CN116520263A - Geometric position-related bistatic radar measurement noise covariance modeling method - Google Patents
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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
Technical Field
The invention belongs to the field of target tracking, relates to the problem that a double-base radar measurement noise covariance is related to a target-radar geometric position relation, and particularly relates to a double-base radar measurement noise covariance model method related to geometric positions.
Background
When target tracking or information fusion is carried out on the bistatic radar in a complex environment, a time-varying mathematical model of measurement noise covariance needs to be established, and the measurement noise covariance model of the bistatic radar is greatly influenced by the geometric position relationship among the target, the transmitting station and the receiving station. In many studies, the measurement noise covariance of a radar is typically modeled as a constant, which is quite different from the measurement noise covariance in an actual radar measurement.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a geometric position related bistatic radar measurement noise covariance model, and the time-varying model of the bistatic radar measurement noise covariance is re-deduced and constructed for solving the problem that the bistatic radar measurement noise covariance is related to the geometric position relation of a target-radar, so that the quantitative relation between the measurement precision and the geometric positions of the target, a transmitting station and a receiving station is accurately described. The measurement noise covariance modeling symbol is shown in the double-base radar geometry and measurement schematic diagram of fig. 1.
1) Signal domain noise covariance
When modeling a target reflected signal received by a radar in a signal domain, the target reflected signal is usually modeled into a delay, a Doppler frequency shift and an incident angle, and when estimating the delay and the Doppler frequency shift in the signal domain, an estimation error is generated, so that the estimation accuracy of the radar signal domain comprises two parts of the delay and the Doppler frequency shift, and the angle is not considered in deduction. By using the signal domain to measurement domain conversion equation for signal domain estimation errors, the accuracy of the target range and Doppler velocity measurements can be obtained.
The fuzzy function of the signal is used to study the measurement and resolution performance of the radar, defined as:
wherein t is time, u (t) is a signal pulse function, τ a And xi a For actual delay and Doppler shift, τ H And xi H For the assumed delay and doppler shift.
The lower boundary of the Kramer is the inverse matrix of the Fisher information matrix, which is the upper boundary of the error variance generated by radar measurement, namely the best estimation accuracy which can be achieved theoretically, and the relationship between the Fisher information matrix and the fuzzy function of the radar signal domain delay and Doppler shift estimation accuracy is generally as follows:
where τ=τ H -τ a ，ξ＝ξ H -ξ a When τ a ＝τ H ，ξ a ＝ξ H When the blur function X (τ H ,τ a ,ξ H ,ξ a ) The maximum absolute value is obtained, k represents the current moment being moment k,for deriving symbols, τ, ζ are delay, doppler shift argument parameters, x k For the state of the object, x T,k For the state of the radar transmitting station, x R,k Is the state of the radar receiving station.
The signal domain delay and doppler shift best estimation accuracy can be described as:
signal domain estimation accuracy J S Regarding the pulse signal and the signal-to-noise ratio transmitted by the radar, 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 fixed constants, only the signal-to-noise ratio is changed, the estimation accuracy J of the radar signal domain can be improved S Simplification:
in the middle of，S 1 、S 2 、S 3 And S is 4 For signal factors which can be calculated from the signal parameters of the radar transmitting station, the signal factor S 2 ＝S 3 ，SNR(x k ,x T,k ,x R,k ) As a function of signal to noise ratio.
Time delay tau (d) of receiving target echo by bistatic radar signal domain k ) The description is as follows:
wherein c is the speed of light, R R,k D is the distance between the radar receiving station and the target k Is the range of the bistatic radar, R T,k Is the distance between the radar transmitting station and the target.
Doppler shift in the bistatic radar signal domain ζ (v) k ) The description is as follows:
wherein f c For the radar carrier frequency,position vectors for the target, radar receiver station, radar transmitter station, respectively, < >>Motion velocity vectors of target, radar receiving station and radar transmitting station respectively, f c For the radar carrier frequency, v k Doppler velocity measured for a bistatic radar.
The measurement conversion relation from the signal domain to the measurement domain is d k =τc and v k ＝ξc/f c Since ζ (v) is required in calculating the measurement domain estimation accuracy k ) For d k Deriving, so that the distance measurement component is separated in the Doppler shift, for ζ (v k ) Decoupling element conversion is carried out on distance measurement to obtain the R-containing element R,k The form of the variables, the derivation process is as follows:
wherein L is k For the baseline distance between the radar receiving station and the transceiver station, I k Is a double-base radar bisector, and R R,k And R is T,k The angle is beta k /2，v I Is a velocity vectorAnd->In the double-base radar bisector I k Sum of velocity component modes in direction, +.>γ k The value range of (0, pi), theta k And theta RT,k The receiving angles of the radar receiving station to the target and the transmitting station are respectively. In bistatic radar measurement, R can be determined by cosine law R,k Conversion to d k And gamma k The conversion formula is as follows:
use d k Variable versus Doppler shift R R,k The variables are replaced and the final doppler shift can be described as:
wherein, the expression of a is:
simplifying a:
2) Measurement domain noise covariance
The estimation accuracy of the radar measurement domain comprises the estimation accuracy of the distance and Doppler measurement, and the Fisher information matrix J of the radar signal domain S (τ, ζ) performing argument conversion, and converting τ (d) k ) And xi (v) k (d k ) Substituting into fuzzy function to perform variable replacement, and measuring d by using bistatic radar distance k And Doppler velocity measurement v k Deriving as arguments, where v k ＝g(d k ) Finally, a snow cost information matrix of the estimation accuracy of the radar measurement domain distance and the speed measurement is obtained:
the binary function second order chain derivative rule is used for the above formula, wherein the binary function second order chain derivative rule comprises a two-layer function relationship, the first layer function is the relationship of a fuzzy function X (tau, xi) relative to independent variables tau and xi, and the second layer function is tau (d k ) And xi (v) k (d k ) With respect to independent variable d k And v k Finally, the conversion relation of the Fisher information matrix of the signal domain and the measurement estimation precision of the measurement domain can be obtained, the Fisher information matrix of the signal domain is expressed by using the general formula of the signal domain, wherein S is 2 ＝S 3 S is used 2 To replace S 3 The snow-cost information matrix expansion of the radar measurement domain estimation accuracy is described as:
in the method, in the process of the invention,
simplifying the above formula into a quadratic form:
wherein P is k (x k ,x T,k ,x R,k ) A time-varying correction coefficient matrix:
correction coefficient matrix P k The method comprises the conversion relation from a signal domain to a measurement domain and the geometrical position relation of a target-radar, wherein the geometrical position relation of the target-radar is changed at each discrete moment k, and the correction coefficient P of a double base station is changed k The elements of each part of the matrix are as follows:
wherein, the expression of b is:
obtaining a measurement noise covariance matrix of the distance and the speed in a measurement domain by using a second-order accompanying matrix inversion method:
wherein J is 1 J 4 -J 2 J 2 The expression of (2) is as follows:
where SNR (x k ,x T,k ,x R,k ) Item, J 1 (x k ,x T,k ,x R,k ) Item, J 2 (x k ,x T,k ,x R,k ) The influence of the geometric position on the noise covariance of the range and the speed measurement of the bistatic radar is embodied in the term, J 1 J 4 -J 2 J 2 The term does not contain the influence of the geometrical position.
In a bistatic radar system, the radar angle measurement noise variance is only related to the signal-to-noise ratio of the signal, which is related to the distance between the radar and the target, and can be expressed as:
in the method, in the process of the invention,standard deviation is measured for the reference angle.
In summary, the noise covariance R of the bistatic radar measurement can be finally obtained k (x k ,x T,k ,x R,k ) The general formula of (C) is described as follows:
the invention has the technical effects that:
aiming at the problem that the covariance of the measurement noise of the bistatic radar is related to the geometric position relation of the target-radar, firstly, modeling by using a Kelarmerro boundary and a fuzzy function to obtain the best estimation precision of the delay and the Doppler frequency shift of the signal domain of the bistatic radar, namely the measurement noise of the 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, the radar emission signals of different types are described as general description, a time-varying double-base radar measurement noise covariance expression is obtained through calculation according to the radar emission signals of different types, a time-varying model of the double-base radar measurement noise covariance is deduced and constructed again, the measurement noise covariance of the double-base radar is quantized accurately, and the performance of a target tracking algorithm and a fusion algorithm can be improved greatly through the measurement noise covariance model. 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.
Drawings
FIG. 1 is a diagram of a bistatic radar geometry and measurement;
FIG. 2 is a fixed distance simulation scene graph;
FIG. 3 is a fixed acceptance angle simulation scene graph;
FIG. 4 is a comparative flow chart of a fixed acceptance angle tracking comparative example;
FIG. 5 is a graph of the standard deviation of measured noise obtained for a fixed distance example;
FIG. 6 is a graph of the standard deviation of measured noise obtained by a fixed angle of reception example;
FIG. 7 is a plot of the location RMSE obtained for a fixed acceptance angle tracking comparative example;
Detailed Description
The invention is further explained below with reference to the drawings;
in order to verify the relationship between the modeled bistatic radar measurement noise covariance and the target-radar geometric position, the embodiment carries out simulation experiments of the bistatic radar measurement noise covariance and the hypothesis verification thereof. As shown in fig. 2 and 3, the simulation experiment includes a fixed distance experiment and a fixed acceptance angle experiment.
The initial settings of the two simulation experiments performed in this example were as follows:
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, the velocity vectorAnd->In the double-base radar bisector I k Sum v of velocity component modes in direction I =50m/s. In fixed distance experiments, L is maintained k And R is R,k Unchanged, change only theta k Causing the target to perform a clockwise circular motion about the radar receiving station; in the fixed acceptance angle experiment, L is maintained k And theta k Unchanged, only R is changed R,k So that the target is towards theta k The fixed direction of motion. The third experiment is based on the fixed acceptance angle experimental scenario, comparing the influence of fixed measurement noise and time-varying measurement noise on the tracking algorithm, and the flow chart is shown in fig. 4.
The radar signal parameter table of the simulation experiment is shown in Table 1, and the standard deviation of the reference angle measurement is set in the simulationWhen the signal-to-noise ratio of the radar changes along with the geometric position, the signal-to-noise ratio of the radar is within a range due to the limitation of physical components, the actual signal-to-noise ratio SNR of the radar is determined to be between-20 dB and 30dB by consulting literature, and in the scene, the signal constant R in the signal-to-noise ratio is determined 0 Is set to 11000, false alarm rate P FA The radar emission signal model is set to be 0.01, an ATSC signal is adopted, and simulation experiments explore the influence of the change of angles and distances among a target, an emission station and a receiving station on the covariance of radar distance, speed and angle measurement noise.
Table 1 radar signal parameter table
The target-radar geometry effect includes the distance R between the radar receiving station and the target R,k Reception angle θ between radar receiving station and target k Baseline distance L between radar receiving station and radar transmitting station k The simulation experiment uses a control variable method to explore the noise covariance and geometric position of the double-base radar measurementThe relation of the positions is respectively fixed with a distance R R,k Fixed angle of reception theta k And comparing the three simulation experiments with a fixed receiving angle tracking algorithm. In order to explore the effect of the target-radar geometry on the measurement noise covariance in practice, the signal-to-noise ratio also varies with the target-radar position in simulation experiments.
Fixed distance simulation experiments, as shown in FIG. 5, maintain the distance R between the radar receiving station and the target R,k Invariable, exploring the reception angle θ between the radar receiving station and the target k The effect on the radar measurement noise covariance is changed. The signal-to-noise ratio is inversely related to the radar measurement noise covariance, the smaller the signal-to-noise ratio, the greater the measurement noise covariance. As can be seen from the figure, when θ k In the vicinity of pi and R R,k ＜L k When the signal-to-noise ratio of the bistatic radar is large, the signal-to-noise ratio relation judges that the covariance of the radar speed measurement noise at the moment should be minimum, but the actual situation is contrary, the covariance of the bistatic radar speed measurement noise is maximum, which shows that theta k The influence on the measurement noise covariance of the radar speed is maximized; when R is R,k ＞L k At the time of theta k The variation of the signal to noise ratio has a relatively small influence on the measurement noise covariance of the speed of the bistatic radar.
Fixed acceptance angle simulation experiment, as shown in FIG. 6, the acceptance angle θ between the radar receiving station and the target is maintained k Invariable, explore the distance R between the radar receiving station and the target R,k The effect on the radar measurement noise covariance is changed. As known from the fixed distance simulation experiment, when θ k At around pi, θ k The influence of the angle on the measurement noise covariance of the radar speed is maximized, so θ is selected k =0.95 pi as the study parameter of the experiment, and a bistatic radar θ was additionally selected k =0.5pi, 0 and fixed noise as experimental comparisons. As can be seen from the figure, when the bistatic radar receives an angle θ k =0.95 pi and R R,k ＜L k When the bistatic radar velocity measurement noise covariance is greatly affected by the geometric position. When the double base receiving angle theta k Not in the vicinity of piWhen the variance of the noise covariance of the bistatic radar velocity measurement is mainly related to the radar signal-to-noise ratio.
Fig. 7 is a comparison experiment of a fixed acceptance angle tracking algorithm, tracking is performed when the measured noise is fixed and the measured noise is time-varying, and tracking accuracy is compared. From the graph, the time-varying noise built by the method is more fit and practical, and the measurement noise covariance of each moment in the double-base radar tracking process can be accurately calculated, so that the final tracking result is more accurate.
The simulation experiment verifies and analyzes the influence of the target-radar geometric position change on the measurement noise covariance, and compared with the measurement noise covariance constant modeling, the model built by the chapter is closer to the actual complex environment, can be well applied to the field of target tracking and information fusion, for example, can be used for building the simulation actual measurement noise covariance for the tracking and fusion algorithm, so that the performance of the target tracking algorithm and the fusion algorithm is greatly improved. In practical application, the method can be applied to unmanned technology, so that the millimeter wave radar target tracking precision is improved, and the safety performance of the unmanned technology is improved; the method can be applied to missile hitting targets, improve missile hitting hit rate and the like.
Claims (3)
1. The geometric position related double-base radar noise covariance model measurement method is characterized by comprising the following steps of:
s1, signal domain noise covariance
S1-1, estimating the time delay and Doppler shift of a signal domain according to the time delay, doppler shift and incidence angle of a target reflected signal received by a radar in the signal domain,
the fuzzy function of the signal is used to study the measurement and resolution performance of the radar, defined as:
wherein t is time, u (t) is a signal pulse function, τ a And xi a For actual delay and Doppler shift, τ H And xi H For hypothesized delay and doppler shifts;
according to the lower boundary of the Keramelteon, the relationship between the Fisher information matrix and the fuzzy function of the radar signal domain time delay and Doppler frequency shift estimation precision is as follows:
where τ=τ H -τ a ，ξ＝ξ H -ξ a When τ a ＝τ H ，ξ a ＝ξ H When the blur function X (τ H ,τ a ,ξ H ,ξ a ) The maximum absolute value is obtained, k represents the current moment being moment k,for deriving symbols, τ, ζ are delay, doppler shift argument parameters, x k For the state of the object, x T,k For the state of the radar transmitting station, x R,k A state of the radar receiving station;
the signal domain delay and doppler shift best estimation accuracy can be described as:
s1-2 estimating accuracy J of radar signal domain S Simplification:
wherein S is 1 、S 2 、S 3 And S is 4 For signal factors which can be calculated from the signal parameters of the radar transmitting station, the signal factor S 2 ＝S 3 ，SNR(x k ,x T,k ,x R,k ) Is a signal to noise ratio function;
s1-3 bistatic radar signal domain time delay τ (d) for receiving target echoes k ) The description is as follows:
wherein c is the speed of light, R R,k D is the distance between the radar receiving station and the target k Is the range of the bistatic radar, R T,k Is the distance between the radar transmitting station and the target;
doppler shift in the bistatic radar signal domain ζ (v) k ) The description is as follows:
wherein f c For the radar carrier frequency,position vectors for the target, radar receiver station, radar transmitter station, respectively, < >>Motion velocity vectors of target, radar receiving station and radar transmitting station respectively, f c For the radar carrier frequency, v k Doppler velocity measured for a bistatic radar;
s1-4, obtaining final Doppler frequency shift according to Doppler frequency shift of the bistatic radar signal domain, wherein the final Doppler frequency shift is described as follows:
wherein L is k For the baseline distance between the radar receiving station and the transceiver station, gamma k ＝|θ k -θ RT,k |，γ k The value range of (0, pi), I k Is a double-base radar bisector, and R R,k And R is T,k The angle is beta k /2，v I Is a velocity vectorAndin the double-base radar bisector I k The sum of the velocity component modes in the direction, is->And I k Angle formed between them, +.>Is->And I k Angle formed between them, +.>The value range of (2) is [0, pi ]]，d k Range measurement, θ, for bistatic radar k And theta RT,k The expression of a is that the receiving angles of the radar receiving station to the target and the transmitting station are respectively:
s2, measuring domain noise covariance
S2-1 estimation accuracy of radar measurement domain comprises distance and Doppler measurement estimation accuracy, and Fisher information matrix J of radar signal domain S (τ, ζ) performing argument conversion, and converting τ (d) k ) And xi (v) k (d k ) Substituting into the fuzzy function to perform variable replacement, and obtaining the distance d of the bistatic radar k And Doppler velocity v k Is derived as an independent variable, wherein v k ＝g(d k ) Finally obtaining the distance and the speed of the radar measurement domainThe snow information matrix of the estimation precision of the degree measurement has the following expression:
s2-2 uses a binary function second-order chain derivative rule to the above formula, and finally can obtain the conversion relation of the Fisher information matrix of the signal domain and the measurement estimation precision of the measurement domain, and the Fisher information matrix of the signal domain is expressed by a general formula of the signal domain, wherein S is 2 ＝S 3 S is used 2 To replace S 3 The snow-cost information matrix expansion of the radar measurement domain estimation accuracy is described as:
in the method, in the process of the invention,
simplifying the above formula into a quadratic form:
s2-3, obtaining a measurement noise covariance matrix of the distance and the speed in a measurement domain by using a second-order accompanying matrix inversion method:
wherein J is 1 J 4 -J 2 J 2 The expression of (2) is as follows:
where SNR (x k ,x T,k ,x R,k ) Item, J 1 (x k ,x T,k ,x R,k ) Item, J 2 (x k ,x T,k ,x R,k ) The influence of the geometric position on the noise covariance of the range and the speed measurement of the bistatic radar is embodied in the term, J 1 J 4 -J 2 J 2 The term does not contain the influence of the geometric position;
s3, in the double-base radar system, the radar angle measurement noise variance 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, and the angle measurement noise variance can be expressed as:
in the method, in the process of the invention,measuring standard deviation for a reference angle;
s4, combining the steps S1-S3, wherein the time delay tau (d) of the target echo received by the bistatic radar signal domain k ) Finally Doppler shift and measurement noise covariance matrix of distance and speed in measurement domain to finally obtain bistatic radar measurement noise covariance R k (x k ,x T,k ,x R,k ) Is described by the general formula:
s5, receiving signals through the double-base radar, and tracking the signals according to the double-base radar measurement noise covariance obtained in the step S4.
2. A method for measuring a noise covariance model by a geometric position-dependent bistatic radar according to claim 1, wherein the final doppler shift derivation method in step S1-4 is as follows:
the measurement conversion relation from the signal domain to the measurement domain is d k =τc and v k ＝ξc/f c Since ζ (v) is required in calculating the measurement domain estimation accuracy k ) For d k Deriving, so that the distance measurement component is separated in the Doppler shift, for ζ (v k ) Decoupling element conversion is carried out on distance measurement to obtain the R-containing element R,k The form of the variables, the derivation process is as follows:
in bistatic radar measurement, R can be determined by cosine law R,k Conversion to d k And gamma k The conversion formula is as follows:
use d k Variable versus Doppler shift R R,k The variables are replaced and the final doppler shift can be described as:
3. the method of claim 1, wherein in the step S2-2, the matrix of the fischer-tropsch information of the radar measurement domain estimation accuracy is reduced to a quadratic form, P k (x k ,x T,k ,x R,k ) A time-varying correction coefficient matrix:
correction coefficient matrix P k Not only the conversion relation from the signal domain to the measurement domain is included, but also the target-radar is includedGeometric position relation, which changes along with the geometric position relation of the target-radar at each discrete moment k, double base station correction coefficient P k The elements of each part of the matrix are as follows:
wherein, the expression of b is:
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