CN116224320B - Radar target tracking method for processing Doppler measurement under polar coordinate system - Google Patents
Radar target tracking method for processing Doppler measurement under polar coordinate system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The invention discloses a method for realizing target tracking by Doppler measurement under a polar coordinate system, and relates to the field of Doppler radar target tracking. The motion equation in the Cartesian coordinate system is converted into a polar coordinate system, doppler measurement is introduced, and the Doppler measurement is combined with the radial distance and azimuth angle equivalent value to form a state vector, so that the state and observation are in a linear relation, and the posterior estimation of the target state at each moment is obtained through the least square error linear fusion in the fusion stage, so that the influence of nonlinear filtering on estimation precision is avoided, and the target tracking performance is effectively improved.
Description
Technical Field
The invention relates to the field of Doppler radar target tracking, in particular to a radar target tracking method for processing Doppler measurement under a polar coordinate system.
Background
Doppler radar is a common method for detecting the movement of a target, and can detect and track a moving target by utilizing Doppler effect. Because of the working system and the special system environment, the information such as the distance from the target to the observation point, the azimuth angle, the Doppler measurement (radial velocity) and the like can be obtained. At present, doppler radar is widely applied in the fields of airborne fire control, air defense warning, command systems and the like.
In actual target tracking applications, the target motion equation is typically modeled in a Cartesian coordinate system, while radar measurements are typically obtained in polar coordinates. Thus, solving the target state and measurement nonlinearity is a major problem for target tracking. The problem becomes more complex when this measurement information is added to the target tracking due to the strong nonlinearity of the doppler measurement, which can undoubtedly increase the complexity of the tracking system and lead to reduced algorithm estimation performance in environments containing clutter. Currently, most tracking systems only consider radar position measurements (range and angle) and do not take full advantage of doppler measurements, which in fact have the potential to improve tracking performance. Doppler measurements are typically the only measurement that contains target velocity information, from an information perspective, more observed information contributes to improved accuracy, and studies have shown that making full use of Doppler measurements can effectively improve the tracking accuracy of a target.
To solve the radar target tracking problem with doppler measurement, the following nonlinear filtering is generally adopted:
(1) Sequential Extended Kalman Filtering (SEKF) is performed by performing linear de-skewing measurement conversion filtering on the position measurement, and then directly processing the doppler measurement by using the extended kalman filtering. The method has the defects that higher-order terms above the second order are abandoned in the extended Kalman filtering linearization process, and when strong nonlinearity such as Doppler measurement is encountered, errors caused by the method are large, and even the situation of filtering divergence can occur.
(2) Sequential Unscented Kalman Filtering (SUKF), which processes position measurements and Doppler measurements sequentially based on unscented Kalman filtering. The method has the defects that the selection problem of unscented Kalman filtering parameters is not completely solved, and the filtering effect is influenced by the initial filtering value as well as the extended Kalman filtering.
(3) Based on Static Fusion (SFPRE) of predicted value measurement transitions, the method constructs Doppler pseudo-measurements with the product of distance measurements and Doppler measurements, which are processed using unbiased measurement transitions and unbiased measurement transitions, respectively, in order to mitigate strong nonlinear relationships between Doppler measurements and target states. The disadvantage is that the constructed spurious measurements are not true doppler measurements and deviations occur during the measurement transitions, resulting in degradation of the kalman filter performance.
In the filtering, for a nonlinear observation model, some methods such as taylor expansion and sigma point de-linearization are adopted, so that partial information is lost. In addition, the computational complexity is also higher than that of the standard Kalman filter, since additional methods are employed to approximate the nonlinear relationship to the linear relationship. Although the conversion measurement Kalman filtering can use standard Kalman processing after conversion, the conversion state always contains noise in the conversion process, and the accuracy of target positioning is affected.
Therefore, how to eliminate the influence of the strong nonlinearity of the doppler measurement on the tracking accuracy is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the present invention provides a method for implementing target tracking by using doppler measurement in a polar coordinate system, which solves the technical problems existing in the prior art.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for implementing target tracking by doppler measurement in a polar coordinate system, comprising the steps of:
step 1, determining a state equation of a uniform linear motion model and a uniform acceleration linear motion model which contain radial velocity under polar coordinates and have a linear relation with Doppler radar measurement;
step 2, converting process noise under a Cartesian coordinate system of the uniform linear motion model and the uniform acceleration linear motion model into polar coordinates, and calculating the mean value and covariance of the process noise by using a Unscented transformation;
step 3, based on priori information under Cartesian coordinates, carrying out state initialization on state equations of the obtained uniform linear motion model and the uniform acceleration linear motion model, and initializing target states and covariance of a target in polar coordinates by using a Monte Carlo method;
step 4, at the current moment, selecting a motion model according to prior information of the acceleration of the moving object, and calculating a state transition matrix of a state equation under polar coordinates, a process noise driving matrix and statistical characteristics of process noise;
step 5, predicting the target state and covariance in one step under the polar coordinates;
step 6, combining Doppler radar measurement values, and finishing updating of the target tracking state and covariance at the current moment through least square linear fusion;
and 7, circularly executing the steps 4-6 until the target tracking is finished.
Optionally, the specific process of determining the state equation of the uniform linear motion model under the polar coordinate is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, and expressing the state equation of a uniform linear motion model containing radial velocity in the polar coordinate system as:
η RV-CV (k+1)＝Φ RV-CV (k)η RV-CV (k)+Γ RV-CV (k)ω RV-CV (k)；
in the formula ,representing the state of the target at the moment k, wherein θ (k) and r (k) are respectively azimuth angle measurement reality value and distance measurement reality value, and +.>Angular velocity and radial velocity, respectively;represents r (k), ->Covariance between>Var[r(k)]Respectively represent->Variance of r (k), phi RV-CV (k) Is a state transition matrix Γ RV-CV (k) To drive the matrix for process noise ω RV-CV (k) Is process noise.
Optionally, the specific process of determining the state equation of the uniformly accelerated linear motion model under the polar coordinate is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, wherein the state equation of a uniform acceleration linear motion model containing radial velocity in the polar coordinate system is expressed as:
η RV-CA (k+1)＝Φ RV-CA (k)η RV-CA (k)+Γ RV-CA (k)ω RV-CA (k)；
in the formula ,the state of the target at the moment k is represented, T is the Doppler radar sampling time interval, theta (k) and r (k) are respectively azimuth angle measurement reality values and distance measurement reality values,angular velocity and radial velocity, respectively, +.>Angular acceleration and radial acceleration, respectively;represents r (k), ->Covariance between>Represents->Variance of phi RV-CA (k) Is a state transition matrix Γ RV-CA (k) To drive the matrix for process noise ω RV-CA (k) Is process noise.
Optionally, the doppler radar position is located at the origin of coordinates of the polar coordinate system, and the doppler radar measurement equation is specifically expressed as:
Z m (k)＝f(X(k))+V m (k)；
θ(k)＝arctan(y(k)/x(k))；
in the formula ,θm (k)、r m(k) and respectively measuring azimuth angle, distance and Doppler; θ (k), r (k) and +.>Respectively measuring the real value of azimuth angle, the real value of distance and the real value of Doppler;Andrespectively azimuth angle measurement noise, distance measurement noise and Doppler measurement noise, which are zero-mean Gaussian white noise, and the variance is +.> and(σ θ 、σ r andCorresponding standard deviation thereof), and ∈> andIrrelevant, I/O> andIrrelevant, I/O> andHas a correlation coefficient of ρ, i.e., there is +.>
Optionally, step 2 specifically includes:
knowing the mean and variance of the three-dimensional random vector, sampling by sigma points, substituting into a nonlinear function f (&) and obtaining the process noise under polar coordinates by weighting and summing andIs a statistical property of (a);
the specific steps of the mean value and covariance process of the uniform linear motion model and the uniform acceleration linear motion model are as follows:
(1) According to a sigma point sampling rule, generating 2n+1 3-dimensional sample points by means of the mean and variance of the three-dimensional random vector;
(2) Calculating sample points generated by nonlinear function transformation in the step (1);
(3) Determining the weight of the mean value and covariance of each three-dimensional sample point;
(4) Based on the weights obtained in (3), a mean and variance matrix of the mapping is determined.
Optionally, the nonlinear function f (·) in the uniform linear motion model and the uniform acceleration linear motion model is:
wherein , andTangential process noise and radial process noise of the uniform linear motion model;Andtangential process noise and radial process noise of the uniform acceleration linear motion model; andZero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; andZero-mean Gaussian white noise in X and Y directions of the uniform acceleration linear motion model; θ (k) is a random variable subject to normal distribution.
Optionally, the specific process of initializing the state is as follows:
(1) When the model moves linearly at uniform speed, the flute is used for the productionThe mean S (0) and covariance S (0) of the initial target state under the Kalman coordinate system randomly generate N four-dimensional sample pointsj=1, 2,3 … N; when the model is uniform acceleration linear motion, N six-dimensional sample points are randomly generated according to the mean value B (0) and the covariance B (0) of the initial target state under the Cartesian coordinate system>x j and yj Is the position of the random sample point,/-> andIs the velocity of the random sample points, +.> andAcceleration is the random sample point;
(2) Calculating the value η of each state point in the polar coordinates j ；
(3) Calculating the mean and covariance of the state points in the polar coordinates;
optionally, the formula for calculating the value of each state point in the polar coordinates under the uniform linear motion model is:
θ j ＝arctan(y j /x j )；
the formula for calculating the value of each state point in the polar coordinates under the uniform acceleration linear motion model is as follows:
θ j ＝arctan(y j /x j )；
optionally, the specific formula for one-step prediction of the target state and covariance is:
η(k+1,k)＝Φ(k)η(k,k)+Γ(k)ω(k)；
P(k+1,k)＝Φ(k)P(k,k)Φ(k) T +Γ(k)Q(k)Γ(K) T ；
where η (k+1, k) and P (k+1, k) are the target state and covariance, respectively, of the prediction at time k, and Q (k) is the process noise covariance matrix.
Optionally, the specific steps of completing the update of the target tracking state and the covariance at the current moment through the least square error linear fusion are as follows:
η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) -1 η(k+1,k)+P z (k+1,k+1) -1 η z (k+1,k)]；
P(k+1,k+1)＝[P(k+1,k) -1 +P z (k+1,k+1) -1 ] -1 ；
in the calculation, the observation vector and the covariance thereof are expanded and the defect elements are set to zero so as to be suitable for matrix operation;
wherein when the model moves at a uniform speed in a straight line,
when the model is a uniformly accelerated linear motion,
compared with the prior art, the method for realizing target tracking by Doppler measurement in the polar coordinate system is different from all nonlinear filtering algorithms with Doppler measurement in the prior art, adopts a completely different technical thought from the prior art, directly builds a target state equation in the polar coordinate, converts the problem of strong nonlinearity of Doppler measurement into a linear filtering problem, and can finish tracking by combining a standard Kalman filter, thereby overcoming the strong nonlinearity between Doppler measurement and target state, tracking the target with smaller calculated amount and well improving the target tracking precision.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow diagram of the method of the present invention;
FIG. 2a is a graph of error curves of different algorithms of tracking positions under a uniform linear motion model;
FIG. 2b is a graph showing error curves of different algorithms of tracking speed under a uniform linear motion model;
FIG. 3a is a graph showing error curves of different algorithms of tracking positions under a uniform acceleration linear motion model;
FIG. 3b is a graph showing the error of different algorithms of tracking speed under the uniform acceleration linear motion model.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention discloses a method for realizing target tracking by Doppler measurement under a polar coordinate system, which is shown in figure 1 and comprises the following steps:
step 1, determining a state equation of a uniform linear motion model and a uniform acceleration linear motion model which contain radial velocity under polar coordinates and have a linear relation with Doppler radar measurement;
step 2, converting process noise under a Cartesian coordinate system of the uniform linear motion model and the uniform acceleration linear motion model into polar coordinates, and calculating the mean value and covariance of the process noise by using a Unscented transformation;
step 3, based on priori information under Cartesian coordinates, carrying out state initialization on state equations of the obtained uniform linear motion model and the uniform acceleration linear motion model, and initializing target states and covariance of a target in polar coordinates by using a Monte Carlo method;
step 4, at the current moment, selecting a motion model according to prior information of the acceleration of the moving object, and calculating a state transition matrix of a state equation under polar coordinates, a process noise driving matrix and statistical characteristics of process noise;
step 5, predicting the target state and covariance in one step under the polar coordinates;
step 6, combining Doppler radar measurement values, and finishing updating of the target tracking state and covariance at the current moment through least square linear fusion;
and 7, circularly executing the steps 4-6 until the target tracking is finished.
In a specific embodiment, the specific process of determining the state equation of the uniform linear motion model under the polar coordinate is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, and expressing the state equation of a uniform linear motion model containing radial velocity in the polar coordinate system as:
η RV-CV (k+1)＝Φ RV-CV (k)η RV-CV (k)+Γ RV-CV (k)ω RV-CV (k)；
in the formula ,representing the state of the target at the moment k, wherein θ (k) and r (k) are respectively azimuth angle measurement reality value and distance measurement reality value, and +.>Angular velocity and radial velocity, respectively;represents r (k), ->Covariance between>Var[r(k)]Respectively represent->Variance of r (k), phi RV-CV (k) Is a state transition matrix Γ RV-CV (k) To drive the matrix for process noise ω RV-CV (k) Is process noise.
In a specific embodiment, the specific process of determining the state equation of the uniformly accelerated linear motion model in polar coordinates is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, wherein the state equation of a uniform acceleration linear motion model containing radial velocity in the polar coordinate system is expressed as:
η RV-CA (k+1)＝Φ RV-CA (k)η RV-CA (k)+Γ RV-CA (k)ω RV-CA (k)；
in the formula ,the state of the target at the moment k is represented, T is the Doppler radar sampling time interval, theta (k) and r (k) are respectively azimuth angle measurement reality values and distance measurement reality values,angular velocity and radial velocity, respectively, +.>Angular acceleration and radial acceleration, respectively;represents r (k), ->Covariance between>Represents->Variance of phi RV-CA (k) Is a state transition matrix Γ RV-CA (k) To drive the matrix for process noise ω RV-CA (k) Is process noise.
In a specific embodiment, the doppler radar position is located at the origin of coordinates of the polar coordinate system, and the doppler radar measurement equation is specifically expressed as:
Z m (k)＝f(X(k))+V m (k)；
θ(k)＝arctan(y(k)/x(k))；
in the formula ,θm (k)、r m(k) and respectively measuring azimuth angle, distance and Doppler; θ (k), r (k) and +.>Respectively, azimuth angle measurementReal value, distance measurement real value and Doppler measurement real value;Andrespectively azimuth angle measurement noise, distance measurement noise and Doppler measurement noise, which are zero-mean Gaussian white noise, and the variance is +.> and(σ θ 、σ r andCorresponding standard deviation thereof), and ∈> andIrrelevant, I/O> andIrrelevant, I/O> andHas a correlation coefficient of ρ, i.e., there is +.>
In a specific embodiment, step 2 specifically includes:
known three-dimensional random vector andAfter sigma point sampling, substituting a nonlinear function f (·) and then obtaining the process noise +_under polar coordinates by weighting and summing> andIs a statistical property of (a);
taking a uniform linear motion model as an example, the following is obtained andThe specific steps of the process are as follows:
(1) According to sigma point sampling rule, by andGenerating 2n+1 3-dimensional sample points;
wherein n=3;representation matrixI-th column of the square root of the lower triangular decomposition; λ=α 2 (n+k) -n; alpha is a positive number, 10 is taken -4 ≤α≤1；k＝3-n；
(2) Calculating sample points generated by nonlinear function transformation;
Y (i) ＝f[χ (i) ]，i＝0～2n
(3) Determining the weight of the mean value and covariance of each three-dimensional sample point;
wherein, the superscript m is the mean value and c is the covariance; the index is the sampling point; for normal distribution, β=2 is an optimal value;
(4) Determining a mean and variance matrix of the mapping based on the weights obtained in (3);
taking a uniform linear motion model as an example, a constant linear motion model is given andIn the case of a uniform acceleration linear motion model> andThe solving process of (2) is the same as the solving process described above.
In one embodiment, the nonlinear function f (·) in the uniform linear motion model and the uniform acceleration linear motion model is:
wherein , andTangential process noise and radial process noise of the uniform linear motion model;Andtangential process noise and radial process noise of the uniform acceleration linear motion model; andZero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; andZero-mean Gaussian white noise in X and Y directions of the uniform acceleration linear motion model; θ (k) is a random variable subject to normal distribution.
In a specific embodiment, the specific process of performing state initialization is:
(1) When the model moves linearly at a uniform speed, N four-dimensional sample points are randomly generated according to the mean value S (0) and the covariance S (0) of the initial target state in the Cartesian coordinate systemj=1, 2,3 … N; when the model is uniform acceleration linear motion, N six-dimensional sample points are randomly generated according to the mean value B (0) and the covariance B (0) of the initial target state under the Cartesian coordinate system>x j and yj Is the position of the random sample point,/-> andIs the velocity of the random sample points, +.> andAcceleration is the random sample point;
(2) Calculating the value η of each state point in the polar coordinates j ；
(3) Calculating the mean and covariance of the state points in the polar coordinates;
in a specific embodiment, the formula for calculating the value of each state point in the polar coordinates under the uniform linear motion model is:
θ j ＝arctan(y j /x j )；
the formula for calculating the value of each state point in the polar coordinates under the uniform acceleration linear motion model is as follows:
θ j ＝arctan(y j /x j )；
in a specific embodiment, the specific formula for one-step prediction of the target state and covariance is:
η(k+1,k)＝Φ(k)η(k,k)+Γ(k)ω(k)；
P(k+1,k)＝Φ(k)P(k,k)Φ(k) T +Γ(k)Q(k)Γ(K) T ；
where η (k+1, k) and P (k+1, k) are the target state and covariance, respectively, of the prediction at time k, and Q (k) is the process noise covariance matrix.
In a specific embodiment, the specific steps for completing the update of the target tracking state and covariance at the current moment through the least square error linear fusion are as follows:
η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) -1 η(k+1,k)+P z (k+1,k+1) -1 η z (k+1,k)]；
P(k+1,k+1)＝[P(k+1,k) -1 +P z (k+1,k+1) -1 ] -1 ；
in the calculation, the observation vector and the covariance thereof are expanded and the defect elements are set to zero so as to be suitable for matrix operation; wherein when the model moves at a uniform speed in a straight line,
when the model is a uniformly accelerated linear motion,
in a specific embodiment, by using the radar target tracking method of the invention, the tracked target moves in a uniform linear motion in a two-dimensional space, the initial position of the target is (10 km ), the initial speed is (8 m/s,10 m/s), and the Doppler radar at the origin of coordinates provides the range, azimuth angle and Doppler measurement of the target in a sampling period of 1 s. The method proposed by the patent is compared with SEKF, SUKF and SFPRE algorithms with Doppler measurement. The standard deviation of the measured noise is sigma r ＝100m，σ θ ＝1°，Correlation coefficient ρ=0.5, and the results of the root mean square error simulation for different algorithm positions and velocities are shown in fig. 2a, 2 b.
In a specific embodiment, the radar target tracking method of the invention is used for uniformly accelerating linear motion of a tracking target in a two-dimensional space, the initial position of the target is (10 km ), the initial speed is (8 m/s,10 m/s), and the initial acceleration is (2 m/s) 2 ，2m/s 2 ) The doppler radar at the origin of coordinates provides range, azimuth and doppler measurements of the target with a sampling period of 1 s. The method proposed by the patent is compared with SEKF, SUKF and SFPRE algorithms with Doppler measurement. The standard deviation of the measured noise is sigma r ＝100m，σ θ ＝1°，Correlation coefficient ρ=0.5, root mean square error imitation for different algorithm positions and speedsThe true results are shown in fig. 3a and 3 b.
As can be seen from fig. 2a, 2b, 3a and 3b, the position and speed estimation accuracy of each method are improved continuously with time, and the method provided by the invention can reduce the influence of strong nonlinearity of doppler measurement under different motion models, and improve tracking accuracy and convergence speed. For the method provided by the invention, the state vector and the measurement vector can be processed by using a linear Kalman filter, so that the convergence of dynamic estimation is ensured.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A method for implementing target tracking by doppler measurement in a polar coordinate system, comprising the steps of:
step 1, determining a state equation of a uniform linear motion model and a uniform acceleration linear motion model which contain radial velocity under polar coordinates and have a linear relation with Doppler radar measurement;
step 2, converting process noise under a Cartesian coordinate system of the uniform linear motion model and the uniform acceleration linear motion model into polar coordinates, and calculating the mean value and covariance of the process noise by using a Unscented transformation;
step 3, based on priori information under Cartesian coordinates, carrying out state initialization on state equations of the obtained uniform linear motion model and the uniform acceleration linear motion model, and initializing target states and covariance of a target in polar coordinates by using a Monte Carlo method;
step 4, at the current moment, selecting a motion model according to prior information of the acceleration of the moving object, and calculating a state transition matrix of a state equation under polar coordinates, a process noise driving matrix and statistical characteristics of process noise;
step 5, predicting the target state and covariance in one step under the polar coordinates;
step 6, combining Doppler radar measurement values, and finishing updating of the target tracking state and covariance at the current moment through least square linear fusion;
and 7, circularly executing the steps 4-6 until the target tracking is finished.
2. The method for realizing target tracking by utilizing Doppler measurement in a polar coordinate system according to claim 1, wherein the specific process of determining the state equation of the uniform linear motion model in the polar coordinate is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, and expressing the state equation of a uniform linear motion model containing radial velocity in the polar coordinate system as:
η RV-CV (k+1)＝Φ RV-CV (k)η RV-CV (k)+Γ RV-CV (k)ω RV-CV (k)；
in the formula ,representing the state of the target at the moment k, wherein θ (k) and r (k) are respectively azimuth angle measurement reality value and distance measurement reality value, and +.>Angular velocity and radial velocity, respectively;Represents r (k), ->Covariance between>Var[r(k)]Respectively represent->Variance of r (k), phi RV-CV (k) Is a state transition matrix Γ RV-CV (k) To drive the matrix for process noise ω RV-CV (k) Is process noise.
3. The method for realizing target tracking by utilizing doppler measurement in a polar coordinate system according to claim 1, wherein the specific process of determining the state equation of the uniform acceleration linear motion model in polar coordinates is as follows: converting a state equation in a Cartesian coordinate system into a polar coordinate system, wherein the state equation of a uniform acceleration linear motion model containing radial velocity in the polar coordinate system is expressed as:
η RV-CA (k+1)＝Φ RV-CA (k)η RV-CA (k)+Γ RV-CA (k)ω RV-CA (k)；
in the formula ,the state of the target at the moment k is represented, T is the Doppler radar sampling time interval, theta (k) and r (k) are respectively azimuth angle measurement reality values and distance measurement reality values,angular velocity and radial velocity, respectively, +.>Angular acceleration and radial acceleration, respectively;represents r (k), ->Covariance between>Represents->Variance of phi RV-CA (k) Is a state transition matrix Γ RV-CA (k) To drive the matrix for process noise ω RV-CA (k) Is process noise.
4. The method for realizing target tracking by utilizing doppler measurement in a polar coordinate system according to claim 1, wherein the doppler radar position is located at the origin of coordinates in the polar coordinate system, and the equation of the doppler radar measurement is specifically expressed as:
Z m (k)＝f(X(k))+V m (k)；
θ(k)＝arctan(y(k)/x(k))；
in the formula ,θm (k)、r m(k) and respectively measuring azimuth angle, distance and Doppler; θ (k), r (k) andrespectively measuring the real value of azimuth angle, the real value of distance and the real value of Doppler; andRespectively azimuth angle measurement noise, distance measurement noise and Doppler measurement noise, which are zero-mean Gaussian white noise, and the variance is +.> andσ θ 、σ r andFor its corresponding standard deviation, and-> andIrrelevant, I/O> andThe correlation is not carried out and, andHas a correlation coefficient of ρ, i.e., there is +.>
5. The method for achieving target tracking by doppler measurement in a polar coordinate system according to claim 1, wherein the step 2 specifically comprises:
knowing the mean and variance of the three-dimensional random vector, substituting the mean and variance into a nonlinear function f (), and obtaining the process noise under polar coordinates by weighting and summing andIs a statistical property of (a);
the specific steps of the mean value and covariance process of the uniform linear motion model and the uniform acceleration linear motion model are as follows:
(1) According to a sigma point sampling rule, generating 2n+1 3-dimensional sample points by means of the mean and variance of the three-dimensional random vector;
(2) Calculating sample points generated by nonlinear function transformation in the step (1);
(3) Determining the weight of the mean value and covariance of each three-dimensional sample point;
(4) Based on the weights obtained in (3), a mean and variance matrix of the mapping is determined.
6. The method for achieving target tracking by doppler measurement in a polar coordinate system according to claim 5, wherein the nonlinear function f () in the uniform linear motion model and the uniform acceleration linear motion model is:
wherein , andTangential process noise and radial process noise of the uniform linear motion model; andTangential process noise and radial process noise of the uniform acceleration linear motion model; andZero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; andZero-mean Gaussian white noise in X and Y directions of the uniform acceleration linear motion model; θ (k) is a random variable subject to normal distribution.
7. The method for realizing target tracking by utilizing doppler measurement in a polar coordinate system according to claim 1, wherein the specific process of performing state initialization is:
(1) When the model moves linearly at a uniform speed, N four-dimensional sample points are randomly generated according to the mean value S (0) and the covariance S (0) of the initial target state in the Cartesian coordinate systemWhen the model is uniform acceleration linear motion, N six-dimensional sample points are randomly generated according to the mean value B (0) and the covariance B (0) of the initial target state under the Cartesian coordinate system>x j and yj Is the position of the random sample point,/-> andIs the velocity of the random sample points, +.> andAcceleration is the random sample point;
(2) Calculating the value η of each state point in the polar coordinates j ；
(3) Calculating the mean and covariance of the state points in the polar coordinates;
8. the method for realizing target tracking by using doppler measurement in a polar coordinate system according to claim 1, wherein the formula for calculating the value of each state point in the polar coordinate in the uniform linear motion model is:
θ j ＝arctan(y j /x j )；
the formula for calculating the value of each state point in the polar coordinates under the uniform acceleration linear motion model is as follows:
θ j ＝arctan(y j /x j )；
9. the method for achieving target tracking using doppler measurement in a polar coordinate system according to claim 1, wherein the specific formula for one-step prediction of target state and covariance is:
η(k+1,k)＝Φ(k)η(k,k)+Γ(k)ω(k)；
P(k+1,k)＝Φ(k)P(k,k)Φ(k) T +Γ(k)Q(k)Γ(K) T ；
where η (k+1, k) and P (k+1, k) are the target state and covariance, respectively, of the prediction at time k, and Q (k) is the process noise covariance matrix.
10. The method for realizing target tracking by utilizing doppler measurement in a polar coordinate system according to claim 1, wherein the specific steps of completing the target tracking state and covariance update at the current moment by means of least square error linear fusion are as follows:
η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) -1 η(k+1,k)+P z (k+1,k+1) -1 η z (k+1,k)]；
P(k+1,k+1)＝[P(k+1,k) -1 +P z (k+1,k+1) -1 ] -1 ；
in the calculation, the observation vector and the covariance thereof are expanded and the defect elements are set to zero so as to be suitable for matrix operation;
wherein when the model moves at a uniform speed in a straight line,
when the model is a uniformly accelerated linear motion,
in the formula ,θm (k)、r m(k) and respectively measuring azimuth angle, distance and Doppler;Andrespectively azimuth angle measurement noise, distance measurement noise and Doppler measurement noise, which are zero-mean Gaussian white noise, and the variance is +.> andσ θ 、σ r andFor its corresponding standard deviation, and-> andIrrelevant, I/O> andIrrelevant, I/O> andHas a correlation coefficient of ρ, i.e., there is +.>
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