A general filter for measurements with any probability distribution

نویسندگان

  • Yoav Rosenberg
  • Michael Werman
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.

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تاریخ انتشار 1997