SU1608787A1 - Digital filter - Google Patents

Abstract

The invention relates to recursive digital filters and can be used in information-measuring systems with irregular sampling of input signals. The aim of the invention is to extend the functionality by providing filtering of signals with irregular discretization. The Kalman digital filter contains adders 1, 3, 4, 10 and 12, multipliers 2, 6, 7, 8, 9 and 11, delay element 5 and measuring unit 13 of the time interval of deviation from the average value. Such an embodiment of the filter provides filtering of both a regularly sampled signal and a signal with irregular sampling. 1 il.

Description

S L / Pk / k-1 R (k), p-,.

  + Atk.

IPk / k-1 С 2 (tk) + Rk /

I. (18)

Then

Pk + 1 / k Pk + 1 / k + Pk + 1 / kAtk. (19)

Based on (19), equation (11) can be written as follows:

life

Kk + 1

Pn-VkC (4, + 1) + Pi, + VtC (in-t) Dz (tt + 1) Pk + Vt + s (tk. |) Pk - (- Vk D tk + P {k + 1)

k + VfcCJtk + l) Pii + VtC () Atk

Pk + l / | kC (tk + 1) + R (k + 1) Pk + VkC (tk + 1) 4-R (R + 1)

OR kk + i Kk + 1 + Kk + 1 Atk,

(20) (21)

+ U ..- (y () (tk) x (k))}.

Usually C (tk) With const. Denote

B:

d: 1-Kk + iC (tk) a. (28)

Then equation (27) takes the form

x (K + 1) bx (K) k ;; + 1 {y (K + 1) -bCx (K)} + + Atk dBx (K) + Kk-n {y (K + 1) - bcx (K )}. (29)

Equation (29) thus obtained describes the operation of the proposed filter, In the case where Atk, equation (29) reduces to an expression describing the operation of a known filter.

Kalman digital filter works

in the following way.

The signal samples come from the input of the device to the first input of the first adder 1 and the input of the block 13, launching it to the measurement

next interval. In the first adder 1, the difference between the received value of the reference and the predicted value multiplied in the third multiplier 7 by the weighting factor is found. Received

thus, the prediction error enters the first inputs of the first and fourth multipliers 2 and 9. where it is weighted by the respective coefficients. Then it goes to the first inputs of the second 3 and the third 10 adders. On the second adder 3, the predicted sample is corrected without taking into account the deviation of the sampling rate of the filtered signal. And at the third adder 10, a signal component is formed due to the deviation of the sampling rate.

To this end, the second input of the third adder 10 receives the predicted count value weighted at the sixth multiplier 8. The result of the sum is fed to a fifth multiplier 11, where it is weighted by the value of the deviation of the sampling interval from its average value. To find the value of this deviation, the value of the time interval from the moment of arrival of the previous sample to the moment of the current reference from block 13 is fed to the first input of the fifth adder 12 (to the input to be decremented), to the second input of which (the input is subtracted) the average value is given signal sampling interval. The difference thus obtained at the output of the fifth adder 12 is the desired deviation of the sampling interval from its mean value.

The detected components of the signal from the outputs of the second adder 3 and fifth multiplier 11 are fed to the inputs of the fourth adder 4, where they add up the filtered value of the signal, this value is transmitted to the digital output of the Kalman filter, and is also used to predict the next reference. To predict, the filtered sample value through delay element 5 is fed to a second multiplier 6, where it is weighted by an appropriate factor. Further, the cycle of operation of the digital filter is repeated.

Thus, in comparison with the known ones, the proposed Kalman digital filter provides filtering of both a regularly sampled signal, 5 and a signal with irregular sampling.

The formula of the invention Kalman digital filter containing first connected in series

0 the adder, the first input of which is the input of a digital Kalman filter, the first multiplier and the second adder, as well as the delayed elements connected in series, the second multiplier, the output of which is connected to the second input of the second adder, and the third multiplier, the output of which is connected to the second input of the first adder, the second inputs of the first, second and third multipliers are

0 the first, second, and third inputs of the Kalman digital filter coefficients, which is characterized by the fact that, in order to extend the functionality by providing filtering of signals with

5 by irregular discretization, the fourth multiplier connected in series is introduced, the first input of which is connected to the output of the first adder, the third adder, the fifth multiplier and the fourth total0 torus, the second input of which is connected to the output of the second adder, and the sixth multiplier, the input and output of which are connected with the output of the second multiplier and the second input of the third adder

5, respectively, and a serially connected unit measuring the time interval of the deviation from the average value, the input of which is connected to the first input of the first adder, and a fifth adder, the output of which is connected to the second input of the fifth multiplier, and the output of the fourth adder is connected to the input of the delay element, the fourth and fifth, the inputs of the coefficients and the input of the value of the average sampling interval of the Kalman digital filter are the second inputs of the fourth and sixth multipliers, and the fifth adder, respectively.

Claims (1)

Claim A Kalman digital filter containing a first adder connected in series, the first input of which is an input of a Kalman digital filter, a first multiplier and a second adder, as well as a delay element connected in series, a second multiplier whose output is connected to the second input of the second adder, and a third multiplier, the output of which connected to the second input of the first adder, and the second inputs of the first, second and third multipliers are the first, second and third inputs of the coefficients of a digital Kalman filter, o characterized in that, in order to expand the functionality by providing filtering of signals with irregular sampling, a fourth multiplier is introduced in series, the first input of which is connected to the output of the first adder, the third adder, the fifth multiplier and the fourth adder, the second input of which is connected to the output of the second the adder, as well as the sixth multiplier, the input and output of which is connected to the output of the second multiplier and the second input of the third adder, respectively, and connected in series the second unit for measuring the time interval of deviation from the average value, the input of which is connected to the first input of the first adder, and the fifth adder, the output of which is connected to the second input of the fifth multiplier, and the output of the fourth adder is connected to the input of the delay element, the fourth and fifth, coefficient inputs and the input the values of the average sampling interval of the digital Kalman filter are the second inputs of the fourth and sixth multipliers, and the fifth adder, respectively.