Kalman Filter Simulation

In statistics and control theoryKalman filteringalso known as linear quadratic estimation LQEis an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. The Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and dynamically positioned ships. Kalman filters also are one of the main topics in the field of robotic motion planning and control, and they are sometimes included in trajectory optimization. The Kalman filter also works for modeling the central nervous system 's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedbackuse of the Kalman filter supports a realistic model for making estimates of the current state of the motor system and issuing updated commands. The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variablesalong with their uncertainties. Once the outcome of the next measurement necessarily corrupted with some amount of error, including random noise is observed, these estimates are updated using a weighted averagewith more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real timeusing only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required. Using a Kalman filter assumes that the errors are Gaussian. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear. The random processes are therefore described by models such as The question of how the numbers specifying the model are obtained from experimental data will not be considered. Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is a hidden Markov model where the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Also, Kalman filter has been successfully used in multi-sensor fusion [4]and distributed sensor networks to develop distributed or consensus Kalman filter. Richard S. Bucy of the University of Southern California contributed to the theory, leading to it sometimes being called the Kalman—Bucy filter. 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. This Kalman filter was first described and partially developed in technical papers by SwerlingKalman and Kalman and Bucy The Apollo computer used 2k of magnetic core RAM and 36k wire rope [ Clock speed was under kHz [

Kalman filter

The Kalman filter is an algorithm that estimates the state of a system from measured data. It was primarily developed by the Hungarian engineer Rudolf Kalman, for whom the filter is named. There are now several variants of the original Kalman filter. These filters are widely used for applications that rely on estimation, including computer vision, guidance and navigation systems, econometrics, and signal processing. Kalman filters are commonly used in GNC systems, such as in sensor fusion, where they synthesize position and velocity signals by fusing GPS and IMU inertial measurement unit measurements. The filters are often used to estimate a value of a signal that cannot be measured, such as the temperature in the aircraft engine turbine, where any temperature sensor would fail. Using the Kalman filter to estimate the position of an aircraft. See example for details. Tracking the trajectory of a ball. The output of the Kalman filter is denoted by the red circles and the object detection is denoted in black. Notice when the ball is occluded and there are no detections; the filter is used to predict its location. See also: object recognitionvideo processingPID controlparameter estimationpoint cloudbattery state of charge. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Kalman Filter. Search MathWorks. Trial software Contact sales. Guidance, Navigation, and Control Kalman filters are commonly used in GNC systems, such as in sensor fusion, where they synthesize position and velocity signals by fusing GPS and IMU inertial measurement unit measurements.