A Modeling Method for Bistatic Radar Measurement Noise Covariance Related to Geometric Position

Abstract

The present invention discloses a geometric position-related bistatic radar measurement noise covariance model. Aiming at the problem that the bistatic radar measurement noise covariance is related to the geometric position relationship between the target and the radar, a time-varying model of the bistatic radar measurement noise covariance is re-derived and constructed, accurately describing the quantitative relationship between the measurement accuracy and the geometric positions of the target, the transmitting station, and the receiving station. First, the best estimation accuracy of the signal domain time delay and Doppler frequency shift of the bistatic radar is modeled using the Cramer-Rao bound and the ambiguity function. Secondly, the time-varying correction coefficient matrix for the conversion from the signal domain to the measurement domain in the bistatic measurement form is derived. Finally, the time-varying expression of the bistatic radar measurement noise covariance is calculated. The simulation experiment verifies and analyzes that the bistatic radar measurement noise covariance is directly affected by the geometric position relationship among the target, the transmitting station, and the receiving station, and has strong practical engineering applicability.

Description

Technical Field

[0001] The present invention belongs to the field of target tracking, and relates to problems related to the relationship between the measurement noise covariance of a bistatic radar and the geometric positions of the target and the radar. Specifically, it relates to a method for a measurement noise covariance model of a bistatic radar related to geometric positions. Background Art

[0002] When performing target tracking or information fusion on a bistatic radar in a complex environment, it is necessary to establish a time-varying mathematical model of the measurement noise covariance. The measurement noise covariance model of a bistatic radar is greatly affected by the geometric position relationship among the target, the transmitting station, and the receiving station. In many studies, the measurement noise covariance of the radar is usually modeled as a constant, which has a large gap from the measurement noise covariance in actual radar measurements. Summary of the Invention

[0003] Aiming at the deficiencies of the prior art, the present invention proposes a measurement noise covariance model of a bistatic radar related to geometric positions. For the problem related to the relationship between the measurement noise covariance of a bistatic radar and the geometric positions of the target and the radar, a time-varying model of the measurement noise covariance of the bistatic radar is re-derived and constructed, which accurately describes the quantitative relationship between the measurement accuracy and the geometric positions of the target, the transmitting station, and the receiving station. The symbols for measuring noise covariance modeling are shown in Figure 1 the geometric structure and measurement schematic diagram of the bistatic radar.

[0004] 1) Signal domain noise covariance

[0005] When modeling the target reflection signal received by the radar in the signal domain, it is usually modeled as time delay, Doppler frequency shift, and incident angle. When estimating the time delay and Doppler frequency shift in the signal domain, estimation errors will occur. Therefore, the estimation accuracy of the radar signal domain includes two parts: time delay and Doppler frequency shift, and the angle is not considered in the derivation. By using the signal domain to measurement domain conversion equation for the signal domain estimation error, the measurement accuracy of the target distance and Doppler velocity can be obtained.

[0006] The ambiguity function of the signal is used to study the measurement and resolution performance of the radar, and is defined as:

[0007]

[0008] In the formula, t is time, u(t) is the signal pulse function, τ a and ξ a are the actual time delay and Doppler frequency shift, τ H and ξ H are the assumed time delay and Doppler frequency shift.

[0009] The Cramer-Rao lower bound is the inverse matrix of the Fisher information matrix, which is the upper bound of the error variance generated by radar measurement, that is, the best estimation accuracy that can be theoretically achieved. Generally, the relationship between the Fisher information matrix and the ambiguity function for the estimation accuracy of radar signal domain time delay and Doppler frequency shift is as follows:

[0010]

[0011] In the formula, τ = τ H -τ a , ξ = ξ H -ξ a When τ a = τ H , ξ a = ξ H At this time, the ambiguity function X(τ H , τ a , ξ H , ξ a ) obtains the maximum absolute value. k represents the current moment as the k-th moment, is the derivative symbol, τ and ξ are the independent variable parameters of time delay and Doppler frequency shift, x k is the state of the target, x T,k is the state of the radar transmitting station, and x R,k is the state of the radar receiving station.

[0012] The best estimation accuracy of signal domain time delay and Doppler frequency shift can be described as:

[0013]

[0014] The signal domain estimation accuracy J S is related to the pulse signal transmitted by the radar and the signal-to-noise ratio. When the pulse signal transmitted by the radar is different, the signal domain estimation accuracy is also different. When the signal of the radar transmitting station is determined, the signal parameters of the radar transmitting station are all determined fixed constants, and only the signal-to-noise ratio is variable. The estimation accuracy J S of the radar signal domain can be simplified as:

[0015]

[0016] In the formula, S1, S2, S3, and S4 are signal factors that can be calculated according to the signal parameters of the radar transmitting station. The signal factor S2 = S3, and SNR(x k , x T,k , x R,k ) is the signal-to-noise ratio function.

[0017] The time delay τ(d k ) of the bistatic radar signal domain receiving the target echo is described as:

[0018]

[0019] Where c is the speed of light, and R R,k is the distance between the radar receiving station and the target, and d k is the bistatic radar distance, and R T,k is the distance between the radar transmitting station and the target.

[0020] The Doppler frequency shift ξ(v k ) in the signal domain of the bistatic radar is described as:

[0021]

[0022] Where f c is the radar carrier frequency, are the position vectors of the target, radar receiving station, and radar transmitting station respectively, are the velocity vectors of the target, radar receiving station, and radar transmitting station respectively, and f c is the radar carrier frequency, and v k is the Doppler velocity measured by the bistatic radar.

[0023] The measurement conversion relationship from the signal domain to the measurement domain is d k = τc and v k = ξc / f c , because when calculating the estimation accuracy in the measurement domain, the derivative of ξ(v k ) with respect to d k is required. Therefore, the distance measurement component needs to be separated from the Doppler frequency shift, and ξ(v k ) is decoupled and substituted for distance measurement to obtain a form containing the R R,k variable. The derivation process is as follows:

[0024]

[0025] Where L k is the baseline distance between the radar receiving station and the transceiver station, and I k is the bisector of the bistatic radar, and the angle formed with R R,k and R T,k is β k / 2, and v I is the sum of the moduli of the velocity components of the velocity vectors and in the direction of the bisector I k of the bistatic radar. γ k ranges from (0, π), and θ k and θ RT,k are the receiving angles of the radar receiving station for the target and the transmitting station respectively. In the bistatic radar measurement, R R,k can be converted into a form related to d kand γ k The function of... is as follows:

[0026]

[0027] Using d k Replace the variable R in the Doppler frequency shift with the d R,k variable, and finally the Doppler frequency shift can be described as:

[0028]

[0029] In the formula, the expression of a is:

[0030]

[0031] Simplify a:

[0032]

[0033] 2) Measure the noise covariance in the measurement domain

[0034] The estimation accuracy of the radar measurement domain includes the range and Doppler measurement estimation accuracies. Perform independent variable substitution on the Fisher information matrix J S (τ, ξ), substitute τ(d k ) and ξ(v k (d k )) into the ambiguity function for variable substitution, and regard the bistatic radar range measurement d k and the Doppler velocity measurement v k as independent variables for differentiation, where v k = g(d k ). Finally, obtain the Fisher information matrix of the estimation accuracies of the range and velocity measurements in the radar measurement domain:

[0035]

[0036] Apply the second-order chain differentiation rule for binary functions to the above formula, which includes two layers of functional relationships. The first layer of function is the relationship between the ambiguity function X(τ, ξ) and the independent variables τ and ξ, and the second layer of function is the relationship between τ(d k ) and ξ(v k (d k )) and the independent variables d k and v k . Finally, the conversion relationship of the Fisher information matrix between the signal domain and the measurement domain measurement estimation accuracies can be obtained. Express the Fisher information matrix in the signal domain using the general formula in the signal domain. In the general formula, S2 = S3, and use S2 to replace S3. The expansion formula of the Fisher information matrix of the radar measurement domain estimation accuracy is described as:

[0037]

[0038] In the formula,

[0039] Simplify the above formula into the form of a quadratic form:

[0040]

[0041] In the formula, P k (x k , x T,k , x R,k ) is a time-varying correction coefficient matrix:

[0042]

[0043] The correction coefficient matrix P k not only contains the conversion relationship from the signal domain to the measurement domain, but also contains the target-radar geometric position relationship. It changes with the target-radar geometric position relationship at each discrete moment k. Each part of the elements in the bistatic correction coefficient P k matrix is as follows:

[0044]

[0045]

[0046]

[0047]

[0048] In the formula, the expression of b is:

[0049]

[0050] Using the method of finding the inverse of the second-order adjoint matrix, obtain the measurement noise covariance matrix of distance and speed in the measurement domain:

[0051]

[0052] In the formula, the expression of J1J4 - J2J2 is as follows:

[0053]

[0054] In the formula, the SNR(x k , x T,k , x R,k ) term, J1(x k , x T,k , x R,k ) term, J2(x k , x T,k , xR,k ) The influence of geometric position on the range and velocity measurement noise covariance of a bistatic radar is reflected in the term, and the term J1J4 - J2J2 does not contain the influence of geometric position.

[0055] In a bistatic radar system, the variance of radar angle measurement noise is only related to the signal-to-noise ratio of the signal. The signal-to-noise ratio of the signal is related to the distance between the radar and the target. The variance of angle measurement noise can be expressed as:

[0056]

[0057] In the formula, is the reference angle measurement standard deviation.

[0058] In summary, finally, the measurement noise covariance R k (x k , x T,k , x R,k ) can be generally described as:

[0059]

[0060] Technical effects of the present invention:

[0061] Aiming at the problem related to the relationship between the measurement noise covariance of a bistatic radar and the target-radar geometric position, firstly, the Cramer-Rao bound and the ambiguity function are used to model to obtain the best estimation accuracy of the time delay and Doppler frequency shift in the signal domain of the bistatic radar, that is, the measurement noise in the signal domain; secondly, the time-varying correction coefficient matrix for the conversion from the signal domain to the measurement domain in the bistatic measurement form is derived; finally, different types of radar transmitted signals are denoted as a general formula description, and the time-varying expression of the bistatic radar measurement noise covariance is calculated according to different types of radar transmitted signals, and the time-varying model of the bistatic radar measurement noise covariance is re-derived and constructed, accurately quantifying the measurement noise covariance of the bistatic radar. This measurement noise covariance model can greatly improve the performance of target tracking algorithms and fusion algorithms. The simulation experiment verifies and analyzes the direct influence of the bistatic radar measurement noise covariance on the geometric position relationship among the target, the transmitting station, and the receiving station. Description of the drawings

[0062] Figure 1 is the geometric structure and measurement schematic diagram of the bistatic radar;

[0063] Figure 2 is the simulation scenario diagram of the fixed distance;

[0064] Figure 3 is the simulation scenario diagram of the fixed receiving angle;

[0065] Figure 4 is the comparison flow chart of the comparison example of the fixed receiving angle tracking;

[0066] Figure 5 Variation diagram of the standard deviation of measurement noise obtained for the fixed distance example;

[0067] Figure 6 Variation diagram of the standard deviation of measurement noise obtained for the fixed reception angle example;

[0068] Figure 7 Position RMSE diagram obtained for the fixed reception angle tracking contrast example; Detailed implementation manners

[0069] The present invention will be further explained below with reference to the accompanying drawings;

[0070] In order to verify the relationship between the bistatic radar measurement noise covariance modeled by the present invention and the target-radar geometric position, a simulation experiment on the bistatic radar measurement noise covariance and its hypothesis verification was conducted in this embodiment. As Figure 2 and Figure 3 shown, the simulation experiment includes a fixed distance experiment and a fixed reception angle experiment.

[0071] The initial settings of the two simulation experiments conducted in this embodiment are as follows:

[0072] The radar receiving station and the transceiver station are respectively fixed at [0m, 0m] T and [5000m, 0m] T , the baseline distance between the two is L k = 5 km, the target is a movable target, and the velocity vectors and The sum of the moduli of the velocity components in the direction of the bisector I k of the bistatic radar is v I = 50 m / s. In the fixed distance experiment, L k and R R,k are kept unchanged, and only θ k is changed, so that the target makes a clockwise circular motion around the radar receiving station; in the fixed reception angle experiment, L k and θ k are kept unchanged, and only R R,k is changed, so that the target moves in the direction where θ k is fixed. The third experiment is based on the fixed reception angle experiment scenario, and compares the effects of fixed measurement noise and time-varying measurement noise on the tracking algorithm. The flowchart is as Figure 4 shown.

[0073] The radar signal parameters table of the simulation experiment is shown in Table 1. In the simulation, the reference angle measurement standard deviation is set to When the radar signal-to-noise ratio changes with the geometric position, due to the limitations of physical components, the radar signal-to-noise ratio will be within a certain range. By referring to the literature, it is determined that the actual signal-to-noise ratio SNR of the radar is between -20 dB and 30 dB. In the scenario of this paper, the signal constant R0 in the signal-to-noise ratio is set to 11000, and the false alarm rate P FA is set to 0.01. The radar transmitting signal model uses the ATSC signal. The simulation experiment explores the influence of the changes in the angles and distances among the target, the transmitting station, and the receiving station on the radar range, velocity, and angle measurement noise covariance.

[0074] Table 1 Radar Signal Parameter Table

[0075]

[0076] The influence of the target-radar geometric position includes the distance R between the radar receiving station and the target R,k , the receiving angle θ between the radar receiving station and the target k , and the baseline distance L between the radar receiving station and the radar transmitting station k . The simulation experiment uses the control variable method to explore the relationship between the bistatic radar measurement noise covariance and the geometric position, and conducts three simulation experiments of fixing the distance R R,k , fixing the receiving angle θ k , and comparing the fixed receiving angle tracking algorithms respectively. In order to explore the influence of the actual target-radar geometric position on the measurement noise covariance, the signal-to-noise ratio also changes with the target-radar position in the simulation experiment.

[0077] The fixed-distance simulation experiment, as Figure 5 shown, keeps the distance R between the radar receiving station and the target R,k unchanged and explores the influence of the change in the receiving angle θ between the radar receiving station and the target k on the radar measurement noise covariance. The signal-to-noise ratio is inversely proportional to the radar measurement noise covariance. The smaller the signal-to-noise ratio, the larger the measurement noise covariance. It can be seen from the figure that when θ k is near π and R R,k <L k , the signal-to-noise ratio of the bistatic radar is very large. Judging from the signal-to-noise ratio relationship, the radar velocity measurement noise covariance should reach the minimum at this time. However, the actual situation is the opposite, and the bistatic radar velocity measurement noise covariance reaches the maximum. This shows that the influence of θ k on the radar velocity measurement noise covariance reaches the maximum; when R R,k >L k , the change of θ k has a relatively small influence on the bistatic radar velocity measurement noise covariance, and the change of the signal-to-noise ratio has a greater influence on the bistatic radar measurement noise covariance.

[0078] Fixed reception angle simulation experiment, as Figure 6 shown, keep the reception angle θ k between the radar receiving station and the target unchanged, and explore the influence of the distance R R,k between the radar receiving station and the target on the radar measurement noise covariance. From the fixed distance simulation experiment, it can be seen that when θ k is near π, the influence of the θ k angle on the measurement noise covariance of the radar velocity reaches the maximum. Therefore, θ k = 0.95π is selected as the research parameter for this experiment. In addition, the bistatic radar θ k = 0.5π, 0 and fixed noise are selected for experimental comparison. It can be seen from the figure that when the bistatic radar reception angle θ k = 0.95π and R R,k < L k , the influence of the geometric position on the bistatic radar velocity measurement noise covariance is relatively large. When the bistatic reception angle θ k is not near π, the change of the bistatic radar velocity measurement noise covariance is mainly related to the radar signal-to-noise ratio.

[0079] Figure 7 For the comparison experiment of the fixed reception angle tracking algorithm, tracking is carried out under fixed measurement noise and time-varying measurement noise, and the tracking accuracy is compared. It can be seen from the figure that the time-varying noise established by the present invention is more in line with the actual situation, and the measurement noise covariance at each moment during the tracking process of the bistatic radar can be accurately calculated, making the final tracking result more accurate.

[0080] The above simulation experiments verify and analyze the influence of the change of the target-radar geometric position on the measurement noise covariance. Compared with the constant modeling of the measurement noise covariance, the model established in this chapter is closer to the actual complex environment and can be well applied to the field of target tracking and information fusion. For example, it can establish a measurement noise covariance that simulates the actual situation for tracking and fusion algorithms, so that the performance of target tracking algorithms and fusion algorithms has a greater improvement. In practical applications, it can be applied to unmanned driving technology to improve the target tracking accuracy of millimeter-wave radar and the safety performance of unmanned driving technology; it can be applied to missile strike targets to improve the missile strike hit rate, etc.

Claims

1. A geometric position-related bistatic radar measurement noise covariance model method, characterized in that, Including the following steps: S1. Signal domain noise covariance S1-1. For the target reflection signal received by the radar in the signal domain, estimate the signal domain time delay and Doppler frequency shift according to the time delay, Doppler frequency shift, and incident angle. The ambiguity function of the signal is used to study the measurement and resolution performance of the radar, and is defined as: where \(t\) is time, \(u(t)\) is the signal pulse function, \(\tau\) a and \(\xi\) a are the actual time delay and Doppler shift, and \(\tau\) H and \(\xi\) H are the assumed time delay and Doppler shift; According to the Cramer-Rao lower bound, the relationship between the Fisher information matrix of the radar signal domain time delay and Doppler frequency shift estimation accuracy and the ambiguity function is as follows: where τ = τ H - τ a , ξ = ξ H - ξ a , when τ a = τ H , ξ a = ξ H , the ambiguity function X(τ H , τ a , ξ H , ξ a ) obtains the maximum absolute value, k represents that the current moment is the k-th moment, is the derivative symbol, τ and ξ are the independent variable parameters of time delay and Doppler frequency shift, x k is the state of the target, x T,k is the state of the radar transmitting station, x R,k is the state of the radar receiving station; The best estimation accuracy of the signal domain time delay and Doppler frequency shift can be described as: S1-2 Simplify the estimation accuracy J in the radar signal domain S Simplification: wherein, S1, S2, S3, and S4 are signal factors that can be calculated according to the signal parameters of the radar transmitting station, and the signal factor S2 = S3, SNR(x k , x T,k , x R,k ) is a signal-to-noise ratio function; The time delay τ (d k ) for the bistatic radar signal domain to receive the target echo is described as: Where c is the speed of light, R R,k is the distance between the radar receiving station and the target, d k is the bistatic radar distance, R T,k is the distance between the radar transmitting station and the target; The bistatic radar signal domain Doppler frequency shift ξ(v k ) is described as: where f c is the radar carrier frequency, are the position vectors of the target, the radar receiving station, and the radar transmitting station respectively, are the velocity vectors of the target, the radar receiving station, and the radar transmitting station respectively, f c is the radar carrier frequency, v k is the Doppler velocity measured by the bistatic radar; S1-4. Obtain the final Doppler frequency shift according to the bistatic radar signal domain Doppler frequency shift, which is described as: where L k is the baseline distance between the radar receiving station and the transceiver station, and γ k = |θ k - θ RT,k |, the value range of γ k is (0, π), I k is the bisector of the bistatic radar, and the angles formed with R R,k and R T,k are β k / 2, v I is the sum of the moduli of the velocity components of the velocity vectors and in the direction of the bisector I k of the bistatic radar, is the angle formed between and I k , is the angle formed between and I k , the value range of is [0, π], d k is the distance measurement of the bistatic radar, θ k and θ RT,k are respectively the reception angles of the radar receiving station for the target and the transmitting station, and the expression of a is:​ S2. Measurement domain noise covariance The estimation accuracy of the radar measurement domain in S2-1 includes the range and Doppler measurement estimation accuracies. The Fisher information matrix J S (τ, ξ) of the radar signal domain is subjected to independent variable substitution. Substitute τ(d k ) and ξ(v k (d k )) into the ambiguity function for variable substitution. Regard the measurements of the bistatic radar range d k and Doppler velocity v k as independent variables and take the derivative. Among them, v k = g(d k ). Finally, the Fisher information matrix of the estimation accuracies of the radar measurement domain range and velocity measurements is obtained, and the expression is as follows: S2-2. Use the second-order chain derivative rule of the binary function for the above formula. Finally, the conversion relationship of the Fisher information matrix of the signal domain and measurement domain measurement estimation accuracy can be obtained. Express the signal domain Fisher information matrix using the signal domain general formula. In the general formula, S2 = S3. Replace S3 with S2. The expansion of the Fisher information matrix of the radar measurement domain estimation accuracy is described as: In the formula, Simplify the above formula into a quadratic form: S2-3. Use the method of finding the inverse of the second-order adjoint matrix to obtain the measurement noise covariance matrix of the distance and speed in the measurement domain: In the formula, the expression of J1J4 - J2J2 is as follows: wherein, the terms SNR(x k ,x T,k ,x R,k ), J1(x k ,x T,k ,x R,k ), and J2(x k ,x T,k ,x R,k ) reflect the influence of the geometric position on the covariance of the bistatic radar range and velocity measurement noise, and the term J1J4 - J2J2 does not contain the influence of the geometric position; S3. In the bistatic radar system, the variance of the radar angle measurement noise is only related to the signal-to-noise ratio of the signal. The signal-to-noise ratio is related to the distance between the radar and the target. The variance of the angle measurement noise can be expressed as: In the formula, is the standard deviation of the reference angle measurement; S4. In combination with steps S1 - S3, the time delay τ(d k ) of the target echo received in the bistatic radar signal domain, the final Doppler frequency shift, and the measurement noise covariance matrix of the distance and velocity in the measurement domain are used to finally obtain the bistatic radar measurement noise covariance R k (x k , x T,k , x R,k ), the general formula of which is described as: S5. Receive the signal through the bistatic radar and perform signal tracking according to the bistatic radar measurement noise covariance obtained in step S4.

2. A geometric position-related bistatic radar measurement noise covariance model method according to claim 1, characterized in that In the above step S1-4, the derivation method of the final Doppler frequency shift is as follows: The measurement conversion relationship from the signal domain to the measurement domain is d k = τc and v k = ξc / f c , since ξ(v k ) needs to be differentiated with respect to d k when calculating the estimation accuracy of the measurement domain, it is necessary to separate the range measurement component in the Doppler frequency shift, decouple and transform the range measurement of ξ(v k ) to obtain a form containing the R R,k variable. The derivation process is as follows: In bistatic radar measurement, R can be converted into a function of d R,k and γ k by the cosine theorem, and the conversion formula is as follows: k ​ Use d k Replace the variable R in the Doppler frequency shift R,k with the variable, and finally the Doppler frequency shift can be described as:

3. A method for geometric position-related bistatic radar measurement noise covariance model according to claim 1, characterized in that In the step S2-2, in the form where the Fisher information matrix of the radar measurement domain estimation accuracy is simplified into a quadratic form, P k (x k ,x T,k ,x R,k ) is a time-varying correction coefficient matrix: Correction coefficient matrix P k It not only includes the conversion relationship from the signal domain to the measurement domain, but also includes the target-radar geometric position relationship. It changes with the target-radar geometric position relationship at each discrete time k. The dual-base station correction coefficient P k The elements of each part in the matrix are as follows: In the formula, the expression of b is:

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