Abstract
We have developed a sequential recursive Kalman Filter algorithm to filter data in the field of the non-Gaussian noise distribution to be used in measurement instruments. A special feature of the constructed Kalman Filter algorithm to filter data with the non-Gaussian noises is the absence of a need to determine a priori the statistical characteristics of noise. The applicability of the developed Kalman filtering procedure was tested by processing different distribution laws: the Cauchy, Pareto noises, normal and logistic distributions. The effectiveness of the devised filtering procedure is confirmed by applying the filter when processing experimental data with different laws of noise distribution. We have conducted approbation of the developed procedure for the Kalman filtering based on data obtained experimentally, with respect to the superposition of noise distribution laws. The a priori estimate for a filtering error when the number of iterations exceeds 30 tends to zero. The devised filtering procedure employing the Kalman filter could be used when performing the metrological certification of measuring instruments under industrial conditions. Under such circumstances, measuring information could become noisy due to various noises, including those that are not governed by the Gaussian distribution law. The filter could be used when processing data from control systems over state parameters, implemented on the principle of a magnitude threshold control. The applied aspect of the scientific result obtained implies the possibility of extending the scope of application of the classic Kalman filter in measurement instruments. This is a prerequisite for the development of a generic filtering algorithm using the Kalman filter.
Highlights
The Kalman filter is a series recursive algorithm that uses a dynamic system model adopted to provide an estimate
The classic Kalman filter is an equation for the calculation of the first and second moment of a posteriori probability density under given constraints
Since for the normal probability density mathematical expectation and variance matrix fully assign a probability density, we can say that the Kalman filter calculates the a posteriori probability density of the state vector at each point in time
Summary
The Kalman filter is a series recursive algorithm that uses a dynamic system model adopted to provide an estimate. Since for the normal probability density mathematical expectation and variance matrix fully assign a probability density, we can say that the Kalman filter calculates the a posteriori probability density of the state vector at each point in time. It means that it fully describes the state vector as a random vector magnitude [2]. Development of statistical models for indicators of processes in technology and economy [5], forecasting and determining the dynamics of economic indicators [6], cleaning of signals of measuring and radio engineering from noise and interference [7] is solved employing the Kalman filter. The task to develop an effective procedure for filtering using the Kalman filter in the field of noises that differ from the Gaussian distribution in order to apply it in measuring instruments is a relevant scientific and applied task
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