In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization. Kalman filtering also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, the use of Kalman filters provides a realistic model for making estimates of the current state of a motor system and issuing updated commands. The algorithm works via a two-phase process: a prediction phase and an update phase. In the prediction phase, the Kalman filter produces estimates of the current state variables, including their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some error, including random noise) is observed, these estimates are updated using a weighted average, with more weight given to estimates with greater certainty. The algorithm is recursive. It can operate in real time, using only the present input measurements and the state calculated previously and its uncertainty matrix; no additional past information is required. Optimality of Kalman filtering assumes that errors have a normal (Gaussian) distribution. In the words of Rudolf E. Kálmán, "The following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Regardless of Gaussianity, however, if the process and measurement covariances are known, then the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense, although there may be better nonlinear estimators. It is a common misconception (perpetuated in the literature) that the Kalman filter cannot be rigorously applied unless all noise processes are assumed to be Gaussian. Extensions and generalizations of the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Kalman filtering has been used successfully in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filtering. == History == The filtering method is named for Hungarian émigré Rudolf E. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering. Kalman was inspired to derive the Kalman filter by applying state variables to the Wiener filtering problem. Stanley F. Schmidt is generally credited with developing the first implementation of a Kalman filter. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements. It was during a visit by Kálmán to the NASA Ames Research Center that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the Apollo program resulting in its incorporation in the Apollo navigation computer. This digital filter is sometimes termed the Stratonovich–Kalman–Bucy filter because it is a special case of a more general, nonlinear filter developed by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before the summer of 1961, when Kalman met with Stratonovich during a conference in Moscow. This Kalman filtering was first described and developed partially in technical papers by Swerling (1958), Kalman (1960) and Kalman and Bucy (1961). The Apollo computer used 2k of magnetic core RAM and 36k wire rope [...]. The CPU was built from ICs [...]. Clock speed was under 100 kHz [...]. The fact that the MIT engineers were able to pack such good software (one of the very first applications of the Kalman filter) into such a tiny computer is truly remarkable. Kalman filters have been vital in the implementation of the navigation systems of U.S. Navy nuclear ballistic missile submarines, and in the guidance and navigation systems of cruise missiles such as the U.S. Navy's Tomahawk missile and the U.S. Air Force's Air Launched Cruise Missile. They are also used in the guidance and navigation systems of reusable launch vehicles and the attitude control and navigation systems of spacecraft which dock at the International Space Station. == Overview of the calculation == Kalman filtering uses a system's dynamic model (e.g., physical laws of motion), known control inputs to that system, and multiple sequential measurements (such as from sensors) to form an estimate of the system's varying quantities (its state) that is better than the estimate obtained by using only one measurement alone. As such, it is a common sensor fusion and data fusion algorithm. Noisy sensor data, approximations in the equations that describe the system evolution, and external factors that are not accounted for, all limit how well it is possible to determine the system's state. The Kalman filter deals effectively with the uncertainty due to noisy sensor data and, to some extent, with random external factors. The Kalman filter produces an estimate of the state of the system as an average of the system's predicted state and of the new measurement using a weighted average. The purpose of the weights is that values with better (i.e., smaller) estimated uncertainty are "trusted" more. The weights are calculated from the covariance, a measure of the estimated uncertainty of the prediction of the system's state. The result of the weighted average is a new state estimate that lies between the predicted and measured state, and has a better estimated uncertainty than either alone. This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration. This means that Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new state. The measurements' certainty-grading and current-state estimate are important considerations. It is common to discuss the filter's response in terms of the Kalman filter's gain. The Kalman gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively. With a low gain, the filter conforms to the model predictions more closely. At the extremes, a high gain (close to one) will result in a more jumpy estimated trajectory, while a low gain (close to zero) will smooth out noise but decrease the responsiveness. When performing the actual calculations for the filter (as discussed below), the state estimate and covariances are coded into matrices because of the multiple dimensions involved in a single set of calculations. This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances. == Example application == As an example application, consider the problem of determining the precise location of a truck. The truck can be equipped with a GPS unit that provides an estimate of the position within a few meters. The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few meters of the real position. In addition, since the truck is expected to follow the laws of physics, its position can also be estimated by integrating its velocity over time, determined by keeping track of wheel revolutions and the
QF-Test
QF-Test from Quality First Software is a cross-platform software tool for automated testing of programs via the graphical user interface (GUI) test automation). The program is specialized on (Java/Swing, Standard Widget Toolkit (SWT), Eclipse plug-ins and rich client platform (RCP) applications, ULC and JavaFX) cross-web browser test automation of static and dynamic web applications (HTML and web frameworks like Angular, Ext JS, Fluent UI React, Google Web Toolkit (GWT), jQuery UI, jQueryEasyUI Remote Application Platform (RAP), Qooxdoo, RichFaces, Vaadin, React, Smart GWT, Vue.js, ICEfaces and ZK). Version 4.1 added support for macOS and the Apple Safari and Microsoft Edge browsers via the Selenium WebDriver. Representational State Transfer (RESTful) web service testing. From version 5.0, Windows applications can also be tested (classic Win32 applications, .NET framework applications (often developed in C#) based on Windows Presentation Foundation (WPF) or Windows Forms, Windows apps and Universal Windows Platform (UWP) applications using Extensible Application Markup Language (XAML) controls) and modern C++ applications (such as Qt applications). Version 5.3 added support for the Chrome DevTools protocol, which allows browsers to be controlled using CDP drivers. Since then, mobile testing for iOS and Android, accessibility testing of web applications and SmartID, a new approach for more flexible and robust component recognition, have been introduced. Powerful enhancements such as WebAPI testing and AI-assisted validation complement the test automation tool. == Overview == QF-Test (the successor of qftestJUI, available since 2001) enables regression and load testing and runs on Windows, Unix and macOS. It is mainly used commercially by testers, developers or business analysts (modelling, low code approaches) with or without programming knowledge as part of software Quality Assurance. Since December 2008, a webtest add-on is available which allows test automation of browser-based GUIs (such as Internet Explorer, Mozilla Firefox, Google Chrome, Apple Safari, and Microsoft Edge) along with extant Java GUI test functions, which was extended to include JavaFX in July 2014. From 2018, QF-Test version 4.2 can test PDF documents, from 2020 native desktop applications (QF-Test version 5) and in 2022, mobile application testing will be added. The basis for efficient use in test automation is stable component recognition (IDs, logical screen elements, labels, CustomWebResolver, SmartID, ...) with low maintenance effort. == Features == General – QF-Test's capture/replay function enables recording of tests for beginners, while modular programming (modularizing) allows creating large test suites in a concise arrangement. For the advanced user who requires even more control over his application, the tool offers access to internal program structures through the standard scripting languages Jython, the Java implementation of the popular Python language, JavaScript, and Groovy. The tool also offers a batch processing mode, allowing to run tests unattended and then generate XML, HTML and JUnit reports. Thus the tool can be integrated into existing build/test frameworks like Jenkins, Ant or Maven. Another mode is the so-called Daemon mode for distributed test execution. A specific integration with many test management tools exists. There is a test debugger (enabling arbitrary stepping and editing variables at runtime) and a fully automated dependency management that takes care of pre- and postconditions and helps isolating test cases. Data-driven testing with no need for scripting is possible. Web testing: cross-browser on Internet Explorer, Chrome, Firefox, Edge (including Chromium-based), Opera and Safari for static and dynamic websites (HTML5, Ajax, DOM). A headless browser can also be used for testing. QF-Test fully supports frameworks like Angular, React and Vue.js, but also many specific UI toolkits like Smart (GWT), GXT/ExtGWT, ExtJS, ICEfaces, jQuery UI, Kendo UI, PrimeFaces, Qooxdoo, RAP, RichFaces, Vaadin and ZK. Easy integration with Selenium makes it easy to balance development and functional testing. Electron applications can also be tested. Other (e.g., SAP UI5, Siebel Open UI, Salesforce) and future web toolkits can be integrated with little effort. Short-term and individual customisations (CustomWebResolver) are possible via an optimised interface JavaFX, Java Swing, SWT, Eclipse plug-ins and RCP applications and ULC. Support for testing when migrating from JavaSwing or JavaFX to web applications (e.g. via Webswing). Hybrid applications based on multiple technologies are also supported, e.g. applications that integrate HTML content into Java applications using JxBrowser. Windows-based applications (Win32, .NET, Windows Forms, WPF, Windows apps, Qt). Android applications can be tested on real devices and with the Android Studio emulator. iOS applications can also be tested on real devices and with the Xcode Simulator. Testing of PDF documents (document comparisons, checking content, texts, images/graphic objects, layouts, "invisible" or partially hidden objects). QF-Test 9 introduces web accessibility testing to automatically check compliance with WCAG and other standards. QF-Test 10 introduces powerful enhancements for WebAPI testing and AI-assisted validation.
Conservative morphological anti-aliasing
Conservative morphological anti-aliasing (CMAA) is an antialiasing technique originally developed by Filip Strugar at Intel. CMAA is an image-based, post processing technique similar to that of morphological antialiasing. CMAA uses 4 main steps which are image analysis for color discontinuities, locally dominant edge detection, simple shape handling, and lastly symmetrical long edge shape handling. A couple of years after CMAA was introduced, Intel unveiled an updated version which they named CMAA2.
GeoNetwork opensource
The GeoNetwork opensource (GNOS) project is a free and open source (FOSS) cataloging application for spatially referenced resources. It is a catalog of location-oriented information. == Outline == It is a standardized and decentralized spatial information management environment designed to enable access to geo-referenced databases, cartographic products and related metadata from a variety of sources, enhancing the spatial information exchange and sharing between organizations and their audience, using the capacities of the internet. Using the Z39.50 protocol it both accesses remote catalogs and makes its data available to other catalog services. As of 2007, OGC Web Catalog Service are being implemented. Maps, including those derived from satellite imagery, are effective communicational tools and play an important role in the work of decision makers (e.g., sustainable development planners and humanitarian and emergency managers) in need of quick, reliable and up-to-date user-friendly cartographic products as a basis for action and to better plan and monitor their activities; GIS experts in need of exchanging consistent and updated geographical data; and spatial analysts in need of multidisciplinary data to perform preliminary geographical analysis and make reliable forecasts. == Deployment == The software has been deployed to various organizations, the first being FAO GeoNetwork and WFP VAM-SIE-GeoNetwork, both at their headquarters in Rome, Italy. Furthermore, the WHO, CGIAR, BRGM, ESA, FGDC and the Global Change Information and Research Centre (GCIRC) of China are working on GeoNetwork opensource implementations as their spatial information management capacity. It is used for several risk information systems, in particular in the Gambia. Several related tools are packaged with GeoNetwork, including GeoServer. GeoServer stores geographical data, while GeoNetwork catalogs collections of such data.
SAP BTP
SAP Business Technology Platform (SAP BTP) is a platform as a service developed by SAP SE that offers a suite of services including database and data management, AI, analytics, application development, automation and integration all running on one unified platform. == Overview == SAP BTP is made up of four components: Application development and automation: to create applications or extend existing applications. Data and analytics: to access and analyze data across SAP and third-party systems using multi-cloud architecture. Integration: to integrate and connect applications and data. Artificial Intelligence (AI): to access large language models (LLMs) to develop AI. == History == SAP BTP was introduced as part of the SAP strategy to unify its portfolio and cloud offerings under a single platform. The platform was evolved from earlier initiatives such as SAP Cloud Platform and now serves as the central hub for cloud, data, analytics, integration and AI technologies. Initially unveiled as "SAP NetWeaver Cloud" belonging to the SAP HANA Cloud portfolio on October 16, 2012 the cloud platform was reintroduced with the new name "SAP HANA Cloud Platform" on May 13, 2013 as the foundation for SAP cloud products, including the SAP BusinessObjects Cloud. Adoption of the SAP HANA Cloud Platform in 2015 stood at over 4000 customers and 500 partners. In 2016, SAP and Apple Inc. partnered to develop mobile applications on iOS using cloud-based software development kits (SDKs) for the SAP Cloud Platform. On February 27, 2017, SAP HANA Cloud Platform was renamed "SAP Cloud Platform" at the Mobile World Congress. On January 18, 2021, the name "SAP Cloud Platform" was retired from the SAP product portfolio to support SAP BTP. As of October 2024, SAP states that SAP BTP is used by more than 27,000 customers and more than 2,800 partners. Recently, SAP Business One has worked on improving the functionalities of BTP to cater for the demands of digital transformation. The platform offers comprehensive services in AI, application development, automation, integration, data management, and analytics.
Representation collapse
Representation collapse is a phenomenon in machine learning and representation learning where a model maps different inputs to the same or very similar embeddings, which means it loses important information about how the data is spread out. It is frequently encountered in self-supervised learning, especially within contrastive and non-contrastive frameworks, when training objectives or model architectures do not maintain variance across representations. Collapse results in degenerate solutions characterized by uninformative learned features, significantly impairing downstream task performance. Various techniques have been proposed to mitigate representation collapse, including the use of negative samples, architectural asymmetry, stop-gradient operations, variance regularization, and redundancy reduction objectives, as seen in methods such as SimCLR, BYOL, and VICReg. Comprehending and averting representation collapse is regarded as a fundamental challenge in the advancement of stable and efficient self-supervised learning systems.
SAP StreamWork
SAP StreamWork is an enterprise collaboration tool from SAP SE released in March 2010, and discontinued in December 2015. StreamWork allowed real-time collaboration like Google Wave, but focused on business activities such as analyzing data, planning meetings, and making decisions. It incorporated technology from Box.net and Evernote to allow users to connect to online files and documents, and document-reader technology from Scribd allowed users to view documents directly within its environment. StreamWork supported the OpenSocial set of application programming interfaces (APIs), allowing it to connect to tools built by third-party developers, such as Google Docs. A version of StreamWork intended for large enterprises used a virtual appliance based on Novell's SUSE Linux Enterprise to connect it to business systems, including those from SAP.