Frequency Fine Estimation Method in High Dynamic Environment

Abstract

The present invention discloses a method for fine frequency estimation in a high-dynamic environment, comprising the following steps: S1-1, acquiring a received signal; S1-2, calculating the peak value of the received signal; S1-3, roughly estimating the MF parameter through a formula; S2-1, acquiring the observed peak value and converting it into an expression; S2-2, setting a joint probability density function through the peak value expression; S2-3, obtaining an objective function through the joint probability density function and calculating the optimal value of the objective function; S2-4, substituting the optimal value into the expression of the peak value of the received signal, optimizing through singularity segmentation, rewriting the objective function, and obtaining a differential function and a peak error function; S2-5, calculating the feedback error, and through iteration, obtaining an accurate estimated parameter MF. The MF can be calculated through high-dynamic parameters, so as to achieve precise positioning in a high-dynamic environment, and can achieve high detection frequency to realize parameter probability parameter estimation and high-frequency estimation parameter accuracy to achieve frequency parameter capture in a high-dynamic environment.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a method for fine frequency estimation in a high-dynamic environment. Background Art

[0002] In the technology of global navigation satellite system (GNSS) receivers, signal acquisition technology is an important process for estimating code phase and frequency parameters. To achieve fast acquisition with low complexity, traditional methods are proposed based on the fast Fourier transform (FFT). Since the tracking loop bandwidth of navigation receivers is only a few hertz, the number of FFT points needs to be increased. Generally, from the coarse acquisition to the fine acquisition method is to reduce the computational amount. The code phase and the rough frequency of the signal can be obtained from the coarse acquisition method, and then the fine estimation of the frequency parameters can be performed based on the signal with the code phase stripped, and this process belongs to the fine acquisition process.

[0003] In low-dynamic acquisition technology, the signal frequency parameter is Doppler information, and the Doppler accuracy can be obtained from the signal fine acquisition. Nowadays, a variety of methods for accurately estimating the residual Doppler parameters have been proposed. However, since some of these methods are based on detecting the relationship between the peak and the remaining Doppler to improve the Doppler estimation accuracy, this method has limitations on the initial Doppler search step size. Contemporary scholars have proposed to improve the frequency estimation accuracy based on the Schmidt orthogonal method, but the accuracy of frequency parameter estimation needs to be further improved. In high-dynamic acquisition technology, the frequency parameter is composed of Doppler and Doppler rate of change. If the frequency parameter is characterized by a single Doppler, in the case of a relatively high Doppler rate of change, there will be a frequency deviation. The contemporary mainstream algorithm is based on the block accumulation semi-integral coherent accumulation (BASIC) method. This method changes the two-dimensional parameter estimation of estimating Doppler and Doppler rate of change into two steps of separately estimating Doppler and Doppler rate of change through differentiation. Although this method has a low computational amount, the detection probability is not high. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the present invention proposes a method for fine frequency estimation in a high-dynamic environment. This method roughly estimates Doppler and Doppler rate of change through DCFT, models the remaining Doppler and Doppler rate of change as the mean frequency (MF) as a whole, and further uses MLEP to estimate MF to improve the overall frequency parameter estimation accuracy. The present invention improves the frequency estimation accuracy of the GPS L1CA code received signal by the acquisition system in the GPS software receiver system in a high-dynamic environment and reduces the occupation of computing resources. Through the two-step frequency parameter estimation method, MF can be calculated through high-dynamic parameters, thereby laying a theoretical foundation for achieving precise positioning in a high-dynamic environment.

[0005] To solve the above technical problems, the technical solution of the present invention is as follows:

[0006] A method for fine frequency estimation in a high-dynamic environment, comprising the following steps:

[0007] S1. Roughly estimate the parameter MF using DCFT

[0008] S1-1. Obtain the received signal, which is a GPS L1CA code radio frequency signal. After down-conversion, the signal obtained after coarse acquisition is called the post-correlation signal;

[0009] S1-2. Calculate the peak value of the received signal using DCFT;

[0010] S1-3. Roughly estimate the MF parameter through the formula where γ is a coefficient, N is a coefficient, and T S is the sampling frequency;

[0011] S2. Use MLEP to perform a secondary accurate estimation of the parameter MF

[0012] S2-1. Obtain the observed peak value and convert it into an expression;

[0013] S2-2. Set the joint probability density function through the peak value expression;

[0014] S2-3. Obtain the objective function through the joint probability density function and calculate the optimal value of the objective function;

[0015] S2-4. Substitute the optimal value into the expression of the peak value of the received signal, optimize through singular point segmentation, rewrite the objective function, and obtain the difference function and the peak error function;

[0016] S2-5. Calculate the feedback error and obtain the accurate estimated parameter MF through iteration.

[0017] Preferably, in the step S1-1, the expression of the post-correlation signal after coarse acquisition is as follows:

[0018]

[0019] where f0 represents the residual Doppler, that is, the initial frequency, μ represents the chirp rate, T s represents the sampling frequency, b(n) represents the bit signal, and A represents the signal amplitude.

[0020] Preferably, the S1-2 specifically includes

[0021] 1) Perform DCFT processing on the post-correlation signal, and the expression of the processed signal is as follows:

[0022]

[0023] where k T = 0, ±1, ±2,... represents the search range, and α T is the transformation factor;

[0024] 2) When the bit signal b(n) is obtained by other means, such as wireless networks, etc., and is known, the above formula is simplified as follows:

[0025]

[0026] where is the MF parameter corresponding to 0T s to (N - 1)T s ;

[0027] 3) Assume A0 = A d N, and then apply Taylor expansion to obtain |S d (k d , α d )|:

[0028]

[0029] where |S d (k d , α d )| is the amplitude of the signal S d (k d , α d ).

[0030] Preferably, the S1 - 3 specifically includes

[0031] 1) Assume that (k d0 , α d0 ) corresponds to the peak value, and |S d (k d0 , α d0 )| ≥ γA0, and then we get:

[0032]

[0033] where γ is set based on the standard of the size of most useful energy contained in a unit, and the range is determined by the above formula ;

[0034] 2) By setting the values of N· and γ, the maximum value can be obtained, and this maximum value is taken as the value of α0.

[0035] Preferably, in the S2 - 1, the expression of the peak value is;

[0036]

[0037] where is the residual MF. When the unit (k d0 , α d0 ) corresponds to the peak value, w = w i + jw r , where w i and w r both follow the normal distribution;

[0038] In the above S2-2, the joint probability density function of (w i , w r ) is:

[0039]

[0040] where f(w i , w r ) is the joint probability density function of (w i , w r ).

[0041] Preferably, in the above S2-3, based on the maximum likelihood estimation method, the joint probability density function of (w i , w r ) is simplified to obtain the objective function:

[0042]

[0043] For the objective function obtain This is Thus, obtain:

[0044]

[0045] where A′ is the optimal value based on the maximum likelihood estimation.

[0046] Preferably, in the above S2-4, substituting the A′ formula into S d (k d0 , α d0 ) gives:

[0047]

[0048] where S d (k d0 , α d0 ) is the detected peak value in the presence of noise. When , where k = 0, ±1, ±2,... are the singular points, and L k represents the length of k. The singular points are segmented and optimized. At this time, Thus, the rewritten objective function is obtained:

[0049]

[0050] Suppose Obtain:

[0051]

[0052] Wherein Then J i and J r The difference equation of is:

[0053]

[0054] Peak error function and are as follows:

[0055]

[0056] Where (k0,α0) corresponds to

[0057] Preferably, in S2-5, through the J i and J r Difference equation, peak error function and and the rewritten objective function Calculate the feedback error Δω, and the feedback error formula is as follows:

[0058]

[0059] Obtain the optimal solution through iteration That is, the accurate estimated parameter MF is obtained,

[0060] Wherein The integer k in can be determined from the range of The selection ofThe formula of is as follows:

[0061]

[0062] The present invention has the following characteristics and beneficial effects:

[0063] Adopting the above technical solution, the discrete chirp Fourier transform (DCFT) is used to detect the average frequency estimation parameters in a high-dynamic environment, realizing the rough estimation of frequency parameters. Furthermore, the maximum likelihood estimation process (MLEP) is used to accurately estimate the average frequency in a high-dynamic environment. Through the above two-step frequency parameter estimation method, the MF can be calculated through high-dynamic parameters, thereby enabling precise positioning in a high-dynamic environment. Moreover, it can achieve parameter probability estimation with a high detection frequency and high accuracy of frequency estimation parameters to capture frequency parameters in a high-dynamic environment. Brief Description of the Drawings

[0064] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following-described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0065] Figure 1 It is a flowchart of the estimation method according to an embodiment of the present invention.

[0066] Figure 2 It is the Cramer-Rao bound for accurately estimating the average frequency when the integration time is 200 ms in an embodiment of the present invention.

[0067] Figure 3 It is a comparison diagram of the number of complex multiplications between the rough frequency estimation method and the comparison method in an embodiment of the present invention.

[0068] Figure 4 It is a comparison diagram of the detection probabilities between the rough frequency estimation method and the comparison method in an embodiment of the present invention.

[0069] Figure 5 It is a comparison diagram of the number of complex multiplications between the accurate frequency estimation method and the comparison method in an embodiment of the present invention.

[0070] Figure 6 It is a comparison diagram of the average frequency errors in an embodiment of the present invention. Detailed Embodiments

[0071] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0072] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0073] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0074] The present invention provides a method for fine frequency estimation in a high-dynamic environment, as Figure 1 shown, including the following steps:

[0075] S1. Roughly estimate the parameter MF using DCFT

[0076] S1-1. Obtain the received signal, which is a GPS L1CA code radio frequency signal. After down-conversion, the signal obtained after coarse acquisition is called the post-correlation signal;

[0077] S1-2. Use DCFT to calculate the peak value of the received signal;

[0078] S1-3. Roughly estimate the MF parameter through the formula where γ is a coefficient, N is a coefficient, and T S is the sampling frequency;

[0079] S2. Use MLEP to perform secondary accurate estimation of the parameter MF

[0080] S2-1. Obtain the observed peak value and convert it into an expression; <�

[0081] S2-2. Set the joint probability density function through the peak value expression;

[0082] S2-3. Obtain the objective function through the joint probability density function and calculate the optimal value of the objective function;

[0083] S2-4. Substitute the optimal value into the expression of the peak value of the received signal, optimize it through singularity splitting, rewrite the objective function, and obtain the differential function and the peak error function;

[0084] S2-5. Calculate the feedback error and obtain the accurate estimation parameter MF through iteration.

[0085] Furthermore, in the step S1-1, after coarse acquisition, the expression of the post-correlation signal is as follows:

[0086]

[0087] where f0 represents the residual Doppler, that is, the initial frequency, μ represents the chirp rate, T s represents the sampling frequency, b(n) represents the bit signal, and A represents the signal amplitude.

[0088] It should be noted that when the received signal is not synchronized with the local decoded signal or the signal we detect is not the signal we transmitted, that is, in the case of a wrong Doppler detection unit, A≈0. These situations will not be considered when analyzing the signal part below. Or it is assumed that A≠0 is based on a constant set of signal-to-noise ratios (SNRs). Anyway, A cannot be equal to 0, otherwise it will be meaningless. For the GPS L1CA signal, f0 = [-250, 250] Hz, μ = [-500, 500] Hz / s.

[0089] Specifically, the S1-2 specifically includes

[0090] 1) Perform DCFT processing on the post-correlation signal, and the expression of the processed signal is as follows:

[0091]

[0092] where k T = 0, ±1, ±2,... represents the search range, and α T is the transformation factor;

[0093] 4) When the bit signal b(n) is obtained by other means and is known, the above formula is simplified as follows:

[0094]

[0095] where, is the MF parameter corresponding to 0T s to (N-1)T s ;

[0096] 5) Assume A0 = A d N, and then apply Taylor expansion to obtain |S d (k d , α d )|:

[0097]

[0098] Wherein, |S d (k d , α d )| is the amplitude of the signal S d (k d , α d ).

[0099] Specifically, the S1-3 specifically includes

[0100] 1) Assume that (k d0 , α d0 ) corresponds to the peak value, and |S d (k d0 , α d0 )| ≥ γA0, and then obtain:

[0101]

[0102] Where γ is set based on the standard of the size of most useful energy contained in a unit, and the range is determined by the above formula; ;

[0103] 2) By setting the values of N· and γ, the maximum value can be obtained, and this maximum value is taken as the value of α0.

[0104] Specifically, in the S2-1, the expression of the peak value is;

[0105]

[0106] Where is the residual MF. When the unit (k d0 , α d0 ) corresponds to the peak value, w = w i + jw r [[ID=7,3]]where w i and w r both follow the normal distribution;

[0107] In the S2-2, the joint probability density function of (w i , w r ) is:

[0108]

[0109] where f(w i , w r ) is the joint probability density function of (w i , w r ).

[0110] Specifically, in S2-3, based on the maximum likelihood estimation method, the joint probability density function of (w i , w r ) is simplified to obtain the objective function:

[0111]

[0112] For the objective function obtain This is Thus, obtain:

[0113]

[0114] where A′ is the optimal value based on the maximum likelihood estimation.

[0115] Specifically, in S2-4, substituting the A′ formula into S d (k d0 , α d0 ) gives:

[0116]

[0117] where S d (k d0 , α d0 ) is the detection peak in the presence of noise. When , where k = 0, ±1, ±2,... are the singular points, and L k represents the length of k. The singular points are segmented and optimized. At this time, Thus, the rewritten objective function is obtained:

[0118]

[0119] Assume obtain:

[0120]

[0121] where Then the difference equation of J i and J r is:

[0122]

[0123] where T c = cos(TT1), Ts = sin(TT1), T 2c = cos(2TT1), T 2s = sin(2TT1),

[0124] Peak error function and are as follows:

[0125]

[0126] where (k0, α0) corresponds to

[0127] Specifically, in S2-5, through the J i and J r difference equation, peak error function

[0128] and and the rewritten objective function calculate the feedback error Δω, and the feedback error formula is as follows:

[0129]

[0130] Obtain the optimal solution through iteration that is, the accurate estimated parameter MF obtained,

[0131] where the integer k in can be determined from the range, and the selection formula is as follows:

[0132]

[0133] It should be noted that in this embodiment, through multiple simulations, it is obtained that the iteration times I t is optimally 10 times.

[0134] Through the above technical solution, as Figure 2 shown, when the integration time is 200 ms, this embodiment can effectively improve the estimation accuracy.

[0135] Compared with the traditional MF rough estimation method through the technical solution described in this embodiment, as Figure 3 shown, as the integration time increases, for the technical solution provided by this embodiment, the increase in the number of complex multiplications is greater, and the accuracy of the rough estimation is significantly improved, thus laying a foundation for the subsequent accurate estimation.

[0136] Compared with the detection probability of the traditional MF rough estimation method through the technical solution described in this embodiment, as Figure 4As shown, when the sampling time is 200 ms, the chirp rate is 200 Hz / s, and the initial frequency is 100 Hz. In this embodiment, the DCFT method realizes high detection probability estimation of frequency parameters in the MF coarse detection, thus further ensuring the accuracy of the later estimation.

[0137] Compared with the number of complex multiplications of the traditional Schmit in the technical solution provided by this embodiment, as Figure 5 shown, for the MF coarse estimation, the complex multiplication calculation amounts of the traditional Schmit and the proposed MLEP method are compared. The proposed MLEP has a lower complex multiplication calculation amount than the traditional Schmit. As the integration time increases, the change amplitude is small and almost remains unchanged, indicating that the estimation accuracy is very high.

[0138] For the comparison of the average frequency error, as Figure 6 shown, the signal-to-noise ratio of the post-correlation signal is 5 dB. The average frequency search step is 1 rad / s. The proposed method combines DCFT and MLEP, and the DCFT method and the Schmit method are used to compare the estimation accuracy of the frequency parameter MF. The combination of DCFT and MLEP almost remains horizontal as the length of the post-correlation signal increases, indicating that the technical solution disclosed in this embodiment has the highest estimation accuracy for the parameter MF.

[0139] In this embodiment, specific descriptions are given through comparisons:

[0140] Table 1 is obtained according to the existing technology and the proposed method, showing the comparison of the addition calculation amount and the complex multiplication calculation amount between the existing technology method and a frequency fine estimation method of the present invention in a high-dynamic environment

[0141]

[0142]

[0143] In Table 1, the calculation amounts of two precise frequency estimation methods are presented. T α represents the chirp search period, and T f represents the initial frequency search period. C P,M and C P,A can be calculated as follows:

[0144] Calculating the parameter A′ consumes 12 complex multiplications and 1 addition. The values of cos and sin can be obtained by looking up tables, and their calculation amounts can be ignored. In addition, calculating the difference function requires 18*2 complex multiplications and 2*2 additions. Calculating the peak error function requires 5*2 complex multiplications and 1*2 additions. The formula requires 5 complex multiplications and 2 additions. Calculating the feedback function requires 1 addition, and the calculation formula 19 complex multiplications and 3 complex additions are required. The computational complexity of a complex multiplication is equivalent to that of two real number multiplications. So C P,M = L k (51I i + 19) / 2C P,A = L k (9I i + 3) / 2, where I t represents the number of iterations, and L k represents the number of divisions.

[0145] The embodiments of the present invention have been described in detail in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principle and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments including components still fall within the protection scope of the present invention.

Claims

1. A method for fine frequency estimation in a high-dynamic environment, characterized in that It includes the following steps: S1. Roughly estimate the parameter MF using DCFT S1-1. Obtain the received signal, which is a GPS L1 CA code radio frequency signal. After down-conversion, the signal obtained after rough acquisition is called the post-correlation signal; S1-2. Calculate the peak value of the received signal using DCFT; S1-3. Roughly estimate the MF parameter through the formula where γ is a coefficient, N is a coefficient, and T S is the sampling frequency; S2. Use MLEP to perform secondary accurate estimation of the parameter MF S2-1. Obtain the observed peak value and convert it into an expression; S2-2. Set the joint probability density function through the peak value expression; S2-3. Obtain the objective function through the joint probability density function and calculate the optimal value of the objective function; S2-4. Substitute the optimal value into the expression of the peak value of the received signal, optimize through singularity segmentation, rewrite the objective function, and obtain the difference function and the peak error function; S2-5. Calculate the feedback error and obtain the accurate estimated parameter MF through iteration.

2. The frequency fine estimation method in a high-dynamic environment according to claim 1, wherein In S1-1, the expression of the post-correlation signal after rough acquisition is as follows: where f0 represents the residual Doppler, i.e., the initial frequency, μ represents the chirp rate, T s represents the sampling frequency, b(n) represents the bit signal, and A represents the signal amplitude.

3. The frequency fine estimation method in a high-dynamic environment according to claim 2, characterized in that Specifically, S1-2 includes 1) Perform DCFT processing on the post-correlation signal, and the expression of the processed signal is as follows: where k T = 0, ±1, ±2,... represents the search range, and α T is the transformation factor; 2) When the bit signal b(n) is obtained by other means and is known, the above formula is simplified as follows: Among them, is 0T s to (N - 1)T s corresponding MF parameter; 3) Assume A0 = A d N, and then apply Taylor expansion to obtain |S d (k d , α d )|: Among them, |S d (k d ,α d )| is the amplitude of the signal S d (k d ,α d ).

4. The frequency fine estimation method in a high dynamic environment according to claim 3, characterized in that, Specifically, S1-3 includes 1) Assume that (k d0 , α d0 ) corresponds to a peak, and |S d (k d0 , α d0 )| ≥ γA0, and then we get: where γ is set based on the criterion of the size of the most useful energy contained in a unit and is determined by the above formula range; 2) The maximum value can be obtained by setting the values of N and γ, and this maximum value is taken as the value of α0.

5. The frequency fine estimation method in a high dynamic environment according to claim 4, wherein In S2-1, the expression of the peak value is; Among them is the residual MF. When the unit (k d0 , α d0 ) corresponds to the peak value, w = w i + jw r , where w i and w r both follow the normal distribution; In the above S2-2, (w i , w r ) the joint probability density function is as follows: where f(w i , w r ) is the joint probability density function of (w i , w r ).

6. The frequency fine estimation method in a high-dynamic environment according to claim 5, wherein In the step S2-3, based on the maximum likelihood estimation method, simplify the joint probability density function of (w i , w r ) to obtain the objective function: For the objective function Obtain This is Thus, obtain: Among them, A′ is the optimal value based on maximum likelihood estimation.

7. The frequency fine estimation method in a high dynamic environment according to claim 6, characterized in that In S2-4, substitute the A' formula into S d (k d0 ,α d0 ) to obtain: Among them, S d (k d0 , α d0 ) is the detection peak when there is noise. When , where k = 0, ±1, ±2,... are singular points, and the singular points are segmented and optimized. At this time, the rewritten objective function is thus obtained: Hypothesis Obtain the feedback error: Among them then J i and J r The difference equation is: where T c = cos(TT1), T s = sin(TT1), T 2c = cos(2TT1), Peak error function and are as follows: where (k0, α0) corresponds to 8. The frequency fine estimation method in a high-dynamic environment according to claim 7, characterized in that In the above S2-5, through the said J i and J r difference equation, peak error function and and the rewritten objective function calculate the feedback error Δω, and the feedback error formula is as follows: Obtain the optimal solution through iteration That is, the obtained precise estimation parameter MF wherein the integer k in is determined from the range of The formula for selection is as follows:

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