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• Kalman_filter abstract "The Kalman filter, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state. The filter is named for Rudolf (Rudy) E. Kálmán, one of the primary developers of its theory.The Kalman filter has numerous applications in technology. A common application is for guidance, navigation and control of vehicles, particularly aircraft and spacecraft. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics.The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along 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 average, with more weight being given to estimates with higher certainty. Because of the algorithm's recursive nature, it can run in real time using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.It is a common misconception that the Kalman filter assumes that all error terms and measurements are Gaussian distributed. Kalman's original paper derived the filter using orthogonal projection theory to show that the covariance is minimized, and this result does not require any assumption, e.g., that the errors are Gaussian. He then showed that the filter yields the exact conditional probability estimate in the special case that all errors are Gaussian-distributed.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 Bayesian model similar to a hidden Markov model but where the state space of the latent variables is continuous and where all latent and observed variables have Gaussian distributions.".
• Kalman_filter thumbnail Basic_concept_of_Kalman_filtering.svg?width=300.
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• Kalman_filter hasPhotoCollection Kalman_filter.
• Kalman_filter subject Category:Control_theory.
• Kalman_filter subject Category:Hungarian_inventions.
• Kalman_filter subject Category:Linear_filters.
• Kalman_filter subject Category:Markov_models.
• Kalman_filter subject Category:Nonlinear_filters.
• Kalman_filter subject Category:Robot_control.
• Kalman_filter subject Category:Signal_estimation.
• Kalman_filter subject Category:Stochastic_differential_equations.
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• Kalman_filter comment "The Kalman filter, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state.".
• Kalman_filter label "Filtr Kalmana".
• Kalman_filter label "Filtre de Kalman".
• Kalman_filter label "Filtro de Kalman".
• Kalman_filter label "Filtro de Kalman".
• Kalman_filter label "Filtro di Kalman".
• Kalman_filter label "Kalman filter".
• Kalman_filter label "Kalman-Filter".
• Kalman_filter label "Kalman-filter".
• Kalman_filter label "Фильтр Калмана".
• Kalman_filter label "مرشح كالمان".
• Kalman_filter label "カルマンフィルター".
• Kalman_filter label "卡尔曼滤波".
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• Kalman_filter depiction Basic_concept_of_Kalman_filtering.svg.
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