Kalman filter in the context of Soft sensor

A virtual reality headset (VR headset) is a head-mounted device that uses 3D near-eye displays and positional tracking to provide a virtual reality environment for the user. VR headsets are widely used with VR video games, but they are also used in other applications, including simulators and trainers. VR headsets typically include a stereoscopic display (providing separate images for each eye), stereo sound, and sensors like accelerometers and gyroscopes for tracking the pose of the user's head to match the orientation of the virtual camera with the user's eye positions in the real world. Mixed reality (MR) headsets are VR headsets that enable the user to see and interact with the outside world. Examples of MR headsets include the Apple Vision Pro and Meta Quest 3.

VR headsets typically use at least one MEMS IMU for three degrees of freedom (3DOF) motion tracking, and optionally more tracking technology for six degrees of freedom (6DOF) motion tracking. 6DOF devices typically use a sensor fusion algorithm to merge the data from the IMU and any other tracking sources, typically either one or more external sensors, or "inside-out" tracking using outward facing cameras embedded in the headset. The sensor fusion algorithms that are used are often variants of a Kalman filter. VR headsets can support motion controllers, which similarly combine inputs from accelerometers and gyroscopes with the headset's motion tracking system.

Pedometric mapping, or statistical soil mapping, is data-driven generation of soil property and class maps that is based on use of statistical methods. Its main objectives are to predict values of some soil variable at unobserved locations, and to access the uncertainty of that estimate using statistical inference i.e. statistically optimal approaches. From the application point of view, its main objective is to accurately predict response of a soil-plant ecosystem to various soil management strategies—that is, to generate maps of soil properties and soil classes that can be used for other environmental models and decision-making. It is largely based on applying geostatistics in soil science, and other statistical methods used in pedometrics.

Although pedometric mapping is mainly data-driven, it can also be largely based on expert knowledge—which, however, must be utilized within a pedometric computational framework to produce more accurate prediction models. For example, data assimilation techniques, such as the space-time Kalman filter, can be used to integrate pedogenetic knowledge and field observations.

Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs.In control theory, the observability and controllability of a linear system are mathematical duals.

The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer for that system, such as Kalman filters.

Rudolf Emil Kálmán (May 19, 1930 – July 2, 2016) was a Hungarian-American electrical engineer, mathematician, and inventor. He is most noted for his co-invention and development of the Kalman filter, a mathematical algorithm that is widely used in signal processing, control systems, and guidance, navigation and control. For this work, U.S. President Barack Obama awarded Kálmán the National Medal of Science on October 7, 2009.