RU2430382C2 - Method of estimating parameters of wideband radio signals by prony method - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: first, preset signal is used to estimate signal spectral components by Prony's method of least squares. Then, additive deflections in estimation of spectral components are obtained to satisfy difference system obtained by linear forecasting to be used in improvement of earlier estimations. Note here that the latter are taken to be new magnitudes of spectral components in reiterated definition of deflections unless required accuracy is reached.

EFFECT: higher accuracy of estimation.

Description

The invention relates to the field of radio engineering and can be used to improve the accuracy of the assessment of the spectral parameters of radio signals received at the output of the measuring systems for a limited time interval using the parametric description by the Prony method [1]:

where N is the order of the model; A _i , λ _i are the decomposition parameters (spectral components) of the signal x (t) in the Prony series.

A known method of obtaining the parameters A _i , λ _{i of the} exponential series (1) using 2N equidistant samples of the signal x (t), involving the following steps [1]:

1. Finding the coefficients α _n (α _N = 1) that satisfy the system of equations composed of 2N samples of the signal {x _k }

2. Finding the values of z _i that satisfy the condition

3. Finding the coefficients A _i that satisfy the system of equations

4. Finding the coefficients λ _i from the condition

Thus, it is possible to completely restore the signal x (t) by observing its limited fragment on the time interval [0, T].

There is a method of refining the values of the spectral components A _i , λ _i with the number of samples M exceeding 2N. In this case, the values of a _n and A _i when performing steps 1 and 3 are searched by the least squares method [1, 2], and actions 2 and 4 are similar to the case M = 2N.

The disadvantage of these methods is the low accuracy of determining the spectral components of the signal at low signal-to-noise ratios.

The aim of the invention is to increase the accuracy of the assessment of the spectral components of the signal.

The goal is achieved by clarifying the parameters of the expansion of the signal (1) in the Prony series by using linear prediction of the spectral components and repeating the process of finding deviations.

Estimates of the spectral components obtained by the Prony method can be represented as:

- оценки действительных значений параметров A_i,λ_i; ΔA_i, Δλ_i - аддитивные отклонения (поправки) от действительных значений. Полагая отклонения малыми, разложение (1) можно переписать в следующем виде:Where

- estimates of the actual values of the parameters A _i , λ _i ; ΔA _i , Δλ _i - additive deviations (corrections) from the actual values. Assuming the deviations to be small, expansion (1) can be rewritten as follows:

;

- сигнал, соответствующий ряду Прони (1) для параметров

,

.Here

;

- signal corresponding to the Prony series (1) for parameters

,

.

For a sequence of M time samples x [n], we obtain the corrections ΔA _i , Δλ _i from the difference system

which are used to refine the decomposition parameters.

The processing method, which allows to increase the accuracy of the estimation of the spectral parameters of the signal decomposition by the Prony method, is as follows.

,According to the implementation x (t) of the signal available on the observation interval [0, T] (equidistant signal samples), estimates of the expansion parameters are found

,

значения А_i, λ_i, можно повторить процесс нахождения отклонений ΔA_i, Δλ_i до достижения заданной точности.using the prony least squares method. Then, the additive corrections ΔA _i , Δλ _{i are found} that satisfy the system of equations (7). These corrections are used to refine the parameters A _i , λ _i in accordance with (6). Taking as the new parameter values

values of A _i , λ _i , you can repeat the process of finding the deviations ΔA _i , Δλ _i to achieve the specified accuracy.

Thus, the proposed method allows to increase the accuracy of the estimation of the spectral components of the signal in a limited observation interval, which makes it possible to restore the signal with greater accuracy.

Information sources

1. Beatty L.G. and George J.D. Use of the complex exponential expansions as a signal presentation for underwater acoustic calibration. J. Acoust. Soc. Am., V. 63, No. 6, 1978.

2. Marpl.-ml. S.L. Digital spectral analysis and its applications: Per. from English - M .: Mir, 1990. - 584 p. (Prototype).

Claims (1)

A method for increasing the accuracy of parametric decomposition of signals by the Prony method, which consists in the fact that, based on the given signal, using the Lean square method, the estimates of the spectral components of the signal are determined, characterized in that they find additive deviations in the determination of the spectral components that satisfy the difference system obtained by linear forecasting, which are used to refine the initial estimates; moreover, the latter take on new values of the spectral components when re-finding deviations to achieve a given accuracy.