RU2110883C1 - Adaptive filter for estimating transient processes - Google Patents

Abstract

FIELD: computer engineering; filtering signals in special-purpose and hybrid computers and developing computer software. SUBSTANCE: proposed filter is modification of Kalman filter wherein additional parts and connections are introduced to implement optimal correction of filter according to Krasovskii RMS criterion; it incorporates correction filter and error estimating filter, this error being used to adjust main and correction filters with aid of nonterminal control algorithm. EFFECT: improved stability and accuracy of filtration of transient processes. 1 dwg

Description

 The invention relates to computer technology and can be used to filter signals in specialized analog and hybrid computers, as well as for the formation of computer software.

 The traditional theory of optimal estimation requires knowledge of the exact mathematical model of the observed process, as well as the statistical characteristics of its noise and measurement noise [1-7]. In practice, such a condition is difficult to provide. In these cases, traditional filtering methods are unacceptable. The presence of a priori uncertainty leads to the fact that when implementing filtering algorithms, problems arise associated with eliminating the "divergence" of the filter. All methods used to eliminate these shortcomings are associated with a change in the weight of measurements [8, 9] and lead to the creation of suboptimal filtering algorithms and a decrease in the quality of the estimation process.

 Closest to the proposed filter is Kalman [3], the structure of which is shown in the drawing. This filter contains a series-connected subtracting adder 1, a block of variable gain 2, an adder 3, an integrator 4, the output of which the filtered signal as feedback is fed to the second input of the subtracting adder 1, a constant coefficient block 5, the output of which is connected to the second input of the adder 3.

 The disadvantage of this filter is the low accuracy of estimation of non-stationary processes, especially in the presence of inaccurate a priori information about the observed process. This greatly limits the scope of the filter.

 The technical result of the invention is to improve the accuracy of filtering non-stationary processes and ensuring stable operation of the filter in a wide range of conditions for changing the input signal to expand the scope.

 The essence of the invention lies in the fact that the Kalman filter is supplemented by a correction filter with elements and relationships similar to the Kalman filter and a weighting block, the input of the correction filter being connected to the output of the subtracting adder of the Kalman filter, and the output of the correction filter through the weighting block connected to additional inputs adders of both filters.

 The drawing shows a block diagram of an adaptive filter.

 The filter consists of a Kalman I filter, correction filter II, subtracting adders 1.1 ', variable gain blocks 2.2', adders 3.3 ', integrators 4.4', constant coefficient blocks 5.5 ', weight coefficients block 6.

 Adaptive filter works as follows.

фильтра Калмана. В результате этого формирует невязка Z^*, которая через блок переменных коэффициентов усиления 2 поступает на сумматор 3 и далее на интегратор 4. На выходе интегратора 4 формируется оценка измерений

. Одновременно невязка Z^*, содержащая случайную и систематическую составляющие, с выхода сумматора 1 поступает на фильтр коррекции. Фильтр коррекции производит обработку информации аналогично фильтру Калмана. На его выходе формируется оценка невязки

, которая поступает на блок весовых коэффициентов 6 и в вид величины Δ_u подается на дополнительные входы сумматоров 3 и 3'. В результате этого осуществляется настройка как фильтра Калмана, так и фильтра коррекции, устраняется смещение при получении оценки

и обеспечивается устойчивая работа фильтра в широком диапазоне условий изменения входного сигнала.The Kalman filter input receives measurement results. This information on the adder 1 is compared with the output value

Kalman filter. As a result of this, a discrepancy Z ^{* is formed} , which, through a block of variable gain factors 2, goes to the adder 3 and then to the integrator 4. At the output of the integrator 4, a measurement estimate is formed

. At the same time, the residual Z ^* , containing random and systematic components, from the output of the adder 1 is fed to the correction filter. The correction filter performs information processing similarly to the Kalman filter. At its output, an estimate of the residual is formed

, which is supplied to the block of weight coefficients 6 and in the form of the quantity Δ _u is supplied to the additional inputs of the adders 3 and 3 '. As a result of this, both the Kalman filter and the correction filter are set up, the bias is eliminated upon receipt of the estimate

and provides stable filter operation in a wide range of conditions for changing the input signal.

 Supplementing the well-known Kalman filter with a correction filter having the same structure as the Kalman filter allows one to increase the accuracy of filtering substantially unsteady processes in the presence of rough a priori information about the observed process by isolating the magnitude of the offset of the output signal with its subsequent correction. This allows you to expand the scope of the proposed filter.

Sources of information
1. Andreev N.I. The theory of statistically optimal control systems. - M.: Science, 1980.

 2. Brammer K. and Ziffling G. Kalman-Buisey Filter. - M.: Science, 1982.

 3. Kazakov I.E. Statistical theory of control systems in the state space. M .: Nauka, 1975.

 4. The basics of automatic control. / Ed. V.S. Pugacheva. Ed. Z. - M .: Nauka, 1974.

 Pugachev V.S. and Sinitsyn I.N. Stochastic differential systems. - M.: Science, 1985.

 Sage E.P. and White S.Ch. Optimal system management. - M.: Radio and Communications, 1982.

 7. Reference on the theory of automatic control. / Ed. A.A. Krasovsky. - M.: Science, 1987.

 8. Filtering and stochastic control in dynamic systems. / Ed. K.T. Leondes. - M .: Mir, 1980.

 9. Kuzovkov N. T. and Salychev O.S. Inertial navigation and optimal filtering. - M.: Mechanical Engineering, 1982.

Claims (1)

 An adaptive filter for evaluating non-stationary processes, containing a Kalman filter, the input of which is the information input of the adaptive filter, and the output is the output of the adaptive filter and is made on a series-connected subtracting adder, the non-inverting input of which is the input of the Kalman filter, a block of variable gain, adder and integrator, the output of which is the output of the Kalman filter and is connected to the inverting input of the subtracting adder, and with the second input of the adder through a constant coefficients, characterized in that a correction filter, similar to the Kalman filter, and a weight coefficient block are introduced, the output of which is connected to additional inputs of the Kalman filter adders and a correction filter, the input of which is connected to the output of the subtracting Kalman filter adder, and the output to the input of the weight block coefficients.