CN109283522B - Co-location MIMO radar target tracking method based on joint time-space resource management - Google Patents
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Abstract
The invention discloses a co-location MIMO radar target tracking method based on joint time-space resource management, belongs to the field of target tracking, and particularly relates to a division method of multi-target tracking radar resources. The invention considers the problem of system resource allocation on time domain and space domain in the process of tracking the maneuvering target by the MIMO radar. On the premise of ensuring the target tracking precision, the sampling period and the sub-array division number working parameters are adaptively adjusted, and the method has the excellent effect of saving system resources. Because the algorithm is based on a maneuvering target tracking algorithm of nonlinear measurement conversion and is connected with a space-time resource management strategy in parallel, the algorithm has higher tracking precision and fighting efficiency under the MIMO radar maneuvering target tracking scene.
Description
Technical Field
The invention relates to the field of target tracking, and mainly aims to solve the problem of space-time resource management of a co-located MIMO (Multiple-Input Multiple-Output) radar in a maneuvering target tracking process. The method is particularly applied to a maneuvering target tracking process of nonlinear measurement, and the sampling period and the sub-array division number are adjusted in a self-adaptive mode, so that optimal distribution of co-location MIMO radar space-time resources is achieved.
Background
In recent years, MIMO radar has received much attention due to its advantages in target detection parameter estimation, resolving power, interference suppression capability, and the like. (D.J. Rabideau and P.Parker, "Ubiquitous MIMO multiple function digital array and the role of time-energy management in Radar," MIT Lincoln Laboratory, lexington, MA, USA, project Report DAR-4, dec.2003.) MIMO radars can be classified into two categories, statistical (distributed) and co-located (centralized) MIMO radars. In the distributed MIMO Radar, the distance between each transmitting array element is larger, and the distributed MIMO Radar has good space diversity gain, so that the distributed MIMO Radar has lower missed detection probability and better tracking precision (Haimovich A M, blum R S, cimini L J. MIMO Radar with wide Separated Antennas [ J ]. IEEE Signal Processing Magazine,2007, 25 (1): 116-129.), however, the distributed MIMO Radar has the problems that multiple stations are difficult to synchronize in practice, and the distributed MIMO Radar has a certain distance from practical application. The co-location MIMO radar has the advantages that the transmitting array elements are closer in distance, the structure is similar to that of the traditional phased array radar, and compared with a distributed structure, the co-location MIMO radar has better application prospect. The whole array surface of the co-location MIMO radar can flexibly divide sub-arrays, and mutually orthogonal waveforms are transmitted among the sub-arrays to detect the target. Compared with the phased array radar, the waveform diversity gain of the phased array radar has greater potential value in the aspects of target detection, tracking estimation and the like, simultaneously can effectively inhibit multipath clutter, and can effectively reduce the probability of system interception by forming low-gain beams in a space domain (Li J, stoica P. MIMO radar with colorful antennae [ J ]. IEEE Signal Process Mag,2007, 24 (5): 106-114.). Due to the characteristic of flexible division of the subarrays, the number of array elements in each subarray can be adjusted in a self-adaptive mode, so that the width of a transmitting beam of the MIMO radar can be changed, and flexible configuration of system resources on an airspace is achieved. Therefore, the resource management freedom degree of the co-located MIMO radar subarray is larger due to the characteristic of the co-located MIMO radar subarray division.
The technical research of radar resource management is generated by the development of phased array radar. The phased array radar has the capabilities of multiple functions, multiple targets and high self-adaption and is extremely high in flexibility. When the phased array radar realizes various tactical functions, limited resources such as system time, energy, hardware processing units and the like need to be distributed among airspace searching, target tracking and other types of tasks. Therefore, in order to fully exert the performance of the radar, an effective resource management strategy needs to be implemented on the phased array radar, and the configuration of the working parameters of the radar is mainly needed. At present, the self-adaptive time resource allocation has abundant research results. Cohen proposes a method for controlling a sampling period by using a position residual error, and reflects the forward and backward transformation condition of the sampling period by using a recursion formula (see the document: cohen S A. Adaptive variable upper rate algorithm for tracking targets with a phase array Radar [ J ]. IEE Proceedings F-Communications, radar and Signal Processing,2008, 133 (3): 277-280.); van Keuk proposes a formulation giving the sampling interval as a function of the maneuvering parameters and controlling the sampling period with the desired accuracy. (see Van Keuk G, blackman S. On phased-array tracking and parameter control [ J ]. IEEE Transactions on Aerospace & Electronic Systems Aes,1993, 29 (1): 186-194.); the covariance threshold method of prediction error based on covariance control screens out the sampling period that satisfies the condition by comparing the standard deviation of the prediction error of the target with the set threshold (see Watson G A, blair W D. Tracking performance of a phased array Radar with a reliable time controlled use the IMM algorithm [ C ] radio reference, 1994.Record of the 1994IEEE national. IEEE,1994 160-165.. Benoudine proposes a Fast Adaptive IMM Algorithm (FAIMM) based on covariance threshold (see Benoudine H, keche M, ouamri A, et al. Fast Adaptive Update Rate for Phased Array radio Using IMM Target Tracking Algorithm [ C ] IEEE International Symposium on Signal Processing and Information technology. IEEE,2007 277-282.). In addition to controlling the time domain resource, the sampling period, parameters related to the system energy resource can be configured. The Gilson comprehensively considers time and energy resources and gives the relation between the minimum power consumption and the tracking precision of the radar system under the condition of maneuvering target tracking. (see Gilson W H. Minimum power requirements for tracking [ J ] 1990.)
Resource management research for MIMO radar has mainly focused on energy resource management. In different application contexts, the transmission power is optimized based on different optimization criteria. Strictly, junkun proposes a Resource management algorithm in multi-Target Tracking, which aims to consume all resources so as to improve the worst Tracking performance of targets to the maximum extent (Yan J, liu H, bo J, et al. However, considering that the current Tracking precision can be used to adaptively adjust the sampling period in the Tracking process, another MIMO Radar multi-Beam resource management method is proposed, which can adaptively adjust the number of the multi-beams transmitted by the System and adaptively allocate the transmission Power to each transmitted Beam, thereby realizing reasonable configuration of MIMO Radar System resources in the time-space domain (Yan J, liu H, pu W, et al. Joint Beam Selection and Power Allocation for Multiple Target Tracking in networked coordinated MIMO Radar System [ J ]. IEEE Transactions on Signal Processing,2016, 64 (24): 6417-6427.). The above algorithm ignores the effect on the transmit beamwidth caused by MIMO radar sub-array partitioning. Based on the above, the invention provides a Joint Time and Space Resource Management (JTSM) co-location MIMO radar target tracking method. Considering target maneuvering characteristics and nonlinear measurement obtained by the MIMO radar, combining a Sequential Filtering method and an Interactive multi-model method (Sequential Filtering Interactive multi-Models) to serve as a basic target tracking algorithm, and carrying out self-adaptive adjustment on a sampling period and sub-array division number working parameters on the premise of ensuring target tracking accuracy, so that reasonable distribution of system resources on time domain and space domain is realized, and the operational efficiency of the co-located MIMO radar is improved.
Disclosure of Invention
The invention provides a co-location MIMO radar target tracking method based on joint time-space resource management, which is based on a maneuvering target tracking algorithm based on nonlinear measurement, adaptively selects a sampling period and the number of system subarray partitions under the condition of meeting the target expected tracking precision, and realizes the joint distribution of MIMO radar system resources in time domain and space domain.
The technical scheme of the invention is as follows: a co-location MIMO radar target tracking method of joint time and space resource management, firstly, setting the total number of co-location MIMO radar array elements as M; the number of feasible sub-array partitions can form a set which is recorded as
Setting the sampling period set to be
P and Q are the total number of the selectable subarray divisions and the total number of the selectable sampling periods respectively; according to the sampling period T i Sum subarray division number K i Possible values form P × Q space-time parameter combinations
Step 1: calculating the combined predicted state under all feasible space-time parameter combinations
And combining the prediction covariance matrices
Wherein
Representing information relevant to prediction, T l Denotes the sampling period, l =1,2, \ 8230;, P × Q;
suppose that the l-th group of space-time parameters xi is selected l Sampling period T in the combination l The model interaction inputs are used as prediction processing by using a time updating equation (1), and then probability combination is carried out according to an equation (2):
in the formula,
representing the sampling period T l Predicted state of model j under control, F j (T l ) The state transition matrix representing the model j,
representing the state of the interactive estimate at time k-1, G j (T l ) A noise-driven matrix is represented that,
representing the sampling period T l Controlling the covariance of the prediction error, P, of the lower model j 0j (t k-1 ) Representing the mutual estimation error covariance, Q, at time k-1 j (t k-1 ) Representing a process noise autocorrelation matrix;
represents t k The prediction probability of the model j at the moment can be obtained by the prediction probability of each position filter bank and the average value of the pseudo-measurement prediction probabilities, and the calculation method is as follows:
in the formula, pi ij In order to be a matrix of probability transitions,
model prediction probabilities, μ, of the position measurement filter and the pseudo measurement filter of model j, respectively p，i t k-1 ，μ ε，i t k-1 Respectively representing model probabilities of a position measurement filter and a pseudo measurement filter of the previous moment model i;
and 2, step: firstly screening parameter combinations meeting a prediction covariance threshold method;
step 2.1: calculating prediction error covariance
The combined prediction covariance is expressed as
And (3) carrying out coordinate transformation:
wherein the measurement matrix H = diag { [ 10 { [1 { ]]，2} 2×6 Combined prediction covariance
The calculation method can be completed according to the formula (2) in the step l; transformation matrix J p Each element in (1) is composed of a partial derivative of the corresponding position
Wherein,
indicating the predicted distance and the predicted azimuth angle,
representing predicted position coordinates; predicting distance
And predicting the azimuth angle
The prediction states can be combined in step 1
The coordinates of the elements in (1) are obtained after transformation;
the standard deviation of the prediction errors of the distance and the azimuth is as follows:
the right subscript (n, n), n =1,2 indicating the row and column correspondence in the matrix;
step 2.2: calculating a prediction error covariance threshold:
the distance standard deviation threshold value sigma is calculated according to the following formula r，TH Standard deviation threshold value from azimuth angle
Wherein L is g Is a distance from the width of the wave gate, u 0.5α Is normally distributed about a =1-P CL Double-sided quantile of (P) CL Indicating confidence, usually P CL Taking as a constant; m is the total number of array elements; k l As set I space-time parameter xi l Dividing the number of subarrays in the combination; λ is the wavelength of the transmitted signal; d is the distance between each antenna unit;
when the following formula condition is satisfied, the group of space-time parameter combination xi is stored l ＝[T l L l ]
And 3, step 3: secondary screening parameter combinations meeting the prediction detection probability threshold method;
performing secondary screening on the space-time parameter combinations stored in the step 2 by using a prediction detection probability threshold;
step 3.1: calculating the predicted signal-to-noise ratio of the co-located MIMO radar
Step 3.2: calculating a predictive detection probability
And substituting the predicted signal-to-noise ratio calculated in the last step into the following formula to calculate the predicted detection probability:
in the formula, P fa The constant false alarm probability is a constant;
when the sampling period T l And the number K of sub-array divisions l When the controlled detection probability satisfies the following formula, the group of space-time parameter combination xi is stored l ＝[T l K l ]And defined as a feasible parameter combination;
wherein,
the threshold value of the detection probability is a preset constant;
and 4, step 4: judging whether the feasible space-time parameter set is empty: if the signal is an empty set, selecting the combination of the minimum sampling period and the minimum sub-array division number as the optimal parameter, namely T (T) k )＝T min ，K(t k )＝K min Then, directly executing the step 7; if the feasible parameter combination set is not an empty set, executing the step 5;
and 5: computing a covariance matrix of predicted estimation errors
Probability weighting of the prediction estimation error covariance of each model is performed as follows
Wherein the prediction error covariance of model j is
Calculating according to the formula;
wherein, I n An identity matrix of dimension n is represented,
as a vector xi in the l-th group l Gain matrix under control, as shown below;
H j in order to observe the matrix, the system,
is a measurement error covariance matrix;
step 6: determining optimal spatio-temporal parameter combinations
Selecting an optimal parameter combination according to the following formula in the feasible parameter combination set, wherein a subscript o represents an optimal item;
ξ o ＝[T o K o ]＝arg min c(ξ l ) (14)
wherein c (ξ) l ) Representing a vector xi of a time parameter l ＝[T l K l ]Of the composite cost function, in particularThe form is as follows:
in the formula, c 1 ，c 2 Weights normalized for space-time resource consumption and tracking precision cost respectively, and satisfying c 1 +c 2 ＝1 c 1 ，c 2 ≥0；P exp Which represents the covariance of the expected error,
representing a spatio-temporal parameter vector xi l ＝[T l K l ]A prediction estimation error covariance matrix under control;
and 7: carrying out nonlinear measurement conversion by using the optimal parameter combination and the prediction prior information;
calculating the converted measurement value Z c (t k ) Using the sampling period in the optimal space-time parameter combination obtained in step 6 or step 4 as the current sampling period, namely T (T) k )＝T o Thus, the next sampling time is t k ＝t k-1 +T(t k ) Let t be k Available measurements include distance measurements r m (t k ) Azimuthal angle measurement theta m (t k ) And Doppler measurements
Performing measurement conversion according to the formula (16);
wherein ρ represents a correlation coefficient between the distance and the doppler measurement noise; phi is a deviation compensation factor
Representing the azimuthal metrology noise variance, σ r ，
Respectively, the standard deviations of the distance and radial speed measurement errors are related to the sub-array division number K;
calculating a measurement transformation error covariance matrix R by using prediction as prior information j (t k ) (ii) a To concisely represent elements in a matrix, t is agreed k The parameter corresponding to the time is expressed in the form of a subscript k
Covariance matrix R j The calculation method of each element in (1) is as follows:
wherein r is t Predicting a state, θ, for a distance t For the angle prediction state,
In order to predict the state of the speed,
for the distance prediction error variance,
For the angle prediction error variance,
A prediction error variance for the velocity prediction error variance;
and 8: initializing multi-model interactive input estimation;
location measurement estimation of model i at known time t-1
And covariance P i，p t k-1 Calculating the fusion estimation value of each model filter according to the following formula
And estimate error covariance P 0j t k-1
Wherein, pi ij Representing the probability of transition from model i to model j, N representing the total number of object motion models, μ i (t k-1 ) Represents t k-1 Probability of update of the moment motion model i, C j The normalization constant, representing model j, is calculated as:
and step 9: carrying out sequential filtering on each model;
t is obtained in the steps 7 and 8 k Time measurement conversion value Z c (t k ) And the covariance of the measurement error R j (t k ) And t obtained in step 1 k-1 Input estimate X of model j at time 0j t k-1 ，P 0j t k-1 Substituting into the sequential filter of the current model, and performing filtering treatment to obtain
P ε，j (t k )；
Represents the pseudo-metric estimated state of model j, P ε，j (t k ) The pseudo metrology estimation error covariance for model j is represented.
Step 10: calculating the model update probability mu j (t k )
Model j at t k Update probability mu of time j (t k ) Expressed as the position measurement model probability mu p，j (t k ) And the probability mu of the pseudo-metric model ε，j (t k ) The mean value of (a);
wherein, the superscript j represents the motion model, p represents the information related to the position measurement, and epsilon represents the information related to the pseudo measurement; likelihood function Λ of each filter p，j (t k )，Λ ε，j (t k ) The calculation formula is as follows:
where e is the measurement residual, S is the autocorrelation matrix of the residual, C p，j And C ε，j Respectively representing the position measurement and the pseudo measurement normalization constant of the model j;
step 11: state estimation fusion
Mixing t obtained in step 9 k Sequential filtering estimation of time instants
P ε，j (t k ) And the model update probability mu j (t k ) Performing fusion
Wherein,
representing the final filtered estimate state, P (t) k ) Representing the final filtered estimation error covariance.
Step 12: filtering results of each model
P p，j (t k ) (24) in step 8, the next time t is calculated k+1 State estimates and covariance of each model filter input.
Further, the specific method of step 3.1 is as follows:
the stored space-time parameter xi of the first group l The predicted signal-to-noise ratio is calculated according to the following formula
Wherein p is t Peak power for a single antenna of the radar; eta A Is the aperture efficiency of the antenna; σ is the target cross-sectional area representation, λ is the signal wavelength, N 0 For noise power spectral density, [ tau ] B In order to be the beam dwell time,
representing the radial predicted distance of the target to the radar.
Further, the method for calculating the partial symbols in step 7 includes:
in the formula, x t ，
y t ，
Is composed of
The corresponding target in the target prediction system predicts the position and speed in the abscissa direction and the position and speed in the ordinate direction,
representing the correlation coefficient between the predicted distance and the predicted radial velocity, matrix
Is in the form of
Wherein P is xx Representing the predicted position error variance in the x-direction for model j,
represents the error covariance of the predicted position and velocity in the x-direction of model j,
represents the predicted speed error variance in the x-direction for model j; by analogy, the covariance P of the position and the speed in the y direction is obtained yy ，
And
similarly, the covariance P of the predicted position and velocity errors in the x-direction and y-direction can be obtained xy ，
And
optimizing a cost function:
the space-time resource management in the target tracking process of the MIMO radar is to minimize the resource consumption of the system on the premise of meeting the expected tracking precision. The actual tracking precision is very poor due to the excessively small resource consumption, and the requirement of the expected tracking precision is certainly not met; when the consumption of system resources is too large, the expected tracking precision is very high, and although the requirement of the expected tracking precision can be met, the system resources are wasted. Therefore, the optimal amount of system resource consumption should be such that the actual tracking accuracy is as close as possible to the desired tracking accuracy. Secondly, in order to further save the distribution of the system resource consumption in the time domain, the sampling period of the tracking should be increased as much as possible. Based on the method, the MIMO radar target tracking joint space-time resource management method comprehensively considersIn the two aspects, an optimization model equation shown as the formula (31) is established. In the formula, due to the dimension of the difference between the sampling period and the tracking precision, the normalization mode is adopted for processing. Wherein c is 1 ，c 2 For the preset weighting coefficient, the value reflects the attention degree to the system resource and the tracking performance, so the following optimization objective function is established and can be embodied in step 6.
Wherein,
represents the covariance of the prediction estimation error, which is related to the number of sub-array partitions and the radar sampling period. P exp Representing the desired error covariance.
In the target tracking process of the MIMO radar, in order to obtain a measuring point trace of a target, a transmitting beam of the MIMO radar needs to be capable of irradiating the target. When single target tracking is carried out, a beam emitted by the radar system is pointed to be the predicted position of a target, and the uncertainty of the predicted position of the target is described by the predicted covariance matrix of the target. Therefore, to ensure that the target is illuminated, the beam width should cover the "uncertainty" region with a certain probability, which can be characterized by the following equation (32):
in the formula,
standard deviation of prediction error, σ, representing distance and angle r，TH ，
A prediction error standard deviation threshold representing distance and angle.
On the other hand, in order to achieve effective detection of the target, the detection probability of the target must exceed a given threshold value, and is represented by equation (33).
Wherein,
in order to detect the threshold value of the probability,
to predict the detection probability, the calculation formula is as follows:
in the formula, P fa Is the constant false alarm probability; for t k Predicted signal-to-noise ratio of time instants
The calculation method is obtained by equation (9).
In summary, we can obtain an optimization problem model as shown in equation (35).
Wherein, T min And T max Minimum and maximum sampling periods, K, respectively min And K max Numbers are divided for the minimum and maximum subarrays, respectively. To satisfy the constraint conditions, the joint resource management algorithm first establishes P × Q possible parameter combination sets
In order to meet the constraint condition of the prediction covariance threshold, the joint resource management algorithm adopts the step 2 to realize the first screening of the parameter combination set, and in order to meet the detection probability threshold, the step 3 to the parameter combination set is adoptedAnd (5) screening again. And finally, selecting the parameter which minimizes the target function from the feasible parameter combination set which meets the constraint condition, referring to step 6.
The invention considers the problem of system resource allocation on time domain and space domain in the process of tracking the maneuvering target by the MIMO radar. On the premise of ensuring the target tracking precision, the sampling period and the working parameters of the sub-array division number are adaptively adjusted, and the method has the excellent effect of saving system resources. Because the algorithm is based on a maneuvering target tracking algorithm of nonlinear measurement conversion and is connected with a space-time resource management strategy in parallel, the algorithm has higher tracking precision and fighting efficiency under the MIMO radar maneuvering target tracking scene.
Drawings
FIG. 1 is a block diagram of the JTSM algorithm architecture of the present invention;
FIG. 2 is a diagram of a target true track according to an embodiment of the present invention;
FIG. 3 is a graph of model probability transfer and acceleration in an embodiment of the present invention;
FIG. 4 is a diagram of adaptive sampling period variation in an embodiment of the present invention;
FIG. 5 illustrates the number of adaptive sub-array partitions in an embodiment of the present invention;
FIG. 6 is a comparison of the RMSE curves for the fixed and adaptive parameters in accordance with an embodiment of the present invention;
FIG. 7 illustrates an approximation of tracking accuracy and expected value when tracking performance is emphasized in an embodiment of the present invention;
FIG. 8 illustrates cost changes when tracking performance is emphasized in an embodiment of the present invention;
FIG. 9 illustrates the tracking accuracy and expected value approximation at the resource-focused level in an embodiment of the present invention;
FIG. 10 illustrates cost changes at the resource level;
FIG. 11 is a graph of integrated tracking and tracking accuracy and expected value approximation for resource consumption in accordance with an embodiment of the present invention;
FIG. 12 illustrates the cost changes of the integrated trace and resource consumption according to an embodiment of the present invention;
Detailed Description
Setting the motion state of the target:
in the embodiment, the target which does diving motion in the two-dimensional plane is considered. Its initial position is [60km 50km ]](ii) a The initial speed was set at [350m/s,0m/s]. The motion model includes two: acceleration (CA) Constant Velocity (CV); respectively carrying out uniform motion within 1-60 s, 75-125 s and 140-200 s, carrying out uniform acceleration motion within 60-75 s and 125-140 s, wherein the accelerations in two directions are respectively as follows at 60-75 s: a is x ＝-2.2m/s 2 ，a y ＝-2.2m/s 2 (ii) a The accelerations in two directions at 100 to 115s are respectively: 2.2m/s 2 ，a y ＝2.2m/s 2 . Total radar tracking time: 200s; the minimum sampling period is: 0.5s. Optional set of adaptation parameters:
radar-related parameter setting:
peak power P t =1Mw; antenna efficiency eta A =0.5, wavelength λ =7.5cm; array element spacing d =0.5 λ; the number of the array elements is M =2048; target cross-sectional area σ =1m 2 (ii) a Constant false alarm probability P fa ＝1×10 -6 (ii) a Pulse width τ =0.15 μ s; the detection probability threshold is set to
Boltzmann constant k =1.38 × 10 -23 (ii) a Standard temperature T 0 =290K; noise figure N 0 =1. Initial measurement noise setting σ r ＝2m，σ β ＝2°，
c 1 ，c 2 Weights normalized for time resource consumption and tracking accuracy cost, { c 1 ，c 2 Respectively taking initial probabilities of {0.5,0.5} {0.8,0.2} {0.2,0.8} models to be 0.5, and a probability transition matrix is as follows:
width L of range gate g =1575m, bilateral quantile (confidence 0.99 hours) u 0.5a ＝2.5758(P CL = 0.99), the correlation coefficient ρ =0.9.
From the JTSM algorithm simulation results, fig. 2 and fig. 3, it can be seen that the target has two large maneuvers during the whole movement, and the change of the CA and CV model probabilities reflects that the JTSM tracking algorithm can effectively detect the maneuvers and can correspond to the change of the acceleration.
See fig. 4-5 for spatio-temporal parameter variations. In fig. 4, the occurrence of a sampling period that can randomly move is correspondingly reduced, which indicates that the system can effectively perform time resource allocation in the tracking process, and in fig. 5, the number of subarray partitions is gradually reduced along with time, because the target moves away from the observation point, the echo signal-to-noise ratio needs to be ensured within a certain range (so that the detection probability is sufficiently large), and accordingly, the number of subarray partitions is reduced. A small increase in amplitude occurs at the maneuver instant because the target maneuver increases the prediction covariance; the covariance threshold is also adjusted by properly increasing the number of subarray divisions so that the predicted covariance is always within the threshold range. It can be seen that the number of the sub-arrays rises back significantly (around 60 s) at the time of the maneuver at a close distance, and the secondary maneuver at a far distance (around 120 s) is not significantly limited by the signal-to-noise ratio of the echo.
The sampling period and the statistical average of the number of sub-array partitions are selected as fixed parameters to perform simulation in the same scene, as shown in fig. 6. The position RMSE statistics are shown in table 1 below. As can be seen from the variation curve in fig. 6 and the above statistical average, the position RMSE of the adaptive parameter is small compared to the fixed parameter, and therefore, the tracking algorithm of the adaptive resource parameter has higher tracking accuracy.
TABLE 1 statistical averaging of sampling periods and sub-array partition numbers, RMSE statistical averaging
First considering the costWeight is set as the condition of the tracking of the emphasis, and c is selected 1 ＝0.2；c 2 And = 0.8. The system will focus on the requirement of tracking accuracy, and it can be seen from fig. 7 that the tracking accuracy in the case of adaptive parameters is rather close to the tracking accuracy of fixed parameters, and the tracking accuracy curve of fixed parameters may deviate from the expected one in the case of maneuvering. It can be seen from fig. 8 that at the moment of occurrence of the maneuver, the corresponding resource cost (dashed line) has two peaks, and the costs in the other cases are all smaller, and it can be seen that the system resource consumption increases near the maneuver. The composite cost (solid line) is mainly influenced by the tracking cost (point horizontal line), and the trends of the composite cost and the tracking cost are approximately consistent, and the composite cost is also influenced by focusing on the tracking weight.
When the resource cost weight is c 1 =0.8 tracking cost weight as c 2 If =0.2, it can be seen in fig. 9 that the approximation of the tracking accuracy to the desired accuracy is not good. However, the accuracy curve of the adaptive parameter is closer to the desired accuracy curve, and as the observation time increases, the distance increases causing the actual tracking accuracy to deviate from the desired accuracy. From fig. 10, it can be seen that the composite cost is mainly close to the resource, and is also due to the influence of more emphasis on the weight of the resource, and the cost has a trend of increasing significantly when the movement occurs.
The tracking accuracy and the expected value when the weight values are all 0.5 are approximated as shown in fig. 11, and the target comprehensive cost change is shown in fig. 12. In this case, the comprehensive cost is equivalent to the two cases of the emphasis. The cost consumption under each set of weight values is reflected in table 2.
TABLE 4 cost variation statistics under different weighting coefficients
Claims (3)
1. When combinedA common-address MIMO radar target tracking method for empty resource management comprises the steps of firstly setting the total number of common-address MIMO radar array elements as M; the number of feasible sub-array partitions can form a set which is recorded as
Setting the sampling period set to be
P and Q are the total number of the selectable subarray divisions and the total number of the selectable sampling periods respectively; according to the sampling period T i Sum subarray division number K i Possible values are taken to form P × Q space-time parameter combinations
Step 1: calculating the combined predicted state under all feasible space-time parameter combinations
And combining the prediction covariance matrices
Wherein
Representing information relevant to prediction, T l Denotes the sampling period, l =1,2, \ 8230;, P × Q;
suppose that the l-th group of space-time parameters xi is selected l Sample period T in the combination l The model interaction inputs are used as prediction processing by using a time updating equation (1), and then probability combination is carried out according to an equation (2):
in the formula,
representing the sampling period T l Predicted state of model j under control, F j (T l ) The state transition matrix representing the model j,
representing the state of the interactive estimate at time k-1, G j (T l ) A noise-driven matrix is represented that,
representing the sampling period T l Controlling the prediction error covariance, P, of the model j 0j (t k-1 ) Representing the covariance of the mutual estimation error at time k-1, Q j (t k-1 ) Representing a process noise autocorrelation matrix;
represents t k The prediction probability of the model j at the moment can be obtained by the prediction probability of each position filter bank and the average value of the pseudo-measurement prediction probabilities, and the calculation method is as follows:
in the formula, pi ij In order to be a matrix of probability transitions,
model prediction probabilities, μ, of the position measurement filter and the pseudo measurement filter of model j, respectively p，i (t k-1 )，μ ε，i (t k-1 ) Respectively representing model probabilities of a position measurement filter and a pseudo measurement filter of the previous moment model i;
step 2: firstly screening parameter combinations meeting a prediction covariance threshold method;
step 2.1: calculating prediction error covariance
The combined prediction covariance is expressed as
And (3) carrying out coordinate transformation:
wherein the measurement matrix H = diag { [ 10 { [1 { ]],2} 2×6 Combined prediction covariance
The calculation method can be completed according to the formula (2) in the step 1; transformation matrix J p Each element in (1) is composed of a partial derivative of the corresponding position
Wherein,
represents the predicted distance and the predicted azimuth angle,
representing predicted position coordinates; predicting distance
And predicting the azimuth angle
The prediction states can be combined in step 1
The coordinates of the elements in (1) are obtained after transformation;
the standard deviation of the prediction errors of the distance and the azimuth is as follows:
the right subscript (n, n), n =1,2 indicating the row and column correspondence in the matrix;
step 2.2: calculating a prediction error covariance threshold:
the distance standard deviation threshold value sigma is calculated according to the following formula r,TH Standard deviation threshold value from azimuth angle
Wherein L is g Is a distance from the width of the wave gate, u 0.5α Is normally distributed about a =1-P CL Bilateral quantile of (P) CL Indicates the degree of confidence, P CL Is a constant; m is the total number of array elements; k is l As set I space-time parameter xi l Dividing the number of submatrices in the combination; λ is the wavelength of the transmitted signal; d is the distance between each antenna unit;
when the following formula condition is satisfied, the group of space-time parameter combination xi is stored l ＝[T l K l ]
And step 3: secondary screening parameter combinations meeting the prediction detection probability threshold method;
performing secondary screening on the space-time parameter combinations stored in the step 2 by using a prediction detection probability threshold;
step 3.1: calculating the predicted signal-to-noise ratio of the co-located MIMO radar
Step 3.2: calculating a predictive detection probability
And substituting the predicted signal-to-noise ratio calculated in the previous step into the following formula to calculate the predicted detection probability:
in the formula, P fa The constant false alarm probability is a constant;
when the sampling period T l And the number K of sub-array divisions l When the controlled detection probability satisfies the following formula, the group of space-time parameter combination xi l = [ T ] is stored l K l ]And defined as a feasible parameter combination;
wherein,
the threshold value of the detection probability is a preset constant;
and 4, step 4: judging whether the feasible space-time parameter set is empty: if the sub-array is an empty set, selecting the combination of the minimum sampling period and the minimum sub-array division number as the optimal parameter, namely T (T) k )＝T min ,K(t k )＝K min Then, directly executing the step 7; if the feasible parameter combination set is not an empty set, executing the step 5;
and 5: computing a prediction estimation error covariance matrix
Probability weighting of the prediction estimation error covariance of each model is performed as follows
Wherein the prediction error covariance of model j is
Calculating according to the formula;
wherein, I n Representing an identity matrix of dimension n,
as a vector xi in the l-th group l Gain matrix under control, as shown below;
H j in order to observe the matrix, the system,
is a measurement error covariance matrix;
step 6: determining optimal spatio-temporal parameter combinations
Selecting an optimal parameter combination according to the following formula in the feasible parameter combination set, wherein a subscript o represents an optimal item;
ξ o ＝[T o K o ]＝arg minc(ξ l ) (14)
wherein c (ξ) l ) Represents the parameter direction to the timeQuantity xi l ＝[T l K l ]The specific form of the comprehensive cost function is as follows:
in the formula, c 1 ,c 2 Weights normalized for space-time resource consumption and tracking precision cost respectively, and satisfying c 1 +c 2 ＝1，c 1 ,c 2 ≥0；P exp Which represents the covariance of the expected error,
representing a spatio-temporal parameter vector xi l ＝[T l K l ]A prediction estimation error covariance matrix under control;
and 7: carrying out nonlinear measurement conversion by using the optimal parameter combination and the prediction prior information;
calculating the converted measurement value Z c (t k ) Using the sampling period in the optimal space-time parameter combination obtained in step 6 or step 4 as the current sampling period, namely T (T) k )＝T o Thus, the next sampling time is t k ＝t k-1 +T(t k ) Let t be k Available measurements include distance measurements r m (t k ) Azimuthal angle measurement theta m (t k ) And Doppler measurements
Performing measurement conversion according to the formula (16);
wherein ρ represents a correlation coefficient between the distance and the doppler measurement noise; phi is a deviation compensation factor
Represents the variance of the azimuth measurement noise,
respectively, standard deviations of the distance and radial speed measurement errors are related to the sub-array division number K;
calculating a measurement transformation error covariance matrix R by using prediction as prior information j (t k ) (ii) a To express the elements in the matrix concisely, let t k The parameter corresponding to the time instant is indicated in the form of the subscript k
Covariance matrix R j The calculation method of each element in (1) is as follows:
wherein r is t Predicting a state, θ, for a distance t For the angle prediction state,
In order to be in a speed-prediction state,
for the distance prediction error variance,
Error variance is predicted for the angle,
A prediction error variance for the velocity prediction error variance;
and 8: initializing multi-model interactive input estimation;
location measurement estimation of model i at known time t-1
And covariance P i，p (t k-1 ) Calculating the fusion estimation value of each model filter according to the following formula
And estimate error covariance
Wherein, pi ij Representing the probability of transition from model i to model j, N representing the total number of object motion models, μ i (t k-1 ) Represents t k-1 Probability of update of the moment motion model i, C j The normalization constant, representing model j, is calculated as:
and step 9: carrying out sequential filtering on each model;
obtaining t in the steps 7 and 8 k Time measurement conversion value Z c (t k ) And the covariance of the measurement error R j (t k ) And t obtained in step 1 k-1 Input estimate X of model j at time 0j (t k-1 )，P 0j (t k-1 ) (ii) a Substituting into the sequential filter of the current model, and performing filtering treatment to obtain
Represents the pseudo-metric estimated state of model j, P ε,j (t k ) Representing the pseudo metrology estimation error covariance of model j;
step 10: calculating the model update probability mu j (t k )
Model j at t k Update probability mu of time j (t k ) Expressed as the position measurement model probability mu p,j (t k ) Probability mu of sum pseudo measurement model ε,j (t k ) The mean value of (a);
whereinThe superscript j represents the motion model, p represents the information related to position measurement, and epsilon represents the information related to pseudo measurement; likelihood function Λ of each filter p,j (t k ),Λ ε,j (t k ) The calculation formula is as follows:
where e is the measurement residual, S is the autocorrelation matrix of the residual, C p,j And C ε,j Respectively representing the position measurement and the pseudo measurement normalization constant of the model j;
step 11: state estimation fusion
Mixing t obtained in step 9 k Sequential filtering estimation of time instants
And the model update probability mu j (t k ) Performing fusion
Wherein,
representing the final filter estimate state, P (t) k ) Representing the final filtered estimation error covariance;
step 12: filtering results of each model
P p,j (t k ) The next time t is calculated by the equation (24) in step 8 k+1 State estimates and covariance of each model filter input.
2. The method for tracking the co-located MIMO radar target based on joint time and space resource management as claimed in claim 1, wherein the specific method in step 3.1 is as follows:
the stored space-time parameter xi of the first group l The predicted signal-to-noise ratio is calculated according to the following formula
Wherein p is t Peak power for a single antenna of the radar; eta A Is the aperture efficiency of the antenna; σ is the target cross-sectional area representation, λ is the signal wavelength, N 0 For noise power spectral density, τ B For the time of the beam dwell time,
representing the radial predicted distance of the target to the radar.
3. The method for tracking the co-located MIMO radar target in combination with time and space resource management according to claim 1, wherein the calculation method of the partial symbols in the step 7 is as follows:
in the formula,
is composed of
The position and speed in the abscissa direction and the position and speed in the ordinate direction of the corresponding target prediction in the target prediction system,
representing the correlation coefficient between the predicted distance and the predicted radial velocity, matrix
J is the form
Wherein P is xx Representing the predicted position error variance in the x-direction for model j,
represents the error covariance of the predicted position and velocity in the x-direction for model j,
represents the predicted speed error variance in the x-direction for model j; by analogy, the covariance of the position and the speed in the y direction is obtained
And
similarly, the covariance of the predicted position and velocity errors in the x-and y-directions can be obtained
And
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