CN109581355B - Centralized MIMO radar self-adaptive resource management method for target tracking - Google Patents
Centralized MIMO radar self-adaptive resource management method for target tracking Download PDFInfo
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Abstract
The invention belongs to the field of radar target tracking, and particularly relates to a centralized MIMO radar self-adaptive resource management method for target tracking. According to the method, target detection and target tracking are comprehensively considered for the first time, the target detection and the target tracking are linked through a measurement error covariance matrix, and the resource consumption is minimized through adaptive subarray division and a sampling period under the condition that normal target detection is guaranteed; and the tracking precision is improved through the self-adaptive transmitting waveform parameters. When a correlation algorithm is solved, firstly, parameter combinations of feasible subarray division and sampling periods are selected through prediction covariance and a detection probability threshold, and system resources are reasonably distributed; on the basis, the target tracking precision is further improved, the transmitted waveform parameters are self-adapted, a feasible sub-array division, sampling period and transmitted waveform parameter combination set is formed, the optimal sub-array division, sampling period and transmitted waveform parameter combination is selected according to the comprehensive cost minimization principle, and the target tracking precision is improved while the radar system resources are saved.
Description
Technical Field
The invention belongs to the field of radar target tracking, and particularly relates to a centralized MIMO radar self-adaptive resource management method for target tracking.
Background
The MIMO (Multiple-Input Multiple-Output) radar is a new radar system appearing in the beginning of the 21 st century, and the MIMO radar is a hot spot of research and development at present. The MIMO radar can be classified into a distributed MIMO radar and a centralized MIMO radar according to the size of the space between the transmitting and receiving antennas.
The receiving and transmitting antenna units of the centralized MIMO radar are close to each other, the visual angles of the antenna units to the target are approximately the same, and each array element can transmit different signal waveforms, so that waveform diversity is obtained, narrow beams different from the traditional phased array are formed, and the dividing number of the sub-arrays can be adjusted; therefore, the degree of freedom is greater when performing target tracking. MIMO radar has more flexibility in target tracking due to variable subarray division. In the self-adaptive target tracking process of the MIMO radar, besides the traditional controllable parameters, the influence caused by the number of sub-array partitions must be considered, and the effective allocation of system resources in the tracking process can be realized.
The self-adaptive resource management aims to effectively control task working parameters, mainly relates to sampling periods, emission waveform parameters and the like, and can reasonably distribute limited resources of the radar through the self-adaptive working parameters so as to better track targets. The early stage of adaptive resource management is from phased array radar, and for an adaptive sampling period, the traditional method realizes the control of the sampling period by making the covariance of a prediction error smaller than a threshold; for the adaptive transmit waveform parameters, considering the influence of the transmit waveform parameters on the measurement covariance matrix, the traditional method selects the transmit parameters by using the minimum mean square error principle. The method is only directed at the phased array radar, and the target detection and the target tracking are two relatively independent parts due to the self principle and are not directly connected; in the prior art, according to different emphasis points, the two are generally considered respectively and considered separately for target detection or target tracking.
Disclosure of Invention
Aiming at the problems or the defects, the invention provides a centralized MIMO radar self-adaptive resource management method for target tracking in order to solve the efficient allocation of the centralized MIMO radar resource management in the target tracking process.
The specific technical scheme is as follows:
step 1: if the total array element number of the centralized MIMO radar is M, the number of possible sub-arrays is s j ＝2 j-1 ，j＝1,2,…,(log 2 M + 1); let the current time be t k-1 Next time t k Sampling period T of k ＝t k -t k-1 ，T k From a preset set of sampling periods
Selecting. The transmit waveform parameters λ and b are adaptively variable, where λ represents the duration of the waveform and b represents the chirp rate.
For parameter combinations(s) of the number of possible sub-array divisions and the possible sampling periods j ,T l ) Calculating the following correlation quantities;
step 1.1: calculating a predicted radial distance error standard deviation of the tracked target
Standard deviation of predicted azimuth error
The covariance matrix of the predicted position error in the rectangular coordinate system is recorded as
Then there is
Wherein H is a measurement matrix,
and the covariance matrix of the prediction error under the rectangular coordinate system. Prediction position error covariance matrix under polar coordinate system
Is composed of
Wherein
For the Jacobian transformation matrix from rectangular to polar coordinates, the following equation is given
subscripts (k, k), k =1,2 denote diagonal elements.
Step 1.2: calculating detection probability
In which the echo signal-to-noise ratio is predicted
Comprises the following steps:
wherein, B w For the two-way beamwidth of the azimuth at the beam pointing location,
predicted signal-to-noise ratio for beam pointing direction:
wherein M is the number of elements of the radar array, e is the energy of the transmitted waveform, eta A For the duty cycle of the effective area of the antenna,
is an estimate of the target mean RCS, λ 1 Is a function of the wavelength of the light,
is the radial distance of the target from the radar, N 0 Is the noise power spectral density, N 0 ＝kT 0 F 0 K is Boltzmann constant, T 0 For radar receiver temperature, F 0 For the noise figure of the radar receiver, s j The number of MIMO subarrays.
Step 2: selecting parameter combination(s) formed by feasible sub-array division number and sampling period j ,T l ) The method comprises the following steps:
step 2.1: calculating the distance prediction error threshold corresponding to the target
Sum azimuth prediction error threshold
Wherein L is g For range of action during tracking, B(s) j )＝1.76*s j M is the one-way beamwidth, u, at the predicted location of the beam pointing target 0.5α Is a bilateral quantile of a standard normal distribution, P CL Is the confidence level.
Step 2.2: the feasible parameter set is formed by counting the combination of the sub-array division number and the sampling period which meet the following conditions
And q is the number of feasible parameter combinations.
And step 3: based on the parameter combination of the feasible sub-array division number and the sampling period selected in the steps 1 and 2, the transmitted waveform parameters are further considered to form the parameter combination of the sub-array division number, the sampling period and the transmitted waveform parameters
Calculating each parameter combination(s) i ,T i ,λ m ,b n ) Corresponding measurement error covariance matrix R pre (t k ,s i ,T i ,λ m ,b n )；
The measurement covariance matrix is expressed as:
wherein N is pre (t k ,s i ,T i ,λ m ,b n ) Is the measured covariance, σ, of radial distance and radial velocity b，pre (t k ,s i ,T i ) The standard deviation of the azimuth angle measurement error is shown;
standard deviation sigma of azimuth angle measurement error b，pre (t k ,s i ,T i ) The calculation is as follows:
wherein, B w For the two-way beamwidth of the azimuth of the beam pointing position, constant c 1 Is typically 1.57;
and 4, step 4: calculating each parameter combination(s) i ,T i ,λ m ,b n ) Estimate error covariance of target position prediction
The covariance matrix of the estimation error of the target position prediction in the rectangular coordinate system is marked as P pos,pre (t k ,s i ,T i ,λ m ,b n ) Then there is
P pos,pre (t k ,s i ,T i ,λ m ,b n )＝H·P pre (t k ,s i ,T i ,λ m ,b n )·H T (13)
Wherein H is a measureMatrix, P pre (t k ,s i ,T i ,λ m ,b n ) Estimation error covariance matrix, P, for prediction in rectangular coordinate system pre (t k ,s i ,T i ,λ m ,b n ) Using each parameter combination(s) i ,T i ,λ m ,b n ) And (3) filtering and estimating the measurement error covariance matrix.
Wherein P is pos,pre (t k ,s i ,T i ,λ m ,b n ) 1，1 ，P pos,pre (t k ,s i ,T i ,λ m ,b n ) 2,2 Respectively expressed in the parameter combination(s) i ,T i ,λ m ,b n ) The estimation error variance of the lower x-direction prediction and the estimation error variance of the y-direction prediction, subscripts (k, k), k =1,2, denote diagonal elements.
And 5: calculating each parameter combination(s) i ,T i ,λ m ,b n ) The cost function of (2);
wherein, c 1 And c 2 C is a weighting coefficient of time resource tracking precision, and is more than or equal to 0 1 ≤1,0≤c 2 C is less than or equal to 1 and 1 +c 2 =1; the corresponding optimal parameter combination(s) opt ,T opt ,λ opt ,b opt ) Can be expressed as:
(s opt ,T opt ,λ opt ,b opt )＝minC pre (t k ,s i ,T i ,λ m ,b n ) (15)
step 6: using the combination(s) of parameters selected at the current time opt ,T opt ,λ opt ,b opt ) As t k Tracking task parameters at all times, detecting a target and obtaining current measurement;
and 7: filtering by using the measurement obtained in the step 6, and then returning to the step 1 to repeat the steps 1-6 until the tracking time is reached.
The basic schematic diagram of the centralized MIMO radar is shown in fig. 8. The radar array elements emit mutually orthogonal waveforms, and are mutually overlapped in space to form a low-gain wide beam, so that energy coverage is simultaneously realized for a large airspace range, and targets in the large airspace range are simultaneously tracked and searched. When the target is tracked, the target can be irradiated by adopting a high-gain narrow beam at each sampling time, or the target can be selectively irradiated by using a low-gain wide beam, and the variable parameters are as follows: number of subarrays s j Target sampling period T l And a transmit waveform parameter (λ) m ,b n )。
Predicting the echo signal-to-noise ratio: it is assumed that MIMO radar transmit and receive antenna gains may be denoted G, respectively t And G r The target radar cross section is expressed as sigma, and the signal wavelength is lambda 1 Target to radar distance of
The receive power of the receive array can be expressed as:
wherein the transmission gain G t Is in direct proportion to the number of array elements in the subarray and satisfies G t ＝πη A L,η A For antenna aperture efficiency, the receiving gain satisfies G r ＝πη A And M. Assume an effective receive bandwidth of B r Then the predicted echo signal-to-noise ratio of the beam pointing direction can be expressed as:
wherein G is p Representing the processing gain due to matched filtering and equivalent transmit beamforming, satisfies G p ＝τB r And τ is the pulse width of the transmitted signal. By substituting formula (21) for formula (22), further:
wherein e = p t τ；
Considering the influence caused by beam pointing error, the following formula is obtained (see document: zhang Jie. Adaptive target tracking and beam scheduling research [ D ] in phased array and MIMO mode thereof, university of electronic technology, 2017.):
based on the basic working principle of a centralized MIMO radar, the invention comprehensively considers radar system resources and target tracking precision and establishes the following optimization model:
for the amount of radar system resources, we describe using a sampling period; and the target tracking accuracy is described by using the estimation error covariance of the target position prediction. Because the predicted estimation error covariance and the sampling period are two completely different factors in the cost function, and the dimensions are different, the weighted summation cannot be directly performed on the two factors, and for this purpose, the predicted estimation error covariance and the maximum value of the sampling period need to be normalized respectively, so that the cost function expression shown in the above formula can be obtained, wherein the former expression shows that the centralized MIMO radar is divided into s parts j With a sampling period of T j The resource consumption of the time system, the latter expression, working in the centralized MIMO radar, is divided into s j With a sampling period of T j The emission waveform parameter is (lambda) m ,b n ) And tracking precision of the target. Wherein, c 1 And c 2 Respectively is a weighting coefficient of system resources and tracking precision, c is more than or equal to 0 1 ≤1,0≤c 2 C is less than or equal to 1 and 1 +c 2 =1, can be varied by changing c 1 And c 2 The weight value of the target tracking system is used for flexibly balancing the system resource and the target tracking precision.
The constraint (1) is to ensure that the echo signal-to-noise ratio of the target is large enough to be recognized, so as to constrain the detection probability of the target.
The constraint (2) is to ensure that the radial distance prediction standard deviation meets the expected accuracy requirement, and a prediction covariance threshold method is used, and the specific principle is as follows:
assuming that the range of action is L during tracking g The range of the angular one-way beam at the tracking estimation coordinate of the beam pointing target is B(s) j ). The prediction covariance is the centralized numerical reflection of the inaccuracy of the target in the predicted coordinate point, and the prediction standard deviations related to the distance and the direction obtained when the target is in a certain sampling period are respectively
Note that the coordinate system is polar coordinates at this time, and it is assumed that the target real position follows gaussian distribution, and the mean and error covariance thereof are the same as the predicted mean and error covariance. Then the target can be guaranteed to be P ≧ P CL Is illuminated by the transmit beam:
at the same time, wherein
Length between main zones of distance and orientation respectively
Wherein, α =1-P CL . And (3) simplifying the formula to obtain a formula (13) in which the prediction covariance in the polar coordinate direction needs to meet the algorithm steps.
In order to comprehensively consider the reasonable allocation of radar system resources and the target tracking precision, the transmitted waveform parameters are further self-adapted after the feasible sub-array division number and sampling period are determined, and a parameter combination of the sub-array division number, the sampling period and the transmitted waveform parameters is formed
Consider that the transmit waveform parameter only affects the measured covariance Ν of the radial distance and radial velocity pre (t k ,s i ,T i ,λ m ,b n ) Since the measurement of the target angle is not related to the distance and radial velocity measurements, a measurement covariance matrix R can be constructed as shown in the diagonal form of equation (15) pre (t k ,s i ,T i ,λ m ,b n )：
Azimuth measurement variance
Calculated as follows (see literature: balckman S, popoli R.design and analysis of model tracking system [ M ]].MA:Artech House,1999:117-158)：
Wherein, B w For the two-way beamwidth of the azimuth of the beam pointing position, constant c 1 A typical value of (a) is 1.57.
Based on the method, the target detection and the target tracking are comprehensively considered for the first time, the target detection and the target tracking are connected through a measurement error covariance matrix, an adaptive resource management optimal model based on the target tracking is established, the target detection and the target tracking are comprehensively considered by the model, the resource consumption is minimized through adaptive sub-array division and a sampling period under the condition that the normal detection of the target is ensured, and the tracking accuracy is further improved through adaptive transmitting waveform parameters. When a correlation algorithm is solved, the proposed algorithm firstly selects a parameter combination of feasible subarray division number and sampling period through prediction covariance and a detection probability threshold, and adaptively allocates radar system resources; on the basis, the target tracking precision is further improved, the transmitting waveform parameters are selected in a self-adaptive mode, a feasible sub-array division number, sampling period and transmitting waveform parameter combination set is formed, the resource consumption and the target tracking precision of the radar system are comprehensively considered, the optimal sub-array division number, sampling period and transmitting waveform parameter combination are selected according to the comprehensive cost function minimization principle, and the target tracking precision is improved while the resources of the radar system are saved.
In conclusion, the invention comprehensively considers the selection of the sampling period and the transmission waveform parameters, and finally realizes the high-efficiency distribution of the system resources in the tracking process.
Drawings
FIG. 1 is a schematic view of a moving scene of an object in the scene;
FIG. 2 is a comprehensive cost comparison curve in the scene-fixed subarray division and adaptive subarray division tracking process;
FIG. 3 is a comparison curve of the variation of the selected subarray division with the sampling period during the division and tracking processes of a scene-fixed subarray and an adaptive subarray;
FIG. 4 is a comparison curve of the variation of the selected transmit parameters during the scene-fixed subarray division and adaptive subarray division tracking processes;
FIG. 5 is a diagram of a comparison of the RMSE for a fixed transmit parameter and adaptive transmit parameter target for a scene;
FIG. 6 is a comparison curve of the division of the selected subarrays during the tracking of the fixed transmit parameters and adaptive transmit parameters of the second scene with the change of the sampling period;
FIG. 7 is a comparison of the RMSE for a fixed transmit parameter and adaptive transmit parameter target for a scene two;
fig. 8 is a basic schematic diagram of a centralized MIMO radar.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. A single target which does maneuvering motion in a plane is considered to be tracked, and two tracking scenes are set.
Assume that the transmit signal is a chirp signal (LFM) waveform s (t) with a gaussian envelope as follows:
where λ represents the duration of the waveform and b represents the chirp rate, these two parameters being adaptively variable.
The selection range of the emission waveform parameter lambda, b is P = { lambda epsilon [0.0013,0.0404 =],b∈[-500000,500000]-a set of transmitted waveform parameters (λ) of the chirp signal (LFM) (λ is different each time the value of λ is chosen, and the range of b is different, here only the maximum range of b is given) m ,b n ) Is constructed by discretizing the value range of the step length delta lambda and delta b and is expressed as follows:
λ＝λ min +Δλ·m (25)
b＝b min +Δb·n (26)
wherein m and n are the number of lambda and b in the transmit waveform parameter set, respectively.
For LFM, its corresponding Ν pre (t k ,s i ,T i ,λ m ,b n ) The following were used:
wherein f is c Denotes carrier frequency, c denotes speed of light, SNR pre (t k ,s i ,T i ) Signal to noise ratio (SNR) is expressed, and the calculation method is shown in equation (10);
scene one: the motion track of the target is that the starting point of the target is 10000m 2000m]The constant-speed motion state is in the process of time periods of 0-40 s, 80-120 s and 160-200 s, and the uniform acceleration motion state is in the process of time periods of 40-80 s and 120-160 s. Its initial speed is [ -200m/s 100m/s]At 40 to 80s, in the x and y directionsRespectively, acceleration of 10m 2 S and 20m 2 120-160 s, acceleration of 10m 2 S and-30 m 2 /s，(c 1 ＝0.9,c 2 ＝0.1)。
Scene two: the motion track of the target is that the starting point of the target is [300000m 700000m ]]The constant-speed motion state is in the process of time period 0-80 s and 120-200 s, and the uniform acceleration motion state is in the process of time period 80-120 s. Its initial velocity is [20m/s]At 80 to 120s, the acceleration in the x and y directions is 0m 2 S and-1 m 2 And s. Assuming that the target RCS (radar cross section) follows Swerling I type distribution, the average value is 1m 2 ，(c 1 ＝0.9,c 2 ＝0.1)。
The self-adaptive target tracking algorithm provided by the invention is adopted to track the target, and the following statistical results are 100 times of Monte-Carlo:
fig. 1 shows a true motion trajectory and a filtered tracking trajectory of an object of a scene. It can be seen that the algorithm can keep up with the target and has an obvious filtering effect. s adaptive represents the adaptive subarray division case (remaining parameters are adaptively changed), s =1 represents the fixed subarray division case (remaining parameters are adaptively changed), and adaptive represents the adaptive transmit waveform parameter case lamda =0.0404, b =500000 represents the fixed transmit waveform parameter case.
FIG. 2 shows a comprehensive cost comparison curve in the process of dividing and tracking a scene-fixed subarray and an adaptive subarray; as can be seen from fig. 2, the comprehensive cost under the condition of adaptive subarray division is obviously lower than that under the condition of fixed subarray division, which indicates that the centralized MIMO radar effectively reduces the comprehensive cost through adaptive division.
FIG. 3 shows the following (c) 1 ＝0.9,c 2 = 0.1) selected subarray division versus sampling period variation contrast curves in fixed subarray division and adaptive subarray division tracking processes. For the self-adaptive subarray division condition, comprehensively analyzing the selection of the subarray division number and the sampling period: the reason why the larger number of the subarray partitions is selected at the beginning is that the tracking error is larger during initialization, and the larger number of the subarray partitions needs to be selected to meet the requirement of azimuth angle predictionMeasuring the standard deviation threshold requirement, and selecting the minimum subarray division number (subarray division 1) in the uniform motion stage to meet the threshold requirement along with the improvement of the tracking precision, so that the subarray division number is selected to be 1 in the uniform motion stage; the selection of the sampling period also shows the trend, the selected sampling period is smaller at the beginning, and the larger sampling period is selected along with the improvement of the tracking precision.
At 40s-80s, the number of the selected subarray partitions is increased because the target enters a maneuvering process at the stage, at the moment, if a larger sampling period is selected, the covariance of filtering estimation is larger, so that the prediction covariance is larger, and in order to meet the requirement of a threshold, the larger number of the subarray partitions and the larger sampling period meet the requirement; if the number of the sub-array partitions is 1, only a small sampling period is selected in order to meet the threshold requirement. The feasible parameter set combination at this stage can be roughly divided into two types, namely, dividing a large sampling period by a large sub-array and dividing a small sampling period by a small sub-array, and the weight of the cost function at this moment is (c) 1 ＝0.9,c 2 = 0.1), the opposite side is heavier than radar system resources, after balancing the radar system resources and the target tracking precision minimization cost function, a slightly larger subarray division is selected to combine with a larger sampling period, and the number of the subarray divisions in the phase is noted to be in a range of 1 to 2, which indicates that the parameter combination selected by the phase minimization cost function is unstable, but the selected subarray division and the sampling period are corresponding, when the number of the selected subarray division is 2, the selected sampling period is larger, although the tracking precision is poorer, the cost function is minimized at this time due to the slightly larger subarray division and the larger sampling period; when the number of the selected subarray division is 1, the selected sampling period is slightly shorter, and although the radar system resource consumption is slightly larger, the cost function is minimized due to better tracking accuracy.
Starting from 80s to 120s, the target enters a non-maneuvering state in the stage, but due to the hysteresis effect of the maneuvering process, the echo signal-to-noise ratio is reduced due to the increase of the moving distance of the target, so that the prediction covariance is not obviously reduced, and the stage mainly selects a slightly larger sub-array division number and a larger (almost maximum) sampling period to minimize the cost function. Starting from 120s, the number of the sub-array partitions has a rising trend because the target enters a maneuvering state again and the maneuvering degree is larger, similar to the previous situation, in order to meet the threshold requirement and maximize the sampling period, the sub-array partitions selected by selecting the larger sub-array partition and combining the larger sampling period are larger than the sub-array partitions selected by the first maneuvering situation because the tracking error at the stage is larger, and if the larger sampling period is selected, only the larger sub-array partition and combining the larger sub-array partitions meet the precision requirement.
The larger subarray division is still selected at 160s-175s because although the target is in the non-maneuvering state at this time, due to the hysteresis effect of the maneuvering state, the inertia-like interpretation, the process from the maneuvering state to the non-maneuvering state is time-consuming, the larger estimation covariance caused by the maneuvering phase affects the non-maneuvering phase, and the echo signal-to-noise ratio is reduced due to the longer movement of the target at this time, and the double factor affects the selection of the large subarray division for the large number of sampling period combinations. Starting from 175s, the number of subarray partitions begins to decrease, because the stage has smoothly transited from the maneuvering stage to the non-maneuvering stage, the prediction covariance is reduced, and therefore the selected subarray partitions are reduced, and the sampling period is increased. The comprehensive analysis of the selected subarray division and the sampling period shows that the subarray division and sampling period corresponds to the motion state of the target, and the accuracy of the algorithm is verified laterally.
Dividing a fixed subarray: since this is the case with fixed subarray divisions, the selected subarray divisions are all constantly 1. Selecting a sampling period: under the condition of fixed subarray division, in order to meet the requirement of predicting covariance threshold, the threshold requirement can only be met through the change of sampling period, the tracking precision is poor at the initial tracking stage, at the moment, a smaller sampling period is selected, and a larger sampling period is selected at the uniform motion stage along with the improvement of the tracking precision.
Starting from 40s to 80s, the selected sampling period starts to decrease, because the target is in a maneuvering state at this stage, only a small sampling period is selected to meet the tracking accuracy requirement. Starting from 80s to 120s, the selected sampling period starts to increase, because the phase target is in a non-motorized state, and a slightly larger sampling period is selected to meet the accuracy requirement. Starting from 120s to 160s, the selected sampling period is reduced for the second time, because the target enters the maneuvering state for the second time in the stage, the maneuvering degree is larger in the stage compared with the first maneuvering, and the moving distance of the target is increased to reduce the signal-to-noise ratio of the echo, and the accuracy requirement can be met only by selecting a smaller sampling period, so that the selected sampling period is smaller in the stage compared with the first maneuvering. The non-motorized state is entered starting from 160s and the selected sampling period starts to rise again. It can be seen that the choice of sampling period is consistent with the maneuver situation when the number of sub-array partitions is fixed. And comparing the sampling period selected by the adaptive sub-array division with that selected by the fixed sub-array division, wherein the sampling period selected by the adaptive sub-array division is always larger than that selected by the fixed sub-array division, and therefore, the time resource of the radar system is saved through the adaptive sub-array division.
Fig. 4 shows the variation contrast curves of the selected transmission parameters in the fixed subarray division and adaptive subarray division tracking processes, respectively.
To further illustrate the effectiveness of the adaptive transmit parameters, the adaptive transmit parameters are compared to fixed transmit parameters, evaluated with target tracking accuracy, and evaluated with a position error, RMSE, equation shown below.
Position error:
wherein N is MC The number of Monte-Carlo; m n The number of sampling points, x, of the nth Monte-Carlo k For the true value of the target in the x-direction at the kth sampling instant,
for the estimated value of the target in the x-direction at the kth sampling instant in the nth Monte-Carlo k For the true value of the target in the y-direction at the kth sampling instant,
for the nth Monte-Carlo, the target is in the y-direction at the kth sampling timeAn estimate of (c).
FIG. 5 shows a comparison of the RMSE of a fixed transmit parameter and adaptive transmit parameter target of a scene; as can be seen from FIG. 4, the RMSE for the adaptive transmit waveform parameters is slightly better than the fixed transmit waveform parameters at 140s to 200s, but the RMSEs are almost completely coincident before 160 s. The reason is that the target is closer to the radar transmitting station before 140s, the signal-to-noise ratio in the period of time is larger, and according to the formula (31), the influence of the larger signal-to-noise ratio on the measurement covariance matrix plays a decisive role in comparison with the influence of the transmitted waveform parameters on the measurement covariance matrix, so that the RMSE difference in the two conditions in the period of time is not large; after 140s, as the target moves far, the signal-to-noise ratio is reduced, and the transmitted waveform parameters have certain influence on the measurement covariance matrix, so that the advantage of the self-adaptive transmitted waveform parameter condition is slightly achieved.
To illustrate the effectiveness of the adaptive transmit waveform parameters in more detail, we modify the target motion trajectory and set scenario two so that the signal-to-noise ratio of the target is not too large to completely determine the measured covariance matrix. FIG. 7 is a comparison of the RMSE for a fixed transmit parameter and adaptive transmit parameter target for a scene two; as is apparent from fig. 6, the RMSE of the adaptive transmission parameters is generally smaller than that of the fixed transmission parameters, which indicates that the tracking accuracy of the target can be effectively improved by the adaptive transmission parameters.
FIG. 6 is a comparison curve (c) of the division of the selected subarrays against the variation of the sampling period during the tracking of the second fixed transmit parameter and the adaptive transmit parameter of the scene 1 ＝0.9,c 2 = 0.1); as can be seen from fig. 5, the selection of the number of the subarray partitions is almost 2, and no mobility is embodied, because the mobility of the second scenario is relatively small, but the mobility can be seen from the selection of the sampling period.
The radar parameters in the simulation are shown in table 1.
TABLE 1 Radar parameters
In summary, the invention provides a centralized MIMO radar adaptive resource management algorithm based on target tracking. Firstly, selecting parameter combinations of feasible subarray division number and sampling period through predicting covariance and detection probability threshold, and adaptively allocating radar system resources; on the basis, the target tracking precision is further improved, the transmitting waveform parameters are selected in a self-adaptive mode, a feasible sub-array division number, sampling period and transmitting waveform parameter combination set is formed, the resource consumption and the target tracking precision of the radar system are comprehensively considered, and the optimal sub-array division number, sampling period and transmitting waveform parameter combination are selected according to the comprehensive cost function minimization principle. The algorithm provided by the invention improves the target tracking precision while minimizing the radar system resources.
Claims (1)
1. The centralized MIMO radar self-adaptive resource management method for target tracking comprises the following steps:
step 1: if the total array element number of the centralized MIMO radar is M, the number of possible sub-arrays is s j ＝2 j-1 ，j＝1,2,…,(log 2 M + 1); let the current time be t k-1 Next time t k Sampling period T of k ＝t k -t k-1 ，T k From a preset set of sampling periods
Selecting; the transmit waveform parameters λ and b are adaptively variable, where λ represents the duration of the waveform and b represents the chirp rate;
for parameter combinations(s) of the number of possible sub-array divisions and the possible sampling periods j ,T l ) Calculating the following correlation quantities;
step 1.1: calculating the standard deviation of the predicted radial distance error of the tracked target
Standard deviation of predicted azimuth error
The covariance matrix of the predicted position error in the rectangular coordinate system is recorded as
Then there is
Wherein H is a measurement matrix,
a prediction error covariance matrix under a rectangular coordinate system; prediction position error covariance matrix under polar coordinate system
Comprises the following steps:
wherein
For the Jacobian transformation matrix from rectangular to polar coordinates, the following equation is given
subscripts (k, k), k =1,2 denote diagonal elements;
step 1.2: calculating detection probability
In which the echo signal-to-noise ratio is predicted
Comprises the following steps:
wherein, B w For a two-pass beamwidth of the azimuth at the beam pointing location,
predicted signal-to-noise ratio for beam pointing direction:
wherein M is the number of elements of the radar array, e is the energy of the transmitted waveform, eta A For the duty cycle of the effective area of the antenna,
is an estimate of the target mean RCS, λ 1 Is a wavelength, N 0 Is the noise power spectral density, N 0 ＝kT 0 F 0 K is Boltzmann constant, T 0 For radar receiver temperature, F 0 For the noise figure of the radar receiver, s j The number of MIMO subarrays;
step 2: selecting parameter combination(s) formed by feasible sub-array division number and sampling period j ,T l ) The method comprises the following steps:
step 2.1: calculating the distance prediction error threshold corresponding to the target
Sum azimuth prediction error threshold
Wherein L is g For range of action during tracking, B(s) j )＝1.76*s j M is the one-way beamwidth, u, at the predicted location of the beam pointing target 0.5α Is a bilateral quantile of a standard normal distribution;
step 2.2: the feasible parameter set is formed by counting the combination of the sub-array division number and the sampling period which meet the following conditions
q isThe number of feasible parameter combinations;
and step 3: based on the parameter combination of the feasible sub-array division number and the sampling period selected in the steps 1 and 2, the transmitted waveform parameters are further considered to form the parameter combination of the sub-array division number, the sampling period and the transmitted waveform parameters
Calculating each parameter combination(s) i ,T i ,λ m ,b n ) Corresponding measurement error covariance matrix R pre (t k ,s i ,T i ,λ m ,b n )；
The measurement error covariance matrix is expressed as:
wherein N is pre (t k ,s i ,T i ,λ m ,b n ) Is the measured covariance, σ, of radial distance and radial velocity b，pre (t k ,s i ,T i ) The standard deviation of the azimuth angle measurement error is shown;
standard deviation sigma of azimuth angle measurement error b，pre (t k ,s i ,T i ) The calculation is as follows:
wherein, B w For the two-way beamwidth of the azimuth of the beam pointing position, constant c 1 Is typically 1.57;
and 4, step 4: calculating each parameter combination(s) i ,T i ,λ m ,b n ) Estimation of target location predictionError covariance
The covariance matrix of the estimation error of the target position prediction in the rectangular coordinate system is marked as P pos,pre (t k ,s i ,T i ,λ m ,b n ) Then there is
P pos,pre (t k ,s i ,T i ,λ m ,b n )＝H·P pre (t k ,s i ,T i ,λ m ,b n )·H T (13)
Where H is the measurement matrix, P pre (t k ,s i ,T i ,λ m ,b n ) Estimation error covariance matrix, P, predicted in rectangular coordinate system pre (t k ,s i ,T i ,λ m ,b n ) Using each parameter combination(s) i ,T i ,λ m ,b n ) The measured error covariance matrix is obtained by filtering estimation;
wherein P is pos,pre (t k ,s i ,T i ,λ m ,b n ) 1 ， 1 ，P pos,pre (t k ,s i ,T i ,λ m ,b n ) 2,2 Respectively expressed in the parameter combination(s) i ,T i ,λ m ,b n ) The estimation error variance of the lower x-direction prediction and the estimation error variance of the y-direction prediction, subscript (k, k), k =1,2, denotes the diagonal elements;
and 5: calculating each parameter combination(s) i ,T i ,λ m ,b n ) The cost function of (2);
wherein, c 1 And c 2 C is a weighting coefficient of time resource tracking precision, and is more than or equal to 0 1 ≤1,0≤c 2 C is less than or equal to 1 and 1 +c 2 =1; the corresponding optimal parameter combination(s) opt ,T opt ,λ opt ,b opt ) Can be expressed as:
(s opt ,T opt ,λ opt ,b opt )＝minC pre (t k ,s i ,T i ,λ m ,b n ) (15)
and 6: using the combination(s) of parameters selected at the current time opt ,T opt ,λ opt ,b opt ) As t k Tracking task parameters at all times, detecting a target and obtaining current measurement;
and 7: filtering by using the measurement obtained in the step 6, and then returning to the step 1 to repeat the steps 1-6 until the tracking time is reached.
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