CN114114240B - Three-dimensional target tracking method and device of ultra-sparse array under influence of grating lobes - Google Patents
Three-dimensional target tracking method and device of ultra-sparse array under influence of grating lobes 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
- G01S13/726—Multiple target tracking
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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
- 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
- G01S7/28—Details of pulse systems
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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
- 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
- G01S7/35—Details of non-pulse systems
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Abstract
A three-dimensional target tracking method of ultra-sparse array radar under grating lobe ambiguity comprises the following steps: establishing a radar state equation and a radar measurement equation of the ultra-sparse array radar under grating lobe ambiguity; establishing a Kalman filter bank for distinguishing grating lobes and estimating the state of a target according to the radar state equation and the radar measurement equation; initializing the kalman filter bank; acquiring radar target measurement information of the ultra-sparse array radar at each moment; the Kalman filter group performs target tracking according to the initial setting value and radar target measurement information until the target tracking is finished; the influence of grating lobes is eliminated before the signal processing process is carried out, so that the angle measurement blurring phenomenon is eliminated, more accurate target azimuth estimation information is obtained, and more accurate three-dimensional target tracking is realized.
Description
Technical Field
The invention belongs to the technical field of radar data processing, and particularly relates to a three-dimensional target tracking method of an ultra-sparse array under the influence of grating lobes.
Background
Target tracking is the primary function of radar systems, while grating lobes are a factor that has a relatively large impact on the accuracy of target track estimation. The generation of grating lobes is inseparable from the design of the radar antenna itself. When there is a high requirement for the resolution of radar systems, it is often necessary to increase the antenna array aperture, which is equivalent to reducing the beam width in the array signal processing, thereby improving the accuracy of the azimuth estimation. The most intuitive method is to set the array element spacing according to the upper limit of the frequency band of the processed signal, and increase the array aperture by directly increasing the number of array elements, however, the large-area dense array element arrangement mode is too high in cost and is often difficult to realize. In order to reduce the manufacturing cost and complexity of the antenna array, only a design of sparsely arranged antenna units can be adopted, a mode of reducing the number of array elements and channels is adopted to achieve a larger array aperture with a smaller number of array elements, and the expected array performance is achieved with lower cost. However, the grating lobe effect can be caused by the larger array element spacing, and corresponding incoming waves can be generated by the grating lobes, so that the azimuth ambiguity occurs when the target is tracked, and the arrival direction of the target cannot be accurately determined. When multiple targets exist, the grating lobes of the strong targets can cause serious interference to the detection and estimation of targets with weak signal characteristics, and even weak targets can not be detected. In the three-dimensional target tracking, the azimuth angle and the pitch angle are influenced by grating lobe multivalue, and the phenomenon of angle measurement multivalue occurs.
The method commonly used for angle measurement by radar is a phase interferometer direction finding positioning technique, where the direction is obtained by comparing the phases of two antennas. The single baseline phase interference principle is shown in figure 1.
When the angle between the incoming wave direction and the normal direction is phi, the time for the plane wave front to reach the antenna unit 1 and the antenna unit 2 is first and then, and the phase difference exists on the fixed frequency signal. In order to improve the estimation accuracy of the angle of arrival, a method of increasing the base line length is generally employed. But when the base line length is greater than half a wavelength, the existence of grating lobes can not distinguish the true direction of the incoming wave, and a plurality of possible results can be generated, namelyAngle blurring phenomenon. The phase difference is an observed value with 2 pi as a blur, and the relation between the angle observed value and the actual value isWhere k is a number of unknown ambiguity values, the number of which is related to the number of grating lobes. The occurrence of this condition means that k+1 observations occur simultaneously at the same sampling point, one of which is an actual value and the other of which is a blurred value. Considering that grating lobes often appear in pairs and are symmetrically distributed on two sides of a main lobe, the value of k is often a positive number and a negative number in pairs.
Let the array element spacing be d, the wavelength be lambda, phi 0 When the main lobes correspond to angles, grating lobes with the same amplitude as the main lobes also exist in the directions corresponding to the phi. In order to avoid grating lobes, it is necessary. Assume that the target azimuth forms an included angle phi with the array s The position and width of grating lobes can be predicted according to the natural directivity function, and the m-th grating lobe appears in the azimuth of
φ m ＝arccos(cosφ s ±mλ/d),m＝1,2,…,0°＜θ m ＜180°
φ m ＝arccos(cos(2π-φ s )±mλ/d),m＝1,2,…,180°＜θ m ＜360°
Or alternatively
φ m ＝arcsin(sinφ s ±mλ/d),m＝1,2,…,-90°＜θ m ＜90°
φ m ＝arcsin(sin(2π-φ s )±mλ/d),m＝1,2,…,90°＜θ m ＜270°
When m=0, the main maximum position is the position where the other integers m in the measurement area range appear, which are grating lobe positions, and a plurality of grating lobes may exist in the measurement area. When the array element spacing is half the wavelength, i.e. d=λ/2, no grating lobes are present. When d=2λ, and the scanning range is 0. To 180. The corresponding m= -2, -1, 2, for a total of 4 grating lobes, the corresponding angle is 180.,120. ,60. ,0.. When d=3λ, there are 6 corresponding grating lobes, and so on.
When the dimension of the target position change is three-dimensional, two angles are used for representing the target position, one is azimuth angle, the other is pitch angle, and the grating lobes can generate angle measurement multi-value effects on the azimuth angle and the pitch angle.
The main processing thought of aiming at the angle measurement blurring phenomenon caused by grating lobes at present is to optimize the array element arrangement mode of a radar antenna so as to avoid the occurrence of grating lobes, and the problem of grating lobe influence is solved from the thought of directly eliminating the grating lobes. The array grating lobe influence inhibition is realized by the optimized arrangement mode of the antenna array elements, and the method comprises the following methods.
One common method is to avoid grating lobe influence caused by a sparse antenna array by using a combined array method or a means of optimizing a sparse array technology. Studies on such methods include: 1) The array elements are formed in a non-periodic arrangement mode to reduce grating lobe influence caused by the sparse array by optimizing the array surface arrangement of the antenna. The method is to make the subarray direction diagram approach to the flat-top factor direction diagram as much as possible in the electric scanning range and no energy radiation outside the scanning range, so as to disperse the energy of grating lobes again, such as to prevent the grating lobes from generating, or to break the periodicity of the array surface layout by utilizing the random arrangement of subarrays, or to break the regularity of subarrays by adopting the form of unequal interval arrangement of units, and to avoid the generation of grating lobes by adopting the receiving array and the transmitting array with different array element intervals. 2) By optimizing the sparse array, the grating lobe spectrum level is suppressed to the range meeting the requirement by using the minimum active array element number. The periodic structure of the array surface is disturbed to form an aperiodic array, and the radiation units in the array are designed into high-efficiency radiation units, and the two radiation units are organically combined to jointly inhibit grating lobes. Such methods require the design of the shape of the array, the performance against grating lobes being largely determined by the array shape.
The other method is to reduce the array sparseness in the signal processing to resist the grating lobe influence caused by the array sparseness by a virtual interpolation array element method, and to virtually design the layout of the receiving and transmitting array elements to realize more effective virtual array element numbers by reasonably designing the layout of the receiving and transmitting array elements, so that more effective array element numbers can be achieved by the method, and the grating lobe is restrained by the method of optimizing the configuration and the virtual aperture of the array. Other processing methods include a processing method suitable for splitting subarrays by combining a time-domain cross-correlation method and a spatial-domain processing method, an array sound intensity device method, a grating lobe influence suppression algorithm for a step signal, suppression of power transmission of electromagnetic waves by using a spatial filter at a grating lobe position, and the like.
The above-mentioned methods are all fundamentally solving the problems, and avoid the problems by eliminating grating lobes, however, in some cases, the occurrence of grating lobes is unavoidable, for example, a motorized distributed radar, and the radar system can be regarded as a giant antenna array with array elements arranged changed along time, and the shape of the giant antenna array is difficult to maintain in a state that grating lobes do not appear. In addition, the array element arrangement optimization is correspondingly set for specific wavelength, but the wavelength of the radar beam is not fixed, and grating lobes can be caused when the wavelength is shortened and the original array is unchanged. When grating lobes appear, the angle measurement blurring caused by the grating lobes is eliminated, and the angle measurement corresponding to the main lobe is identified, so that the radar can still realize continuous tracking of the target under the influence of the grating lobes, and higher estimation accuracy is ensured.
Disclosure of Invention
Aiming at the defects, a target tracking method based on a Kalman filter bank is provided, and the main lobe and the grating lobe corresponding angles are distinguished by utilizing different performances of the Kalman filter, so that the tracking precision is improved.
The three-dimensional target tracking method of the ultra-sparse array radar under grating lobe ambiguity is characterized by comprising the following steps:
respectively establishing a radar state equation and a radar measurement equation of the ultra-sparse array radar under grating lobe ambiguity;
establishing a Kalman filter for distinguishing grating lobes and estimating the state of a target according to the radar state equation and the radar measurement equation;
initializing the Kalman filter;
acquiring radar target measurement information of the ultra-sparse array radar at each moment;
and (3) performing target tracking according to the initial set value, the radar state equation and the radar measurement equation until the target tracking is finished.
A three-dimensional object tracking device of ultra-sparse array radar under grating lobe ambiguity, the device comprising:
the equation construction module is used for respectively establishing a radar state equation and a radar measurement equation of the ultra-sparse array radar under grating lobe ambiguity;
the Kalman filter construction module is used for establishing a Kalman filter for distinguishing grating lobes and estimating the state of a target according to the radar state equation and the radar measurement equation;
an initialization module for initializing the Kalman filter;
the measurement information acquisition module is used for acquiring radar target measurement information of the ultra-sparse array radar at each moment;
and the target tracking module is used for tracking the target according to the initial setting value and the radar target measurement information until the target tracking is finished.
The invention has the advantages that:
the angle measurement fuzzy resolution method based on the Kalman filter group is realized by utilizing a plurality of Kalman filters to respectively carry out parameter estimation on a plurality of angle measurement generated by grating lobes and main lobes together, and distinguishing the main lobe from the grating lobe according to deviation values obtained by different Kalman filters, so that the information corresponding to the main lobe is directly used by subsequent signal processing, and the influence caused by the grating lobes is avoided. According to the method, the influence of grating lobes can be eliminated before the signal processing process is carried out, so that the angle measurement blurring phenomenon is eliminated, more accurate target azimuth estimation information is obtained, and more accurate three-dimensional target tracking is realized.
Drawings
FIG. 1 is a single-base line phase interference schematic;
FIG. 2 is a schematic diagram of a system architecture;
FIG. 3 is a schematic diagram of simulation results;
Detailed Description
The invention will be further described with reference to the accompanying drawings, it being understood that the description is only for the purpose of illustrating and explaining the invention, and not for the purpose of limiting the same.
The application scene of the method is that when the grating lobes cannot be avoided, signals corresponding to the main lobes and the grating lobes are distinguished by using the Kalman filter bank, so that the influence caused by the grating lobes is eliminated before the signal processing process starts, three-dimensional target tracking is realized, and the estimation result of the target azimuth is ensured to have higher precision. The method solves the problem that the prior art lacks a corresponding method after grating lobes appear, and provides guarantee for three-dimensional target tracking of the distributed ultra-sparse array.
According to the grating lobe formation mechanism, the Kalman filter is utilized to distinguish which angle measurement is the observation value corresponding to the main lobe from the angle measurement ambiguity phenomenon, and modeling is needed to be carried out on the angle measurement ambiguity phenomenon so as to be combined with the Kalman filter. The angle measurement blurring phenomenon can be regarded as that a plurality of different measurement angles exist at the same sampling point, but in actual measurement, due to the limitation of the scanning range of the radar antenna, the number of the measurement angles existing at the same sampling point often does not meet the condition that blurring values appear in pairs, and the angle measurement blurring phenomenon has certain random distribution characteristics.
In the actual working process of the radar antenna, due to the relationship between the radar scanning range and the positions of the main lobe and the grating lobe, the following three situations may occur: 1. the measured value obtained at one sampling point contains the measured value of the corresponding main lobe, and the measured values corresponding to the grating lobes are in pairs; 2. the measured value obtained at one sampling point contains the measured value of the corresponding main lobe, and the measured values corresponding to the grating lobes do not appear in pairs; 3. the measurement taken at one sampling point does not contain a measurement of the corresponding main lobe. For the Kalman filter bank, only which main lobe is the main lobe can be distinguished, so that the target azimuth is calculated according to the main lobe information, and the target azimuth cannot be obtained from the grating lobe information, and therefore, the main lobe identification work can be completed only for the first two cases. For the third case, considering that the main lobe is required to be ensured to be always within the scanning range when the target tracking is performed, and even if the main lobe information is not available, the target tracking can be considered as impossible, so the third case is not considered in the algorithm of the application.
For radar scanning range changes, which result in changes in the number of angles of measurement, different Kalman filter sets can be constructed for different scanning ranges. Considering that the number and distribution of grating lobes can be calculated according to a related formula, the number of grating lobes contained in a scanning range can be directly calculated on the premise that a radar construction mode or a multi-radar combination distribution mode can be determined, so that the number of Kalman filters is determined, and subsequent algorithm design work is completed. In the Kalman filter estimation process, the radar scanning range should be maintained in an initial setting state, otherwise, the Kalman filter set cannot correspond to the actual situation due to the change of the scanning range, and the estimation work cannot be completed.
The Kalman filter generally used in anomaly detection is essentially an anomaly detection method based on a simulation algorithm, and the implementation flow of the method has two parts: on the one hand, residual errors occur; another aspect is the residual decision. The occurrence of the residual represents how much to represent the amount of abnormal events based on one or a set of functions built by the device model; the decision of the residual error represents the establishment of proper threshold and decision criteria to explore the source of the abnormality based on the determined residual error value, which is the basic flow of the residual error decision. The anomaly detection process based on the Kalman filter comprises the following steps: firstly, the deviation of the predicted value and the actual measured value of the Kalman filter is compared to obtain a residual signal, namely a residual Weighted Square Sum (WSSR), the quantity of which represents the quantity of abnormal states, so as to judge whether the device has faults. Secondly, evaluating based on the abnormality of residual errors, and if no abnormality exists in the device, ensuring that the residual error value of the device is in a certain small range in theory; however, if an abnormality exists, the residual error is about to have a large error, and the residual error value can be used to judge whether the abnormal condition exists or not, judge the type, the range and other related data of the abnormality, and complete the detection of the abnormality.
The method aims at the problem of abnormality detection of angle measurement multiple values, and the corresponding method is to process a Kalman filter group constructed based on Kalman filters with differences of a plurality of input information. The Kalman filter group comprises n Kalman filters, wherein the part related to the ambiguity k is removed from the augmentation state variable of each Kalman filter, n is the total number of angle measurement groups (each angle measurement group comprises an azimuth angle and a pitch angle) received by the radar, and each Kalman filter receives the detection value of 1 angle measurement group. And judging whether the main lobe or the grating lobe corresponding to any angle measurement group is the main lobe or the grating lobe through 1 Kalman filter corresponding to the main lobe or the grating lobe. After the Kalman filter bank passes through the calculation of the residual errors, n residual errors are obtained. When the ith angle measurement is the angle measurement corresponding to the main lobe, the information obtained by the ith Kalman filter does not contain interference of a fuzzy value, the estimation result is more accurate, and the residual value is approximately equal to 0. However, the angle corresponding to the other kalman filter is the angle corresponding to the grating lobe, and the estimation process is interfered by the fuzzy value, so that a certain deviation exists between the final estimation result and the measured value, and the residual value is increased due to the prediction deviation. According to the comparison of different orders of magnitude of residual values of the n Kalman filters, the minimum value can be identified, and the minimum value and the other residual values are different in orders of magnitude, so that the corresponding angle of the main lobe can be determined.
When the Kalman filter bank carries out angle measurement fuzzy processing, the value of the threshold value is the key of main lobe judgment. Setting the threshold corresponding to the WSSR can improve the probability of successful main lobe resolution on a smaller value, but because of noise interference, the probability of misjudgment is increased, the main lobe is also judged as a grating lobe, and setting the threshold on a larger value can lead to the opposite result, so that the setting of the threshold has great influence on the main lobe resolution function of the hybrid Kalman filter bank. A reasonable threshold setting mode is to establish a series of corresponding thresholds according to different measurement accuracy of radars in different monitoring areas, so that accuracy of angle measurement fuzzy processing is improved.
In the principle, the application provides a target tracking method based on a distributed sparse array under the influence of grating lobe angle measurement ambiguity, which comprises the following implementation steps:
step S00: and establishing a radar state equation under the condition that grating lobes influence exists.
When the grating lobes exist, the radar can generate a plurality of angle measurement values due to the influence of the grating lobes, different angle measurement values can correspond to different fuzzy numbers, and the state equation established does not set the fuzzy numbers because the occurrence of the fuzzy numbers does not influence the state parameters of the monitored object, and the state equation of the corresponding monitored object can be expressed as shown in the following formula
Where x, y and z are the azimuth information of the monitored object,and->For the speed components of the monitored object in the x-axis, y-axis and z-axis, +.>The state equation contains system process noise W, and the covariance matrix is
Q＝E(WW T )
Step S01: and establishing a measurement equation of the distributed array radar with grating lobes.
Parameters that the radar can measure include target distance, target speed, and multiple angulations due to grating lobes. Since it is not possible to determine which is the main lobe and which is the grating lobe at first, the angles of the multiple different lobes can be numbered, wherein the output equation corresponding to the ith lobe is
Wherein r is the monitored object or the mineThe distance between the two points is reached,is the speed of the monitored object, < >>Is the azimuth angle of the monitored object, theta is the pitch angle of the monitored object, k fw,i And k fy,i The corresponding fuzzy values of azimuth angle and pitch angle respectively, the output equation contains measurement noise W, and the covariance matrix is
R＝E(WW T )
Step S02: and establishing a Kalman filter model for distinguishing grating lobes and estimating the target state according to the state equation in the step S00 and the measurement equation in the step S01. A kalman filter is built for each angle and then a kalman filter bank is formed.
The state space model of the Kalman filter corresponding to the ith angle measurement is constructed based on the state equation described in step S00 and the measurement equation described in step S01. The structure of the Kalman filter of the angle measurement corresponding to the ith lobe is that
Wherein x is kal,i 、y kal,i And z kal,i The estimated azimuth information of the monitored target for the ith kalman filter, and->Velocity components of the monitored object in the x, y and z axes estimated for the ith Kalman filter, r kal,i Monitored object and radar estimated by Kalman filterDistance between (I) and (II)>Is the velocity of the monitored object estimated by the Kalman filter, < >>Is the azimuth angle theta of the monitored object estimated by the Kalman filter kal,i Is the pitch angle of the monitored object estimated by the Kalman filter. WSSR (Wireless sensor System) i The sum of squares is weighted for the residual between the estimated result and the measured result of the ith kalman filter. And judging which filter corresponds to the main lobe angle measurement according to the difference of residual weighted square sums calculated by different Kalman filters, thereby avoiding grating lobe influence.
As can be seen from the above equation, the two fuzzy values are not included in the augmentation state variables of the kalman filter, because if the kalman filter is used to directly estimate the fuzzy values caused by the grating lobes when tracking the three-dimensional object, the kalman filter needs to estimate five augmentation state variables including the speed corresponding to the x, y and z axes and two fuzzy values because the kalman filter has the fuzzy values, and the measurable output available for the kalman filter has only four parameters including the azimuth angle, the pitch angle, the speed and the distance, if the augmentation state variables include two fuzzy values, the parameters to be estimated are more than the input parameters of the kalman filter, so that the estimation of the kalman filter cannot be performed.
In order to distinguish the main lobe from the grating lobe without introducing an augmentation state variable, the method is adopted to indirectly embody the influence caused by the fuzzy value by using other numerical values.
The calculation of the gain matrix K in this filter is as follows. Since the gain matrix of the Kalman filter cannot be directly calculated by the nonlinear output equation, small-deviation linearization calculation is required to be performed on the nonlinear equation, so that the gain matrix is obtained
Where r is the distance between the monitored object and the radar,is the speed of the monitored object, < >>Is the azimuth angle of the monitored object, theta is the pitch angle of the monitored object, and V is the measurement noise. H is the output equation
In view of the robustness of the kalman filter, the kalman filter should meet the corresponding quadratic index, and the gain of the kalman filter needs to minimize the quadratic index. According to the extremum principle, the optimal gain matrix formula can be derived as
K＝PH T R -1
Wherein P is a time update matrix which can be calculated by a Li-Karl equation corresponding to a linear system
Where Q is the covariance matrix of the system noise W, q=e (WW T ) R is the covariance matrix of the measurement noise V, r=e (VV T )。
Since the system constituting the Kalman filter is a nonlinear system, the gain matrix K needs to be updated according to the change of the system operation state, and a specific update equation is that
P＝FPF T +Q
K＝PH T (HPH+R) -1
P＝P-KHP
Step S03: and the distributed array radar observes the target to obtain observation values of the target at all times.
Step S04: and (3) performing initial setting on the target tracking process according to the Kalman filter in the step S02 and the target radar observed value in the step S03.
The main purpose of this step is to perform an initialization setting of the kalman filter bank. Firstly, determining the number of the augmentation state variables of a Kalman filter according to the number of the angles in the received observation value; the Kalman filter is then given an initial value of a set of target information before the start of its estimation operation, and the values of the gain matrix K within the Kalman filter are calculated from the initial value.
Step S05: and (3) performing target tracking from the k moment to the k+1 moment according to the initial setting value of the step S04 and the Kalman filter bank constructed in the step S02 until the target tracking is finished.
Since the initial value cannot completely coincide with the actual state of the target, there is a certain deviation, the kalman filter needs to calculate a new estimated value in the subsequent estimation process, so that the new estimated value is continuously approximated to the observed value, and the deviation is eliminated. However, only the angle of measurement corresponding to the main lobe is not interfered by the fuzzy value, the estimated deviation of the Kalman filter corresponding to the main lobe can be minimized, the weighted residual square sum WSSR calculated by the Kalman filter corresponding to the Kalman filter is minimized in order of magnitude, and the WSSR calculated by other Kalman filters is larger in order of magnitude than the calculated result corresponding to the main lobe, so that the angle of measurement corresponding to the main lobe can be distinguished.
According to the target tracking method for the distributed sparse array when grating lobes exist, the main lobes and the corresponding measuring angles of the grating lobes can be distinguished, and accurate target information can be obtained.
In practical application, as shown in fig. 2, a certain distributed base radar system can be regarded as a large sparse antenna array, and due to the influence of grating lobes, a target signal received by the radar system comprises a plurality of different angles, a kalman filter estimates the target azimuth and the fuzzy number according to the received information, and when the estimated information of the filter has higher matching degree with an observed value, the state parameters estimated by the filter can accurately reflect the current state of an object.
The method is verified by simulation experiments. The tracked target in the simulation runs at a fixed rate, while the radar keeps track of the target. Pair in simulationAnd->Process noise interference with a mean square error of 0.05 is applied, measurement noise interference with a mean square error of 1 is applied to the distance r, the azimuth angle +.>And the pitch angle θ is applied with a measurement noise disturbance with a mean square error of 0.05, and the velocity V is applied with a measurement noise disturbance with a mean square error of 0.05. The Kalman filter bank needs to process angle measurement ambiguity under noise interference, resolve the angle measurement corresponding to the main lobe and the grating lobe, and effectively locate and track the target.
As can be seen from fig. 3 corresponding to the simulation result, the WSSR calculated by the kalman filter based on the main lobe information is significantly smaller than the WSSR obtained based on the grating lobe information, and which is the main lobe is determined according to the difference of the WSSRs, so that the influence of the grating lobes is avoided. Because no interference of the fuzzy value exists, the estimation result of the Kalman filter corresponding to the main lobe is more accurate, the deviation is smaller, the corresponding WSSR is closer to 0, the WSSR value calculated by the Kalman filter corresponding to the grating lobe is larger, and through the difference, which is the angle measurement corresponding to the main lobe can be judged from a plurality of angle measurement.
Finally, it should be noted that: the foregoing is merely illustrative of the present invention and is not to be construed as limiting thereof, and although the present invention has been described in detail, it will be apparent to those skilled in the art that modifications may be made to the foregoing embodiments, or equivalents may be substituted for elements thereof. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The three-dimensional target tracking method of the ultra-sparse array radar under grating lobe ambiguity is characterized by comprising the following steps:
respectively establishing a radar state equation and a radar measurement equation of the ultra-sparse array radar under grating lobe ambiguity;
establishing a Kalman filter for distinguishing grating lobes and estimating the state of a target according to the radar state equation and the radar measurement equation;
initializing the Kalman filter;
acquiring radar target measurement information of the ultra-sparse array radar at each moment;
performing target tracking according to the initial set value, the radar state equation and the radar measurement equation until the target tracking is finished;
the radar state equation of the ultra-sparse array radar under the condition of grating lobe ambiguity is established,
the radar state equation satisfies the following relation:
where x, y and z are the azimuth information of the monitored object,and->For the speed components of the monitored object in the x-axis, y-axis and z-axis, +.>The state equation contains system process noise W;
the radar measurement equation satisfies the following relation: the output equation corresponding to the ith lobe is
Where r is the distance between the monitored object and the radar,is the speed of the monitored object, < >>Is the azimuth angle of the monitored object, theta is the pitch angle of the monitored object, k fw,i And k fy,i The fuzzy values corresponding to the azimuth angle and the pitch angle respectively, and the output equation comprises measurement noise V;
the Kalman filter satisfies the following relation: establishing a Kalman filter group, wherein each filter corresponds to one angle measurement, and the nonlinear Kalman filter corresponding to the angle measurement of the ith lobe constructed in the filter group has the structure that
Wherein x is kal,i 、y kal,i And z kal,i The estimated azimuth information of the monitored target for the ith kalman filter, and->Velocity components of the monitored object in the x, y and z axes estimated for the ith Kalman filter, r kal,i Is the distance between the monitored object and the radar estimated by the Kalman filter,/and the radar>Is the velocity of the monitored object estimated by the Kalman filter, < >>Is the azimuth angle theta of the monitored object estimated by the Kalman filter kal,i Is the pitch angle of the monitored object estimated by the Kalman filter, and WSSR i And judging which filter corresponds to the main lobe angle measurement according to the difference of the residual weighted square sums calculated by different Kalman filters, so as to avoid grating lobe influence, wherein K is a gain matrix.
2. The method of claim 1 wherein the gain matrix K in the filter is calculated by, for a nonlinear output equationPerforming small deviation linearization calculation to obtain
Where r is the distance between the monitored object and the radar,is the speed of the monitored object, < >>Is the azimuth angle of the monitored object, theta is the pitch angle of the monitored object, V is the measurement noise, H is the corresponding linearization parameter matrix,
where H is the output equationIs a deviator of (a)The number matrix and the gain matrix formula are as follows
K＝PH T R -1
Wherein P is a time update matrix calculated by a Li-Carl equation corresponding to a linear system
Where Q is the covariance matrix of the system noise W, q=e (WW T ) R is the covariance matrix of the measurement noise V, r=e (VV T )。
3. The method of claim 2, wherein the gain matrix K is updated according to a change in system operating conditions, the update equation being P = FPF T +Q
K＝PH T (HPH+R) -1
P=P-KHP。
4. The method according to claim 1, wherein the number of the augmented state variables of the kalman filter is first determined according to the number of angles in the received observations when the kalman filter bank is initialized; the Kalman filter is then given an initial value of a set of target information before the start of its estimation operation, and the values of the gain matrix K within the Kalman filter are calculated from the initial value.
5. The method of claim 4, wherein the angles of the main lobe are not disturbed by the fuzzy values, the residual weighted sum of squares WSSR calculated by the corresponding kalman filter is smallest in magnitude, and the WSSRs calculated by other kalman filters are larger in magnitude than the results of the calculation corresponding to the main lobe, so as to distinguish the angles of the main lobe.
6. A three-dimensional object tracking device under grating lobe ambiguity for an ultra-sparse array radar employing the method of claim 1, said device comprising:
the equation construction module is used for respectively establishing a radar state equation and a radar measurement equation of the ultra-sparse array radar under grating lobe ambiguity;
the Kalman filter construction module is used for establishing a Kalman filter for distinguishing grating lobes and estimating the state of a target according to the radar state equation and the radar measurement equation;
an initialization module for initializing the Kalman filter;
the measurement information acquisition module is used for acquiring radar target measurement information of the ultra-sparse array radar at each moment;
and the target tracking module is used for tracking the target according to the initial set value, the radar state equation and the radar measurement equation until the target tracking is finished.
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