigation. Navigating automated land vehicles requires at least sub-meter level positioning accuracy with the lowest possible cost. The Global Navigation Satellite System (GNSS) Single-Frequency Precise Point Positioning (SF-PPP) is capable of achieving sub-meter level accuracy in benign GNSS conditions using low-cost GNSS receivers. However, SF-PPP alone cannot be employed for land vehicles due to frequent signal degradation and blockage. In this paper, real-time SF-PPP is integrated with a low-cost consumer-grade Inertial Navigation System (INS) to provide a continuous and precise navigation solution. The PPP accuracy and the applied estimation algorithm contributed to reducing the effects of INS errors. The system was evaluated through two road tests which included open-sky, suburban, momentary outages, and complete GNSS outage conditions. The results showed that the developed PPP/INS system maintained horizontal sub-meter Root Mean Square (RMS) accuracy in open-sky and suburban environments. Moreover, the PPP/INS system could provide a continuous real-time positioning solution within the lane the vehicle is moving in. This lane-level accuracy was preserved even when passing under bridges and overpasses on the road. The developed PPP/INS system is expected to benefit low-cost precise land vehicle navigation applications including level 2 of vehicle automation which comprises services such as lane departure warning and lane-keeping assistance.

Feature selection in computer-aided breast cancer diagnosis via dynamic contrast-enhanced magnetic resonance images.

The accuracy of computer-aided diagnosis (CAD) for early detection and classification of breast cancer in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is dependent upon the features used by the CAD classifier. Here, we show that fast orthogonal search (FOS), which provides a more efficient iterative manner of computing stepwise regression feature selection, can select features with predictive value from a set of kinetic and texture candidate features computed from dynamic contrast-enhanced magnetic resonance images. FOS can in minutes search candidate feature sets of millions of terms, which may include cross-products of features up to second-, third- or fourth-order. This method is tested on a set of 83 DCE-MRI images, of which 20 are for cancerous and 63 for benign cases, using a leave-one-out trial. The features selected by FOS were used in a FOS predictor and nearest-neighbour predictor and had an area under the receiver operating curve (AUC) of 0.889 and 0.791 respectively. The FOS predictor AUC is significantly improved over the signal enhancement ratio predictor with an AUC of 0.706 (p = 0.0035 for the difference in the AUCs). Moreover, using FOS-selected features in a support vector machine increased the AUC over that resulting when the features were manually selected.

Modeling and syndromic surveillance for estimating weather-induced heat-related illness.

This paper compares syndromic surveillance and predictive weather-based models for estimating emergency department (ED) visits for Heat-Related Illness (HRI). A retrospective time-series analysis of weather station observations and ICD-coded HRI ED visits to ten hospitals in south eastern Ontario, Canada, was performed from April 2003 to December 2008 using hospital data from the National Ambulatory Care Reporting System (NACRS) database, ED patient chief complaint data collected by a syndromic surveillance system, and weather data from Environment Canada. Poisson regression and Fast Orthogonal Search (FOS), a nonlinear time series modeling technique, were used to construct models for the expected number of HRI ED visits using weather predictor variables (temperature, humidity, and wind speed). Estimates of HRI visits from regression models using both weather variables and visit counts captured by syndromic surveillance as predictors were slightly more highly correlated with NACRS HRI ED visits than either regression models using only weather predictors or syndromic surveillance counts.

Neutropenia Prediction Based on First-Cycle Blood Counts Using a FOS-3NN Classifier.

Background. Delivery of full doses of adjuvant chemotherapy on schedule is key to optimal breast cancer outcomes. Neutropenia is a serious complication of chemotherapy and a common barrier to this goal, leading to dose reductions or delays in treatment. While past research has observed correlations between complete blood count data and neutropenic events, a reliable method of classifying breast cancer patients into low- and high-risk groups remains elusive. Patients and Methods. Thirty-five patients receiving adjuvant chemotherapy for early-stage breast cancer under the care of a single oncologist are examined in this study. FOS-3NN stratifies patient risk based on complete blood count data after the first cycle of treatment. All classifications are independent of breast cancer subtype and clinical markers, with risk level determined by the kinetics of patient blood count response to the first cycle of treatment. Results. In an independent test set of patients unseen by FOS-3NN, 19 out of 21 patients were correctly classified (Fisher's exact test probability P < 0.00023 [2 tailed], Matthews' correlation coefficient +0.83). Conclusions. We have developed a model that accurately predicts neutropenic events in a population treated with adjuvant chemotherapy in the first cycle of a 6-cycle treatment.

A comparison of methods for forecasting emergency department visits for respiratory illness using telehealth Ontario calls.

OBJECTIVES: Anticipating increases in hospital emergency department (ED) visits for respiratory illness could help time interventions such as opening flu clinics to reduce surges in ED visits. Five different methods for estimating ED visits for respiratory illness from Telehealth Ontario calls are compared, including two non-linear modeling methods. Daily visit estimates up to 14 days in advance were made at the health unit level for all 36 Ontario health units. METHODS: Telehealth calls from June 1, 2004 to March 14, 2006 were included. Estimates generated by regression, Exponentially Weighted Moving Average (EWMA), Numerical Methods for Subspace State Space Identification (N4SID), Fast Orthogonal Search (FOS), and Parallel Cascade Identification (PCI) were compared to the actual number of ED visits for respiratory illness identified from the National Ambulatory Care Reporting System (NACRS) database. Model predictor variables included Telehealth Ontario calls and upcoming holidays/weekends. Models were fit using the first 304 days of data and prediction accuracy was measured over the remaining 348 days. RESULTS: Forecast accuracy was significantly better (p < 0.0001) for the 12 Ontario health units with a population over 400,000 (75% of the Ontario population) than for smaller health units. Compared to regression, FOS produced better estimates (p = 0.03) while there was no significant improvement for PCI-based estimates. FOS, PCI, EWMA and N4SID performed worse than regression over the remaining smaller health units. CONCLUSION: Telehealth can be used to estimate ED visits for respiratory illness at the health unit level. Non-linear modeling methods produced better estimates than regression in larger health units.

PCI-SS: MISO dynamic nonlinear protein secondary structure prediction.

BACKGROUND: Since the function of a protein is largely dictated by its three dimensional configuration, determining a protein's structure is of fundamental importance to biology. Here we report on a novel approach to determining the one dimensional secondary structure of proteins (distinguishing alpha-helices, beta-strands, and non-regular structures) from primary sequence data which makes use of Parallel Cascade Identification (PCI), a powerful technique from the field of nonlinear system identification. RESULTS: Using PSI-BLAST divergent evolutionary profiles as input data, dynamic nonlinear systems are built through a black-box approach to model the process of protein folding. Genetic algorithms (GAs) are applied in order to optimize the architectural parameters of the PCI models. The three-state prediction problem is broken down into a combination of three binary sub-problems and protein structure classifiers are built using 2 layers of PCI classifiers. Careful construction of the optimization, training, and test datasets ensures that no homology exists between any training and testing data. A detailed comparison between PCI and 9 contemporary methods is provided over a set of 125 new protein chains guaranteed to be dissimilar to all training data. Unlike other secondary structure prediction methods, here a web service is developed to provide both human- and machine-readable interfaces to PCI-based protein secondary structure prediction. This server, called PCI-SS, is available at http://bioinf.sce.carleton.ca/PCISS. In addition to a dynamic PHP-generated web interface for humans, a Simple Object Access Protocol (SOAP) interface is added to permit invocation of the PCI-SS service remotely. This machine-readable interface facilitates incorporation of PCI-SS into multi-faceted systems biology analysis pipelines requiring protein secondary structure information, and greatly simplifies high-throughput analyses. XML is used to represent the input protein sequence data and also to encode the resulting structure prediction in a machine-readable format. To our knowledge, this represents the only publicly available SOAP-interface for a protein secondary structure prediction service with published WSDL interface definition. CONCLUSION: Relative to the 9 contemporary methods included in the comparison cascaded PCI classifiers perform well, however PCI finds greatest application as a consensus classifier. When PCI is used to combine a sequence-to-structure PCI-based classifier with the current leading ANN-based method, PSIPRED, the overall error rate (Q3) is maintained while the rate of occurrence of a particularly detrimental error is reduced by up to 25%. This improvement in BAD score, combined with the machine-readable SOAP web service interface makes PCI-SS particularly useful for inclusion in a tertiary structure prediction pipeline.

Predicting node positivity in gastric cancer from gene expression profiles.

Lymphovascular invasion (LVI) in gastric cancer is readily demonstrated pre-operatively by mucosal biopsy during endoscopy, which can also provide samples for gene expression profiling. We have examined gene expression associated with lymphovascular invasion in a cohort of gastric cancer patients and have developed a 28-gene predictor of tumor aggressiveness for forecasting risk of node positivity (N+), which could potentially be useful pre-operatively. The resulting model's ranking of increasing tumor aggressiveness correlated positively with N+ status, reaching statistical significance, and was three times the correlation of LVI with N+ status.

Predicting survival in follicular lymphoma using tissue microarrays.

A tissue microarray (TMA) containing diagnostic biopsies was used to develop predictors of outcome in a group of 105 patients having advanced-stage follicular lymphoma (FL). The patients were staged and uniformly treated, and the usable cases had been randomly divided into a subgroup of 50 patients with outcomes identified, and a reserved subgroup of 43 patients whose outcomes were masked for blind testing of the predictors. Using training-input data from some patients with known outcomes, parallel cascade identification developed two predictors of overall survival based on a number of biomarkers. Both predictors had statistically significant performance over the remaining patients with known outcomes. The first predictor had been identified with model architectural settings and encoding scheme chosen, for the particular training input used, to enhance classification accuracy over remaining patients in the known subgroup. The second predictor was obtained without changing the settings and encoding scheme, but from an entirely different training input corresponding to novel cases from the TMA. Not surprisingly, the first predictor showed much higher accuracy over the known subgroup, but when tested over the reserved subgroup of 43 patients, averaged about 58% correct and did not reach statistical significance. The other predictor performed very similarly over the known and the reserved subgroups, with prediction on the reserved subgroup highly significant at p = 0.0056 in Kaplan-Meier survival analysis. We conclude that a predictor based on a number of biomarkers obtainable at diagnosis has the potential to improve prediction of overall survival in FL.

On the advantages of multi-input single-output parallel cascade classifiers.

Parallel Cascade Identification (PCI) has been successfully applied to build dynamic nonlinear systems that address diverse challenges in the field of bioinformatics. PCI may be used to identify either single-input single-output (SISO) or multi-input single-output (MISO) models. Although SISO PCI models have typically sufficed, it has been suggested that MISO PCI systems could also be used to form bioinformatics classifiers, and indeed they were successfully applied in one study. This paper reports on the first systematic comparison of MISO and SISO PCI classifiers. Motivation for using the MISO structure is given. The construction of MISO parallel cascade models is also briefly reviewed. In order to compare the accuracy of SISO and MISO PCI classifiers, genetic algorithms are applied to optimize the model architecture on a number of equivalent single-input and multi-input biological training datasets. Through evaluation of both model structures on independent test datasets, we establish that MISO PCI is capable of building classifiers of equal accuracy to those resulting from SISO PCI models. Moreover, we discuss and illustrate the benefits of the MISO approach, including significant reduction in training and testing times, and the ability to adjust automatically the weighting of individual inputs according to information content.

Applications of nonlinear system identification in molecular biology.

Here we show how nonlinear system identification techniques, such as fast orthogonal search (FOS) and the orthogonal search method (OSM), can be used to analyze gene expression profiles and predict the class to which a profile belongs.

On predicting medulloblastoma metastasis by gene expression profiling.

Accurately predicting clinical outcome or metastatic status from gene expression profiles remains one of the biggest hurdles facing the adoption of predictive medicine. Recently, MacDonald et al. (Nat. Genet. 2001, 29, 143-152) used gene expression profiles, from samples taken at diagnosis, to distinguish between clinically designated metastatic and nonmetastatic primary medulloblastomas, helping to elucidate the genetic mechanisms underlying metastasis and suggesting novel therapeutic targets. The obtained accuracy of predicting metastatic status does not, however, reach statistical significance on Fisher's exact test, although 22 training samples were used to make each prediction via leave-one-out testing. This paper introduces readily implemented nonlinear filters to transform sequences of gene expression levels into output signals that are significantly easier to classify and predict metastasis. It is shown that when only 3 exemplars each from the metastatic and nonmetastatic classes were assumed known, a predictor was constructed whose accuracy is statistically significant over the remaining profiles set aside as a test set. The predictor was as effective in recognizing metastatic as nonmetastatic medulloblastomas, and may be helpful in deciding which patients require more aggressive therapy. The same predictor was similarly effective on an independent set of 5 nonmetastatic tumors and 3 metastatic cell lines also used by MacDonald et al.

Using the fast orthogonal search with first term reselection to find subharmonic terms in spectral analysis.

The fast orthogonal search (FOS) algorithm has been shown to accurately model various types of time series by implicitly creating a specialized orthogonal basis set to fit the desired time series. When the data contain periodic components, FOS can find frequencies with a resolution greater than the discrete Fourier transform (DFT) algorithm. Frequencies with less than one period in the record length, called subharmonic frequencies, and frequencies between the bins of a DFT, can be resolved. This paper considers the resolution of subharmonic frequencies using the FOS algorithm. A new criterion for determining the number of non-noise terms in the model is introduced. This new criterion does not assume the first model term fitted is a dc component as did the previous stopping criterion. An iterative FOS algorithm called FOS first-term reselection (FOS-FTR), is introduced. FOS-FTR reduces the mean-square error of the sinusoidal model and selects the subharmonic frequencies more accurately than does the unmodified FOS algorithm.

Recognition of adenosine triphosphate binding sites using parallel cascade system identification.

Parallel cascade identification (PCI) is a method for approximating the behavior of a nonlinear system, from input/output training data, by constructing a parallel array of cascaded dynamic linear and static nonlinear elements. PCI has previously been shown to provide an effective means for classifying protein sequences into structure/function families. In the present study, PCI is used to distinguish proteins that are binding to adenosine triphosphate or guanine triphosphate molecules from those that are nonbinding. Classification accuracy of 87.1% using the hydrophobicity scale of Rose et al. (Hydrophobicity of amino acid residues in globular proteins. Science 229:834-838, 1985), and 88.8% using Korenberg's SARAH1 scale, are obtained, as measured by tenfold cross-validation testing. Nearest-neighbor and K-nearest-neighbor (KNN) classifiers are constructed, and the resulting accuracy is, respectively, 88.0% and 90.8% on the SARAH1-encoded test data set, as measured by the above testing protocol. Significantly improved classification accuracy is achieved by combining PCI and KNN classifiers using quadratic discriminant analysis: accuracy rises from 87.9% (PCI) and 87.4% (KNN) to 96.5% for the combination, as measured by twofold cross-validation testing on the SARAH1-encoded test data set.

Gene expression monitoring accurately predicts medulloblastoma positive and negative clinical outcomes.

Prediction of medulloblastoma clinical outcome is crucial to personalizing treatment, both to identify high-risk patients for aggressive or alternative therapy and to spare those at low risk from excessive treatment. The best predictors [Pomeroy et al. (2002) Nature 415, 436-442], based on gene expression monitoring at diagnosis, have shown much less accuracy in recognizing patients with eventual failed outcomes - <50% for the predictor making fewest total errors - than those who would survive, while a single gene predictor exhibited reverse asymmetry. Such inaccuracy in recognizing one of the outcomes is a problem for clinical use. We hypothesized that a non-linear model could be built to significantly improve prediction of medulloblastoma outcome, thereby promoting use of gene-expression-based predictors in a clinical setting. In fact, this approach resulted in fewer errors and much less asymmetry in prediction, and bidirectional accuracy of about 80% could be obtained via its combination with other methods. Indeed, three combinations of methods were identified that yielded significantly better predictions of clinical outcome than previously attained, making feasible predictors of medulloblastoma treatment response with greatly improved bidirectional accuracy essential for clinical use.

Parallel cascade recognition of exon and intron DNA sequences.

Many of the current procedures for detecting coding regions on human DNA sequences combine a number of individual techniques such as discriminant analysis and neural net methods. Recent papers have used techniques from nonlinear systems identification, in particular, parallel cascade identification (PCI), as one means for classifying protein sequences into their structure/function groups. In the present paper, PCI is used in a pilot study to distinguish exon (coding) from intron (noncoding; interspersed within genes) human DNA sequences. Only the first exon and first intron sequences with known boundaries in genomic DNA from the beta T-cell receptor locus were used for training. Then, the parallel cascade classifiers were able to achieve classification rates of about 89% on novel sequences in a test set, and averaged about 82% when results of a blind test were included. In testing over a much wider range of human nucleotide sequences, PCI classifiers averaged 83.6% correct classifications. These results indicate that parallel cascade classifiers may be useful components in future coding region detection programs.

Prediction of treatment response using gene expression profiles.

This paper concerns prediction of clinical outcome from gene expression profiles using work in a different area, nonlinear system identification. In particular, the approach can predict long-term treatment response from data of a landmark article by Golub et al. (Golub, T. R.; Slonim, D. K.; Tamayo, P.; Huard, C.; Gaasenbeek, M.; Mesirov, J. P. et al. Science 1999, 286, 531-537) that has not previously been achieved with these data. The present paper shows that, for these data, gene expression profiles taken at time of diagnosis of acute myeloid leukemia contain information predictive of eventual response to chemotherapy. This was not evident in previous work; indeed, the Golub et al. article did not find a set of genes strongly correlated with clinical outcome. However, the present approach can accurately predict outcome class of gene expression profiles even when the genes do not have large differences in expression levels between the classes.