Sine frequency modulation signal parameter estimation method with high anti-noise characteristic

Abstract

The invention provides a sine frequency modulation signal parameter estimation method with a high anti-noise characteristic, and the method specifically comprises the steps: searching an optimal phase pre-modulation coefficient # imgabs0 # in a search space, modulating an input signal through employing the optimal phase pre-modulation coefficient # imgabs1 #, positioning a modulated signal peak value, employing the signal peak value and a frequency corresponding to the signal peak value, and carrying out the estimation of the sine frequency modulation signal parameter through employing the optimal phase pre-modulation coefficient # imgabs0 # and the optimal phase pre-modulation coefficient # imgabs1 #. And obtaining estimation of sine frequency modulation signal parameters according to all possible values of the stationary phase point t0, and finally obtaining optimal estimation by solving the maximum value of a quasi maximum likelihood function. The anti-noise characteristic of the algorithm is effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of radar signal processing, and in particular relates to a method for estimating parameters of a sinusoidal frequency modulation signal. Background Art

[0002] Sine frequency modulated signals are widely used in the field of radar signal processing, and estimating their parameters has very practical application value. The spectrum peak method [1] is a widely used method for estimating the parameters of sinusoidal frequency modulated signals. This method uses the frequency and amplitude corresponding to the spectrum peak to estimate the sinusoidal frequency modulated signal. The algorithm has low computational complexity and is easy to meet the needs of real-time computing scenarios. However, since the signal amplitude is easily affected by noise, the accuracy of this algorithm is poor. Summary of the invention

[0003] In view of this, the present invention proposes a method for estimating the parameters of a sinusoidal frequency modulation signal with high noise resistance, which locates the signal peak, uses the frequency corresponding to the peak and all possible values ​​of the stationary phase point to obtain the estimation of the parameters of the sinusoidal frequency modulation signal, and finally obtains the optimal estimation by finding the maximum value of the quasi-maximum likelihood function. Compared with the above methods, the algorithm's noise resistance is effectively improved.

[0004] The specific technical solutions are as follows:

[0005] A method for estimating the parameters of a sinusoidal frequency modulated signal with high noise immunity, which searches for the optimal phase premodulation coefficient in the search space. Using the optimal phase premodulation coefficient The input signal is modulated, the peak of the modulated signal is located, and the signal peak, the frequency corresponding to the signal peak, and all possible values ​​of the fixed phase point t0 are used to obtain the estimation of the parameters of the sinusoidal frequency modulated signal. Finally, the optimal estimate is obtained by finding the maximum value of the quasi-maximum likelihood function.

[0006] Furthermore, the search space of the phase modulation coefficient d satisfies the following conditions:

[0007] |-ab 2 sin(bt+c)+d|>0,

[0008] Where B = [abc] T is the estimated parameter of the sinusoidal frequency modulated signal, where the sinusoidal frequency modulated signal is expressed as follows:

[0009] s(t)=e jθ(t) =e jasin(bt+c) ,0≤t≤T,

[0010] Where T is the total sampling time.

[0011] Furthermore, the optimal phase premodulation coefficient The method to determine is:

[0012] Pre-modulating the input signal;

[0013] Performing Fourier transform on the modulated signal;

[0014] Find the peak of the Fourier transformed amplitude spectrum;

[0015] A function of the peak amplitude relative to the phase premodulation coefficient is constructed, and the phase premodulation coefficient corresponding to the maximum peak amplitude is the optimal phase modulation coefficient.

[0016] Furthermore, the estimation method of parameter b is:

[0017] Using the optimal phase premodulation coefficient Modulate the input signal and perform Fourier transform to find the frequency ω corresponding to the two adjacent spectrum peaks after the transform i+1 ,ω i , use the spectrum peak to get the parameter b, the specific calculation formula is as follows:

[0018]

[0019] Furthermore, the method for determining parameters a and c is as follows:

[0020] Step 1) Establish the functional relationship between parameters a, c and the stationary phase point t0 respectively. The specific formula is as follows:

[0021]

[0022] Where ω is the optimal phase premodulation coefficient Modulate the input signal and find the frequency corresponding to any spectral peak on the Fourier transformed signal;

[0023] Step 2) traverse all possible values ​​of t0 for calculation, and then calculate the quasi-maximum likelihood function, and obtain the optimal estimation of the sinusoidal frequency modulation signal parameters a and c by finding the maximum value of the quasi-maximum likelihood function.

[0024] Intentional Effect

[0025] 1. The present invention limits the search space of the phase modulation coefficient d, making it more efficient to determine the optimal phase modulation coefficient;

[0026] 2. The present invention uses the optimal phase premodulation coefficient to construct a phase premodulation function. With the help of the phase premodulation function, the energy of the sinusoidal frequency modulation signal can be more concentrated in several spectrum peaks. The amplitudes of these spectrum peaks are higher than the noise amplitude, which is conducive to finding the spectrum peaks;

[0027] 3. If the method in reference [1] is used directly, both the spectrum peak amplitude and the frequency corresponding to the spectrum peak must be used simultaneously. However, the spectrum peak amplitude will be seriously polluted under strong noise interference, which directly leads to the failure of method 1. Therefore, in order to avoid the influence of noise on the spectrum peak amplitude, this method only uses the position of the spectrum peak, that is, the frequency corresponding to the spectrum peak, and then completes the parameter estimation by searching all possible values ​​of the stationary phase point, thereby avoiding the dependence on the spectrum peak amplitude and realizing parameter estimation under strong noise interference;

[0028] 4. The method described in the present invention has high estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Detailed flow chart of an embodiment of the present invention DETAILED DESCRIPTION

[0030] Part I. Basic Principles

[0031] The sinusoidal frequency modulated signal is generally expressed as

[0032] s(t)=e jθ(t) =e jasin(bt+c) ,0≤t≤T (2)In the formula, B=[abc] T is the parameter to be estimated, and T is the total sampling time.

[0033] The basic principle of the estimation algorithm is as follows:

[0034] 1) First, phase premodulation is performed on s(t), and the modulation formula is as follows:

[0035]

[0036] Where d represents the phase premodulation coefficient.

[0037] 2) When certain conditions are met, the stationary phase principle can be used to obtain an approximate formula for the Fourier transform of the signal after phase premodulation.

[0038] in,

[0039] The Fourier transform of the signal after phase premodulation is defined as:

[0040]

[0041] The conditions are expressed as follows,

[0042] |-ab 2 sin(bt+c)+d|>0 (5)

[0043] Formula (1.4) represents the search space of the phase premodulation coefficient d.

[0044] The approximate formula of Fourier transform is as follows:

[0045]

[0046] In the formula, t0 is called the phase point, which satisfies

[0047] φ′(t)=θ′(t0)-ω=ab sin(bt0+c)+dt0-ω=0. (7)

[0048] 3) In addition, according to the derivation results of the literature [1], the peak value of the amplitude spectrum satisfies the following formula:

[0049] -ab 2 cos(bt0+c)+d=0 (8)

[0050] |S m (jω)|There will be several spectral peaks, and the distance between adjacent spectral peaks satisfies

[0051]

[0052] Where ω i Indicates |S m (jω)|The i-th peak position. Positioning|S m (jω)| After finding two adjacent spectral peaks, the parameter b can be estimated according to the following formula, that is

[0053]

[0054] According to the estimated value of parameter b, by combining equations (7) and (8), we can know that the frequency ω corresponding to the i-th spectrum peak is i Meet the following conditions

[0055]

[0056] Assuming that t0 is known, the estimation of the parameters a and c of the sinusoidal FM signal can be obtained by equation (11), as follows:

[0057]

[0058] In practice, t0 is unknown, but since it satisfies 0≤t0≤T, the ergodic method can be used to calculate all possible values ​​of t0, and then the quasi-maximum likelihood function is calculated. The optimal parameter estimate of the sinusoidal FM signal is obtained by finding the maximum value of the quasi-maximum likelihood function.

[0059] Part II: Method Calculation Process

[0060] Input: x[n] = x(nT s ),n=0,1,...,N-1.T sis a uniform sampling interval.

[0061] 1: Loop through d in the search space:

[0062]

[0063] 2: Using the current phase premodulation coefficient d, construct the phase premodulation function g[n] according to the following formula:

[0064]

[0065] 3: Use g[n] to pre-modulate the input signal according to the following formula

[0066]

[0067] 4: For the modulated signal x l [n] is Fourier transformed. In the following formula, k is newly introduced because after DFT operation, the frequency domain representation of the signal is obtained, which is completely different from the time domain representation of the original signal. Therefore, a new symbol k is used to represent it.

[0068] y l [k] = DFT(x l [n]),k=0,1,2,...,N-1 (15) 5: Find the peak of the Fourier transform amplitude spectrum,

[0069]

[0070] 6: Construct a function of the peak amplitude relative to the phase premodulation coefficient,

[0071]

[0072] 7: End For

[0073] 8: Find S m The phase premodulation coefficient corresponding to the maximum value of (l), that is, the optimal phase premodulation coefficient

[0074] in

[0075]

[0076] 9: Search Two adjacent spectral peaks are denoted as ω1 and ω2, and the parameter b is calculated according to formula (10).

[0077] 10: Traverse all possible values ​​of the stationary phase point t0

[0078] Fort0=pT s ,p=0,1,...,N-1

[0079] 11: Exploit The frequency position of the first spectrum peak is ω1, and any other ω can also be selected i , estimate the parameters a and c according to (12)

[0080]

[0081] in,

[0082] 12: Calculate the quasi-maximum likelihood function

[0083]

[0084] 13: End For

[0085] 14: Find the maximum value |Q[p]| maximum

[0086]

[0087] Output: Final estimate of signal parameters

[0088] References:

[0089] [1]X.Jiang, S.Wu, Y.Chen, and L.Qiu, "Parameter Estimation for SinusoidalFrequency-modulated Signals Using Phase Modulation," IEEE Signal Processing Letters, vol.28, pp.76-80, Oct.2021.

Claims

1. A method for estimating parameters of a sinusoidal frequency modulation signal with high noise immunity, characterized in that: Find the optimal phase premodulation coefficient in the search space Using the optimal phase premodulation coefficient The input signal is modulated, the peak of the modulated signal is located, and the signal peak, the frequency corresponding to the signal peak, and all possible values ​​of the fixed phase point t0 are used to obtain the estimation of the parameters of the sinusoidal frequency modulated signal. Finally, the optimal estimate is obtained by finding the maximum value of the quasi-maximum likelihood function.

2. A method for estimating parameters of a sinusoidal frequency modulation signal with high noise immunity according to claim 1, characterized in that: The search space of the phase modulation coefficient d satisfies the following conditions: <h2 style=";text-align:left;direction:ltr">|-ab<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> sin(bt+c)+d|>0, Where B = [abc] T is the estimated parameter of the sinusoidal frequency modulated signal, where the sinusoidal frequency modulated signal is expressed as follows: s(t)=e jθ(t) =e jasin(bt+c) ,0≤t≤T, Where T is the total sampling time.

3. A method for estimating parameters of a sinusoidal frequency modulation signal with high noise immunity according to claim 1, characterized in that: Optimal phase premodulation coefficient The method to determine is: Pre-modulating the input signal; Performing Fourier transform on the modulated signal; Find the peak of the Fourier transformed amplitude spectrum; A function of the peak amplitude relative to the phase premodulation coefficient is constructed, and the phase premodulation coefficient corresponding to the maximum peak amplitude is the optimal phase modulation coefficient.

4. A method for estimating parameters of a sinusoidal frequency modulation signal with high noise immunity according to claim 3, characterized in that: The estimation method of parameter b is: Using the optimal phase premodulation coefficient Modulate the input signal and perform Fourier transform to find the frequency ω corresponding to the two adjacent spectrum peaks after the transform i+1 ,ω i , use the spectrum peak to get the parameter b, the specific calculation formula is as follows:

5. A method for estimating parameters of a sinusoidal frequency modulation signal with high noise immunity according to any one of claims 1 to 4, characterized in that: The method for determining parameters a and c is: Step 1) Establish the functional relationship between parameters a, c and the stationary phase point t0 respectively. The specific formula is as follows: Where ω is the optimal phase premodulation coefficient Modulate the input signal and find the frequency corresponding to any spectral peak on the Fourier transformed signal; Step 2) traverse all possible values ​​of t0 for calculation, and then calculate the quasi-maximum likelihood function, and obtain the optimal estimation of the sinusoidal frequency modulation signal parameters a and c by finding the maximum value of the quasi-maximum likelihood function.

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