CN116520263A - A Geometric Position-Dependent Bistatic Radar Measurement Noise Covariance Modeling Method - Google Patents

Abstract

The invention discloses a geometric position related bistatic radar measurement noise covariance model, which is used for redefining and constructing a time-varying model of the bistatic radar measurement noise covariance aiming at the problem that the bistatic radar measurement noise covariance is related to the geometric position relation of a target-radar, and accurately describing the quantitative relation between measurement precision and the geometric positions of the target, a transmitting station and a receiving station. Firstly, modeling by using a Keramen boundary and a fuzzy function to obtain the optimal estimation accuracy of the delay and the Doppler shift of a bistatic radar signal domain; secondly, a time-varying correction coefficient matrix of the conversion from the signal domain to the measurement domain under the double-base measurement form is deduced; finally, a time-varying bistatic radar measurement noise covariance expression is calculated. Simulation experiments prove and analyze that the covariance of the noise measured by the double-base radar is directly influenced by the geometric position relationship among the target, the transmitting station and the receiving station, and the method has strong practical engineering applicability.

Description

A Geometric Position-Dependent Bistatic Radar Measurement Noise Covariance Modeling Method

technical field

The invention belongs to the field of target tracking, and relates to a problem related to bistatic radar measurement noise covariance and target-radar geometric position relationship, in particular to a geometric position-related bistatic radar measurement noise covariance model method.

Background technique

When performing target tracking or information fusion on bistatic radar in a complex environment, it is necessary to establish a time-varying mathematical model of measurement noise covariance. The measurement noise covariance model of bistatic radar is largely affected by the target, transmitting station, receiving The influence of the geometric position relationship between stations. In many studies, the measurement noise covariance of radar is usually modeled as a constant, which has a large gap with the measurement noise covariance in actual radar measurement.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention proposes a geometric position-dependent bistatic radar measurement noise covariance model, and aims at the problem that the bistatic radar measurement noise covariance is related to the target-radar geometric position relationship, and re-deduces and constructs The time-varying model of bistatic radar measurement noise covariance accurately describes the quantitative relationship between measurement accuracy and the geometric positions of targets, transmitting stations, and receiving stations. The measurement noise covariance modeling symbol is shown in Fig. 1 for the geometric structure and measurement diagram of the bistatic radar.

1) Signal domain noise covariance

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, there will be Estimation error, so the estimation accuracy of the radar signal domain includes two parts, the time delay and the Doppler frequency shift, and the derivation does not consider the angle. By using the signal domain to measurement domain conversion equation for the signal domain estimation error, the measurement accuracy of target range and Doppler velocity can be obtained.

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

where t is time, u(t) is the signal pulse function, τ _a and ξ _a are actual time delay and Doppler frequency shift, τ _H and ξ _H are hypothetical time delay and Doppler frequency shift.

The Cramereau lower bound is the inverse matrix of the Fisher information matrix, which is the upper bound of the error variance generated by the radar measurement, that is, the best estimation accuracy that can be achieved in theory. In general, the radar signal domain delay and Doppler frequency shift The relationship between the Fisher information matrix of the estimated accuracy and the fuzzy function is as follows:

In the formula, τ=τ _H -τ _a , ξ=ξ _H -ξ _a , when τ _a =τ _H , ξ _a =ξ _H , the fuzzy function X(τ _H ,τ _a ,ξ _H ,ξ _a ) is obtained The maximum absolute value, k means that the current moment is time k, is the derivation symbol, τ and ξ are the time delay and Doppler frequency shift independent variable parameters, 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 signal domain time delay and Doppler frequency shift can be described as:

The signal domain estimation accuracy _JS 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 fixed constants, and only the signal-to-noise ratio changes, which can simplify the estimation accuracy J _S of the radar signal domain:

In the formula, S ₁ , S ₂ , S ₃ and S ₄ are signal factors that can be calculated according to the signal parameters of the radar transmitting station, signal factor S ₂ =S ₃ , SNR(x _k ,x _T,k ,x _{R, k} ) is the signal-to-noise ratio function.

The time delay τ(d _k ) of receiving the target echo in the bistatic radar signal domain is described as:

In the formula, c is the speed of light, R _R,k is the distance between the radar receiving station and the target, d _k is the distance of the bistatic radar, and R _T,k is the distance between the radar transmitting station and the target.

Bistatic radar signal domain Doppler 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 motion velocity vectors of the target, radar receiving station, and radar transmitting station respectively, f _c is the radar carrier frequency, and v _k is the Doppler velocity measured by the bistatic radar.

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 derived with respect to d _k when calculating the estimation accuracy of the measurement domain, the Doppler frequency shift To separate the distance measurement component in ξ(v k ), the distance measurement decoupling commutation is performed on ξ(v _k ), and the form containing R _R,k variables is obtained. The derivation process is as follows:

In the formula, L _k is the baseline distance between the radar receiving station and the transceiver station, I _k is the bistatic radar bisector, and the angle formed by R _R,k and R _T,k is β _k /2, v _I is the velocity vector and /> The sum of the moduli of the velocity components in the direction of the bistatic radar bisector I _k , /> The value range of γ _k is (0, π), and θ _k and θ _RT,k are the receiving angles of the radar receiving station to the target and the transmitting station, respectively. In bistatic radar measurement, R _R,k can be converted into a function of d _k and γ _k by the law of cosines, and the conversion formula is as follows:

Use the d _k variable to replace the R _R,k variable in the Doppler frequency shift, and the final Doppler frequency shift can be described as:

In the formula, the expression of a is:

Simplify a:

2) Measurement domain noise covariance

The estimation accuracy of the radar measurement domain includes distance and Doppler measurement estimation accuracy. The Fisher information matrix J _S (τ,ξ) in the radar signal domain is transformed into independent variables, and τ(d _k ) and ξ(v _k ( d _k )) is substituted into the fuzzy function for variable substitution, and the bistatic radar distance measurement d _k and Doppler velocity measurement v _k are regarded as independent variables for derivation, where v _k =g(d _k ), and finally the radar measurement is obtained Fisher information matrix for estimated accuracy of domain distance and velocity measurements:

The above formula uses the second-order chain derivation rule of the binary function, which contains two layers of functional relationships. The first layer of functions is the relationship between the fuzzy function X(τ,ξ) with respect to the independent variables τ and ξ, and the second layer of functions As the relationship between τ(d _k ) and ξ(v _k (d _k )) with respect to the independent variables d _k and v _k , the Fisher information matrix transformation relationship of the measurement estimation accuracy in the signal domain and the measurement domain can be finally obtained, and the signal domain fee The snow information matrix is represented by a general formula in the signal domain, where S ₂ = S ₃ , and S ₂ is used to replace S ₃ . The Fisher information matrix expansion of the estimation accuracy in the radar measurement domain is described as:

In the formula,

Simplify the above formula into a quadratic form:

In the formula, P _k (x _k ,x _T,k ,x _R,k ) is the time-varying correction coefficient matrix:

The correction coefficient matrix P _k not only includes the conversion relationship from the signal domain to the measurement domain, but also includes the geometric position relationship between the target and the radar. It will change with the geometric position relationship between the target and the radar at each discrete time k. The dual base station correction coefficient P _k The elements of each part of the matrix are as follows:

In the formula, the expression of b is:

Using the method of second-order adjoint matrix inversion, the measurement noise covariance matrix of distance and velocity in the measurement domain is obtained:

In the formula, the expression of J ₁ J ₄ -J ₂ J ₂ is as follows:

In the formula, the term SNR(x _k ,x _T,k ,x _R,k ), the term J ₁ (x _k ,x _T,k ,x _R,k ), the term J ₂ (x _k ,x _T,k ,x _{R, k} ) items reflect the influence of geometric position on bistatic radar range and velocity measurement noise covariance, J ₁ J ₄ -J ₂ J ₂ items do not include the influence of geometric position.

In a bistatic radar system, the noise variance of the radar angle measurement is only related to the signal-to-noise ratio of the signal, and 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, Measure the standard deviation for the reference angle.

In summary, the general formula of bistatic radar measurement noise covariance R _k (x _k ,x _T,k ,x _R,k ) can be described as:

Technical effect of the present invention:

Aiming at the problem that the bistatic radar measurement noise covariance is related to the target-radar geometric position relationship, firstly, the optimal estimation accuracy of bistatic radar signal domain time delay and Doppler frequency shift is obtained by using Cramereau bound and ambiguity function modeling. 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 deduced; finally, different types of radar transmission signals are recorded as general descriptions, and according to different types of radar transmission signals The time-varying bistatic radar measurement noise covariance expression is calculated, and the time-varying model of the bistatic radar measurement noise covariance is re-derived and constructed, and the measurement noise covariance of the bistatic radar is accurately quantified. The measurement noise covariance model It can greatly improve the performance of target tracking algorithm and fusion algorithm. The simulation experiment verifies and analyzes the measurement noise covariance of the bistatic radar is directly affected by the geometric position relationship among the target, the transmitting station and the receiving station.

Description of drawings

Figure 1 is a schematic diagram of the geometric structure and measurement of the bistatic radar;

Figure 2 is a fixed-distance simulation scene diagram;

Figure 3 is a simulation scene diagram of a fixed acceptance angle;

Fig. 4 is a comparison flow chart of a fixed acceptance angle tracking comparison example;

Fig. 5 is the change diagram of the standard deviation of measurement noise obtained by the example of fixed distance;

Fig. 6 is the change diagram of the standard deviation of measurement noise obtained by the example of fixed acceptance angle;

Figure 7 is the RMSE diagram of the position obtained by the fixed receiving angle tracking comparison example;

Detailed ways

Below in conjunction with accompanying drawing, the present invention will be further explained;

In order to verify the relationship between the bistatic radar measurement noise covariance modeled in the present invention and the target-radar geometric position, this embodiment conducts a simulation experiment of the bistatic radar measurement noise covariance and its hypothesis verification. As shown in Figure 2 and Figure 3, the simulation experiment includes a fixed distance experiment and a fixed acceptance angle experiment.

The initial settings of the two simulation experiments carried out in this embodiment are as follows:

Fix the radar receiving station and transceiver station at [0m,0m] ^T and [5000m,0m] ^T respectively, the baseline distance between them is L _k =5km, the target is a movable target, and the velocity vector and /> The sum v _I of the velocity component modes in the direction of the bistatic radar bisector I _k =50m/s. In the fixed distance experiment, keep L _k and _RR,k unchanged, and only change θ _k to make the target move clockwise around the radar receiving station; in the fixed receiving angle experiment, keep L _k and θ _k unchanged , only change R _R,k to make the target move towards the fixed direction of θ _k . The third experiment compares the influence of fixed measurement noise and time-varying measurement noise on the tracking algorithm based on the fixed acceptance angle experiment scenario. The flow chart is shown in Figure 4.

The radar signal parameter table of the simulation experiment is shown in Table 1. In the simulation, the standard deviation of the reference angle measurement is set as When the radar signal-to-noise ratio changes with the geometric position, the radar signal-to-noise ratio will be within a range due to the limitation of physical components. By consulting the literature, it is determined that the actual radar signal-to-noise ratio SNR is between -20dB and 30dB. In this paper In the scene, the signal constant R ₀ in the signal-to-noise ratio is set to 11000, and the false alarm rate P _FA is set to 0.01. The radar transmission signal model uses ATSC signals. The simulation experiment explores the angle, Effect of changing range on noise covariance of radar range, velocity and angle measurements.

Table 1 Radar signal parameter table

The target-radar geometric position influence includes the distance R _R,k between the radar receiving station and the target, the receiving angle θ _k between the radar receiving station and the target, the baseline distance L _k between the radar receiving station and the radar transmitting station, 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 with a fixed distance R _R,k , a fixed receiving angle θ _k and a comparison of tracking algorithms at a fixed receiving angle. In order to explore the influence of the target-radar geometric position on the measurement noise covariance in practice, the signal-to-noise ratio also changes with the target-radar position in the simulation experiment.

The fixed distance simulation experiment, as shown in Figure 5, keeps the distance R _R,k between the radar receiving station and the target unchanged, and explores the influence of the change of the receiving angle θ _k between the radar receiving station and the target 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 will be. 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 relationship of the signal-to-noise ratio, the noise covariance of the radar speed measurement at this time should reach However, the actual situation is just the opposite, the bistatic radar velocity measurement noise covariance reaches the maximum, which shows that θ _k has the greatest influence on the radar velocity measurement noise covariance; when R _R,k >L _k , the θ _k The measurement noise covariance of the bistatic radar velocity is relatively small when the change is made, but the SNR change has a great influence on the measurement noise covariance of the bistatic radar.

The fixed receiving angle simulation experiment, as shown in Figure 6, keeps the receiving angle θ _k between the radar receiving station and the target unchanged, and explores the effect of the change of the distance R _R,k between the radar receiving station and the target on the radar measurement noise covariance Influence. From the fixed-distance simulation experiment, it can be seen that when θ _k is near π, the influence of θ _k angle on the measurement noise covariance of radar velocity reaches the maximum, so θ _k = 0.95π is selected as the research parameter of this experiment, and a double base Radar θ _k =0.5π, 0 and fixed noise are used as experimental comparisons. It can be seen from the figure that when the bistatic radar receiving angle θ _k =0.95π and R _R,k <L _k , the geometric position of the bistatic radar speed measurement noise covariance is greatly affected. When the bistatic receiving angle θ _k is not near π, the variation of the bistatic radar velocity measurement noise covariance is mainly related to the radar signal-to-noise ratio.

Fig. 7 is a comparison experiment of tracking algorithms with fixed receiving angle, tracking is performed 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 practical, and the measurement noise covariance at each moment in the bistatic radar tracking process can be accurately calculated, making the final tracking result more accurate.

The above simulation experiments verified and analyzed the influence of the target-radar geometric position change on the measurement noise covariance. Compared with the measurement noise covariance constant modeling, the model established in this chapter is closer to the actual complex environment and can be well applied to target tracking. In the field of information fusion, for example, the covariance of simulated actual measurement noise can be established for tracking and fusion algorithms, which greatly improves the performance of target tracking algorithms and fusion algorithms. In practical applications, it can be applied to unmanned driving technology to improve the accuracy of millimeter-wave radar target tracking and improve the safety performance of unmanned technology; it can be applied to missile strike targets to improve the hit rate of missile strikes, etc.

Claims (3)

1. a geometric position-dependent bistatic radar measurement noise covariance model method, is characterized in that, comprises the steps: S1, signal domain noise covariance S1-1 Estimate the time delay and Doppler frequency shift in the signal domain according to the time delay, Doppler frequency shift and incident angle of the target reflection signal received by the radar in the signal domain, The ambiguity function of the signal is used to study the measurement and resolution performance of the radar, which is defined as: where t is time, u(t) is the signal pulse function, τ _a and ξ _a are actual time delay and Doppler frequency shift, τ _H and ξ _H are hypothetical time delay and Doppler frequency shift; According to the Cramereau lower bound, the relationship between the Fisher information matrix and the ambiguity function of radar signal domain time delay and Doppler frequency shift estimation accuracy is as follows: In the formula, τ=τ _H -τ _a , ξ=ξ _H -ξ _a , when τ _a =τ _H , ξ _a =ξ _H , the fuzzy function X(τ _H ,τ _a ,ξ _H ,ξ _a ) is obtained The maximum absolute value, k means that the current moment is time k, is the derivation symbol, τ and ξ are the time delay and Doppler frequency shift independent variable parameters, 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 signal domain time delay and Doppler frequency shift can be described as: S1-2 simplifies the estimation accuracy J _S of the radar signal domain: In the formula, S ₁ , S ₂ , S ₃ and S ₄ are signal factors that can be calculated according to the signal parameters of the radar transmitting station, signal factor S ₂ =S ₃ , SNR(x _k ,x _T,k ,x _{R, k} ) is a signal-to-noise ratio function; The time delay τ(d _k ) of receiving target echo in S1-3 bistatic radar signal domain is described as: In the formula, c is the speed of light, R _R,k is the distance between the radar receiving station and the target, d _k is the distance of the bistatic radar, R _T,k is the distance between the radar transmitting station and the target; Bistatic radar signal domain Doppler 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 motion velocity vectors of the target, the radar receiving station, and the radar transmitting station respectively, f _c is the radar carrier frequency, and v _k is the Doppler velocity measured by the bistatic radar; S1-4 According to the Doppler frequency shift in the bistatic radar signal domain, the final Doppler frequency shift is obtained, which is described as: In the formula, L _k is the baseline distance between the radar receiving station and the transceiver station, γ _k = |θ _k -θ _RT,k |, the value range of γ _k is (0, π), and I _k is the bibase The radar bisector, the angle between R _R,k and _RT,k is β _k /2, and v _I is the velocity vector and The sum of the moduli of the velocity components in the direction of the bistatic radar bisector _Ik , for /> The angle formed between and I _k , /> for /> The angle formed between and I _k , /> The value range of is [0, π], the distance measurement of d _k bistatic radar, θ _k and θ _RT,k are the receiving angles of the radar receiving station to the target and the transmitting station respectively, and the expression of a is: S2. Measurement domain noise covariance S2-1 The estimation accuracy of the radar measurement domain includes distance and Doppler measurement estimation accuracy. The Fisher information matrix J _S (τ,ξ) in the radar signal domain is converted into independent variables, and τ(d _k ) and ξ( v _k (d _k )) is substituted into the fuzzy function for variable substitution, and the measurement of bistatic radar distance d _k and Doppler velocity v _k is regarded as independent variables for derivation, where v _k =g(d _k ), and finally The Fisher information matrix of the estimated accuracy of the range and velocity measurements in the radar measurement domain is obtained, and the expression is as follows: S2-2 Using the second-order chain derivation rule of the binary function on the above formula, the Fisher information matrix conversion relationship of the measurement and estimation accuracy in the signal domain and the measurement domain can be finally obtained, and the Fisher information matrix in the signal domain can be used by the general formula in the signal domain It means that in the general formula, S ₂ =S ₃ , using S ₂ to replace S ₃ , the Fisher information matrix expansion of radar measurement domain estimation accuracy is described as: In the formula, Simplify the above formula into a quadratic form: S2-3 Using the second-order adjoint matrix inversion method, the measurement noise covariance matrix of distance and velocity in the measurement domain is obtained: In the formula, the expression of J ₁ J ₄ -J ₂ J ₂ is as follows: In the formula, the term SNR(x _k ,x _T,k ,x _R,k ), the term J ₁ (x _k ,x _T,k ,x _R,k ), the term J ₂ (x _k ,x _T,k ,x _{R, k} ) items reflect the influence of geometric position on bistatic radar range and speed measurement noise covariance, J ₁ J ₄ -J ₂ J ₂ items do not include the influence of geometric position; S3. In a bistatic radar system, the noise variance of the radar angle measurement is only related to the signal-to-noise ratio of the signal, and the signal-to-noise ratio is related to the distance between the radar and the target. The noise variance of the angle measurement can be expressed as: In the formula, Measure the standard deviation for the reference angle; S4, in combination with steps S1-S3, the time delay τ(d _k ) of receiving the target echo in the bistatic radar signal domain, the final Doppler frequency shift and the measurement noise covariance matrix of distance and velocity in the measurement domain, finally obtain the bistatic radar The general formula of base radar measurement noise covariance R _k (x _k ,x _T,k ,x _R,k ) is described as: S5. Receive signals through the bistatic radar, and perform signal tracking according to the bistatic radar measurement noise covariance obtained in step S4. 2. the bistatic radar measurement noise covariance model method related to a kind of geometric position according to claim 1, is characterized in that, in described step S1-4, final Doppler frequency shift derivation method 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 derived with respect to d _k when calculating the estimation accuracy of the measurement domain, the Doppler frequency shift To separate the distance measurement component in ξ(v _{k ), the distance measurement decoupling commutation is performed on ξ(v k} ), and the form containing R _R,k variables is obtained. The derivation process is as follows: In bistatic radar measurement, R _R,k can be converted into a function of d _k and γ _k by the law of cosines, and the conversion formula is as follows: Use the d _k variable to replace the R _R,k variable in the Doppler frequency shift, and the final Doppler frequency shift can be described as: 3. the bistatic radar measurement noise covariance model method related to a kind of geometric position according to claim 1, is characterized in that, in described step S2-2, the Fisher information matrix formula of radar measurement domain estimation accuracy is simplified as In the quadratic form, P _k (x _k ,x _T,k ,x _R,k ) is a time-varying correction coefficient matrix: The correction coefficient matrix P _k not only includes the conversion relationship from the signal domain to the measurement domain, but also includes the geometric position relationship between the target and the radar. It will change with the geometric position relationship between the target and the radar at each discrete time k. The dual base station correction coefficient P _k The elements of each part of the matrix are as follows: In the formula, the expression of b is: