A general filter for measurements with any probability distribution
نویسندگان
چکیده
The KulmanJilter is a very eficient optimal$ltel; however it has the precondition that the noises of the process and of the measurement are Gaussian. In this paper we introduce ‘The General Distribution Filter’ which is an optimal jilter that can be used even where the distributions are not Gaussian. An eficient practical implementation of theJilter is possible where the distributions are discrete and compact or can be approximated as such. The problem is that when the measurement is not a Gaussian distribution, the Kalman filter cannot be used. This was the motivation to develop the general distribution filter which can be used for any distribution function. As we will see, although the filter is defined for any probability distribution of the measurement, an efficient computer implementation of this filter is possible when the probability distribution of the measurement is discrete or can be approximated as such. 1. Definition of the problem The notion of filtering is connected with that of a process. The process state at time t is described by a vector, which is unknown and must be computed. An example of such a process is a moving vehicle, where the state is the vehicle’s position and speed. The information about the process comes from measurements, where the connection between the process and the measurement is known. Usually there is noise in the system, so that the measurement is described by its probability distribution. We will demonstrate a tracking application where the distributions cannot be approximated as Gaussian, and the Kalman filter cannot be used. As a better alternative, the measurement’s distribution is represented as a probability matrix, and the filtering is achieved using the general distribution filter. In the appendix we show that the Kalman filter is a special case of the general distribution filter.
منابع مشابه
Unscented Auxiliary Particle Filter Implementation of the Cardinalized Probability Hypothesis Density Filters
The probability hypothesis density (PHD) filter suffers from lack of precise estimation of the expected number of targets. The Cardinalized PHD (CPHD) recursion, as a generalization of the PHD recursion, remedies this flaw and simultaneously propagates the intensity function and the posterior cardinality distribution. While there are a few new approaches to enhance the Sequential Monte Carlo (S...
متن کاملExtended Kalman filtering with stochastic nonlinearities and multiple missing measurements
In this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of me...
متن کاملUsing Weibull probability distribution to calibrate prevailing wind applying in oil spill simulation
In the Persian Gulf, the major source of oil pollution is related to the transportation of tankers, offshore production and discharges by coastal refineries. The water dynamical field has been obtained using a new hydrodynamic model. Local wind is recognized as the principal driving force combining to the water dynamic field to determine oil drift on the sea surface. The Weibull probability dis...
متن کاملDoppler and bearing tracking using fuzzy adaptive unscented Kalman filter
The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using the Doppler and Bearing measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. Several techniques were studied to deal with this topic, such as the unscented Kalman filter. Nevertheless, the performance of the filter depends directly on the...
متن کاملCalculation of wedged dose distributions using an analytical method
Introduction: Wedge filters are used in radiotherapy to modify photon beam and improve dose uniformity in the target volume. Determination of wedge dose distribution is important to improve treatment planning accuracy. The utilization of treatment planning software to obtain dose distribution is not always available. In this work an analytical model has been developed to calcu...
متن کامل