CN113204019B - Passive high-speed intersection target direct orbit determination method and system - Google Patents
Passive high-speed intersection target direct orbit determination method and system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/505—Systems of measurement based on relative movement of target using Doppler effect for determining closest range to a target or corresponding time, e.g. miss-distance indicator
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
- G01S13/583—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets
- G01S13/584—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets adapted for simultaneous range and velocity measurements
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- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention provides a passive high-speed intersection target direct orbit determination method and a system, wherein the method comprises the following steps: obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target; performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot; and obtaining a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model. The method solves the problem that the traditional algorithm for positioning the target track based on Doppler frequency and phase difference is limited by priori knowledge by positioning the track of the high-speed intersection target movement, and improves the accuracy of positioning the target track in a passive high-speed intersection scene.
Description
Technical Field
The invention relates to the technical field of target orbit determination, in particular to a passive high-speed intersection target direct orbit determination method and system.
Background
The hit precision of the missile is a primary index for realizing 'acupoint pressing' accurate hit, and the hit precision is realized and improved, and accurate and quantitative evaluation is required by depending on a range test. For this reason, in missile design verification, qualification sizing, production wholesale inspection and training-equipped range tests, it is necessary to measure the end trajectory of the missile relative to the target, i.e., to measure vector miss distance, to guide development, assessment performance, inspection quality and to evaluate training level.
The active radar is arranged on the target to directly measure the relative trajectory, so that the method is not limited by the range and meteorological conditions, and is the most widely applied technical means for measuring off-target at present. However, the measured missile is a body with larger geometric dimension, but is not an ideal point scattering source, and is limited by factors such as electromagnetic scattering characteristics of a body target, and the accuracy is further improved by adopting a vector off-target measuring method of the active radar, so that the off-target measuring accuracy of deep sub-meter level is very difficult to realize. Considering that a telemetry transmitter is usually arranged on a tested missile, the telemetry transmitter can be considered to passively receive telemetry transmission signals of a tested target, and the signal processing is carried out on the telemetry transmission signals to realize passive radio vector off-target measurement. The method can simplify the target-carrying equipment, and more importantly, avoids the main limiting factors of the measuring precision of the active radar, namely the physical dimension of the measured target and the electromagnetic scattering characteristic of the body target. In addition, the received telemetry signal has high signal-to-noise ratio, so that the measurement accuracy of the vector off-target quantity can be greatly improved.
In the existing scheme, some research results have been presented for the single-station passive orbit determination problem, and the main idea is to use information such as the implicit doppler frequency and the Angle Of Arrival (AOA) in the received signal to realize the orbit determination. However, the existing single-station passive orbit determination method firstly tries to extract intermediate information such as an arrival phase difference, a pseudo Doppler frequency and the like from an observed signal, and then uses the relationship between the intermediate information and the track parameter of a measured target to realize track determination, and the method often has the problem that the pseudo Doppler frequency is difficult to accurately extract, so that the existing single-station passive orbit determination method has lower precision and even fails. Therefore, a need exists for a passive method and system for direct tracking of high-speed meeting targets that addresses the above-described issues.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a passive high-speed intersection target direct track-fixing method and system.
The invention provides a passive high-speed intersection target direct track-fixing method, which comprises the following steps:
obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target;
performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot;
and obtaining a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
According to the method for directly tracking the passive high-speed intersection target provided by the invention, the complex baseband signal in each observation time slot is obtained based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target, and the method comprises the following steps:
acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal;
and carrying out quadrature receiving processing on the telemetry receiving array vector signals through the nominal telemetry carrier frequency to obtain complex baseband signals in each observation time slot.
According to the passive high-speed intersection target direct orbit determination method provided by the invention, the complex baseband discrete sampling sequence is as follows:
r k ＝β k A k (p 0 ,v)s k +n k k＝0,...,K-1；
wherein r is k Representing the complex baseband discrete sample sequence, beta, in the kth observation time slot k Representing the complex propagation coefficient of the signal arriving at the observation station in the kth observation time slot, A k (p 0 V) an array response vector representing the arrival of a signal at an observation station in the kth observation time slot, s k A complex envelope representing the arrival of the signal at the observation station in the kth observation time slot, n k Representing observed noise.
According to the method for directly tracking the passive high-speed intersection target provided by the invention, the track parameter estimation result of the measured target is obtained according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model, and the method comprises the following steps:
estimating the motion trail of the detected target to obtain an estimated trail of the detected target;
respectively carrying out grid division on the estimated existence domain of the initial position and the estimated existence domain of the speed of the detected target according to the estimated track by a grid search method, and obtaining a cost function value corresponding to each grid node by the intersection target track parameter estimation model;
and taking the track parameter corresponding to the grid node when the cost function value is the maximum as the track parameter estimation result of the measured target.
According to the passive high-speed intersection target direct orbit determination method provided by the invention, the intersection target track parameter estimation model is as follows:
wherein p is 0 Representing the initial position of the object to be measured, v representing the velocity of the object to be measured,and K represents the kth observation time slot, and the K observation time slots are all formed by a Doppler discrete change sequence reconstructed by unknown track parameters of a measured target, an array response vector and a complex baseband discrete sampling sequence.
According to the passive high-speed intersection target direct orbit determination method provided by the invention, the method further comprises the following steps:
PCM-FM signals transmitted by telemetry transmitters of the object under test are received by a single observation station.
The invention also provides a passive high-speed intersection target direct track-fixing system, which comprises:
the signal processing module is used for obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured object;
the signal sampling module is used for carrying out snapshot sampling on the complex baseband signal to obtain a complex baseband discrete sampling sequence in each observation time slot;
and the orbit determination module is used for acquiring the track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
According to the passive high-speed intersection target direct orbit determination system provided by the invention, the signal processing module comprises:
the signal receiving unit is used for acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal;
and the signal orthogonal processing unit is used for carrying out orthogonal receiving processing on the telemetry receiving array vector signals through nominal telemetry carrier frequency to obtain complex baseband signals in each observation time slot.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the passive high-speed meeting target direct tracking method as any one of the above when executing the program.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of a passive high-speed rendezvous target direct tracking method as described in any of the above.
According to the passive high-speed intersection target direct orbit determination method and system, the problem that the traditional algorithm for target orbit positioning based on Doppler frequency and phase difference is limited by priori knowledge is solved by positioning the tracks of the high-speed intersection targets, and the accuracy of target orbit positioning in a passive high-speed intersection scene is improved.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a passive high-speed meeting target direct track-fixing method provided by the invention;
FIG. 2 is a schematic view of an observation scene provided by the present invention;
FIG. 3 is a schematic diagram of a position vector parameter estimation result provided by the present invention;
FIG. 4 is a schematic diagram of a speed vector parameter estimation result provided by the present invention;
FIG. 5 is a schematic diagram of scalar parameter estimation results provided by the present invention;
FIG. 6 is a schematic diagram of a simulation result of a track provided by the present invention;
FIG. 7 is a schematic diagram of a simulation result of the track two provided by the present invention;
FIG. 8 is a schematic diagram of a trace three simulation result provided by the present invention;
FIG. 9 is a schematic diagram of a simulation result of telemetry parameters provided by the present invention;
FIG. 10 is a schematic diagram of a telemetry parameter two-simulation result provided by the present invention;
FIG. 11 is a schematic diagram of a telemetry parameter three-simulation result provided by the invention;
FIG. 12 is a schematic diagram of a passive high-speed meeting target direct tracking system according to the present invention;
fig. 13 is a schematic structural diagram of an electronic device provided by the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Pulse code modulation-frequency modulation (PCM-FM) telemetry is a type of continuous phase modulation signal that has a dramatic change in doppler frequency in high speed convergence scenarios, further enhancing the non-stationary nature of the telemetry received signal. Therefore, the premise of accurately acquiring the implicit pseudo Doppler frequency information in the telemetry receiving signal is that the telemetry parameter of the transmitting end is known in advance, then the local regenerated modulation signal which does not contain Doppler frequency is accurately demodulated and reconstructed at the receiving end, and finally Doppler frequency information is extracted by using the demodulation result. In practical application, because telemetry parameters cannot be completely known, the delay alignment effect in the demodulation reconstruction or demodulation process is not ideal, doppler frequency information cannot be accurately extracted, and therefore the accuracy of the existing single-station passive orbit determination method based on Doppler frequency and phase difference information is reduced or even fails. Based on the above, the invention combines the direct positioning idea, and provides a direct orbit determination method (Direct Trajectory Determination, DTD for short) for realizing target track determination by utilizing a single static observation station. Assuming that the speed and the initial position of the high-speed intersection target are unknown, reconstructing an expected observation signal by constructing a Doppler frequency-phase difference change sequence containing the two unknown parameters, and establishing a least square model by combining an actual observation signal, thereby directly determining the track of the measured target. The invention starts from analyzing a PCM-FM observation data model, theoretically deduces the condition of unknown signal waveform, and determines the optimizing cost function of the DTD and the lower boundary of the Clamamaro.
Fig. 1 is a schematic flow chart of a passive high-speed intersection target direct track-fixing method provided by the invention, and as shown in fig. 1, the invention provides a passive high-speed intersection target direct track-fixing method, which comprises the following steps:
step 101, obtaining complex baseband signals in each observation time slot based on PCM-FM signals transmitted by a telemetry transmitter on a measured object.
In the present invention, PCM-FM signals transmitted by telemetry transmitters on a target under test are received by a single observation station. Fig. 2 is a schematic view of an observation scene provided by the present invention, as shown in fig. 2, in an actual application scene, only one stationary observation station is used for determining a track of a measured object. The antenna array element placement position of the observation station can be shown by referring to fig. 2, the antenna array element placement position starts to rotate clockwise from the upper left corner, the antenna array element 1, the antenna array element 2 and the antenna array element 3 are marked as array element intervals in sequence, the antenna array element 1 is defined as a reference array element, and the antenna array element is positioned at the origin of a coordinate system; the connection line between the reference array element and the target and the plane (namely the XOY plane) where the observation station is positioned are marked as beta; the projection of the connecting line between the reference array element and the target on the plane (XOY plane) of the observation station is recorded as alpha with the positive angle of the X axis; initial position p of intersecting object (i.e. measured object) at zero time of observation 0 ＝[x 0 y 0 z 0 ] T Speed v= [ v x v y v z ] T . Then under the condition of uniform linear motion, the track equation of the measured object is:
p t ＝p 0 +vt； (1)
wherein p is t And the spatial position of the measured object at the time t is represented. In the invention, the carrier frequency of the PCM-FM signal of the telemetry transmitter of the measured object is f c The maximum modulation frequency deviation is delta f max Then at time t, the telemetry transmit signal is:
wherein A is c For the amplitude of the transmitted signal, m (τ) is the signal of pulse code modulation (Pulse Code Modulation, PCM) serial code pre-filtered by a shaping filter,is the initial phase of the carrier.
Further, the obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured object specifically includes:
and acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal.
In the present invention, the telemetry signal is considered to be a plane wave when arriving at the observation station, i.e. the complex envelopes of the elements of the telemetry signal arriving at the observation station at the same time are the same. The telemetry receiving array vector signals of the observation station are:
wherein s is r (t) represents a telemetry receiving array vector signal of the observation station at time t, | x I 2 Representing euclidean norms, beta t Representing the complex propagation coefficient, alpha, of the signal arriving at the observation station at time t t (p 0 V) an array response vector representing the arrival of the signal at the observation station at time t, A r In order to receive the signal amplitude,is the initial phase of the received signal; />The propagation delay of a transmitted signal from a transmitting antenna to a receiving antenna is represented, where R (t) is the distance from the telemetry transmitting antenna to the receiving antenna of the observation station and c is the propagation velocity of the electromagnetic wave.
Further, orthogonal receiving processing is carried out on the telemetry receiving array vector signals through the nominal telemetry carrier frequency, and complex baseband signals in each observation time slot are obtained.
In the present invention, the received telemetry receive array vector signal s is at the nominal telemetry carrier frequency r (t) performing quadrature reception processing, the resulting complex baseband signal can be expressed as:
wherein A is B For the amplitude of the complex baseband signal,is the initial phase of the complex baseband signal; Δf is the actual telemetry transmission carrier frequency f c With a nominal set telemetry receiver local frequency f c The difference between', Δf=f c -f c ′；/>Representing the doppler frequency shift caused by radial motion between the object under test and the observation station. In the invention, an observation station is set to observe the intersection target K times, the duration T of the observation time slot is short enough to meet the assumption that the position and the speed of the intersection target in a single observation time slot are kept unchanged, and the complex propagation coefficient beta of the signal reaching the observation station in the kth observation time slot k And array response vector alpha k (p 0 V) is unchanged, combining equation (8) and equation (9), complex baseband signal r in kth observation time slot k (t) can be expressed as:
p k ＝p 0 +vT(k-1)； (15)
wherein s is k (t) is the complex envelope of the signal arriving at the observation station in the kth observation time slot, p k For the position of the intersection target in the kth observation time slot, n k And (t) is observation noise.
Step 102, performing snapshot sampling on the complex baseband signal to obtain a complex baseband discrete sampling sequence in each observation time slot.
In the present invention, if the signal is sampled N times in each observation time slot, i.e. sampling intervalThe complex baseband discrete sample sequence within the kth observation time slot can be expressed as:
wherein,the following matrices are now defined:
wherein,representing Kronecker product, diag represents vector diagonalization operations, whereby, based on equations (17) and (18), the complex baseband discrete sample sequence within each observation time slot can be expressed as:
r k ＝β k A k (p 0 ,v)s k +n k k＝0,...,K-1； (19)
wherein r is k Representing the complex baseband discrete sample sequence, beta, in the kth observation time slot k Representing the complex propagation coefficient of the signal arriving at the observation station in the kth observation time slot, A k (p 0 V) an array response vector representing the arrival of a signal at an observation station in the kth observation time slot, s k A complex envelope representing the arrival of the signal at the observation station in the kth observation time slot, n k Representing observed noise.
Step 103, obtaining the track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
In the present invention, the problem of determining the trajectory of a high-speed meeting target can be summarized as how to obtain the data from a given observation r k (namely, the complex baseband discrete sampling sequence in each observation time slot) directly extracts the track parameter information such as the initial position, the speed and the like of the measured object. Let the observation noise n k Independent of the signal and obeys zero-mean Gaussian distribution, and has a power sigma 2 The maximum likelihood criterion is then equivalent to the least squares criterion, with respect to the observed quantity r k The logarithmic form of the maximum likelihood function of (2) is:
the problem of estimating the trajectory parameters for the meeting target can be converted into the following optimizing model:
due to beta k Sum s k The method does not contain the track information of the detected target and does not lose generality k || 2 =1. When order f 1 (p 0 V) maximum, the complex propagation coefficient beta k Least squares estimation of (2)
Will beCarrying out formula (20) to obtain:
due to only A k (p 0 V) includes information on the position and velocity of the object to be measured, thereby letting f 1 (p 0 V) maximizing the equivalent of f 2 (p 0 V) minimization of:
wherein,
in the present invention, since the signal waveform is unknown, f 2 (p 0 The maximization of v) is equivalent to s k Maximization of quadratic form, i.e. the problem of optimizing equation (21) can be translated into finding Θ k (p 0 Maximum eigenvalue problem of v):
wherein lambda is max { x } represents the maximum eigenvalue operation of taking the matrix { x }; matrix Θ k (p 0 V) is an N-dimensional square matrix, and increasing the snapshot number N means a sharp increase in the matrix eigenvalue decomposition calculation amount. To reduce the complexity of the algorithm, consider a given matrix X ε C N×1 ，XX H And X is H The non-zero eigenvalues of X agree, so equation (25) is again equivalent to:
wherein,and because only one observation station exists in the actual scene of the invention, the complex problem of solving the eigenvalue is avoided. Finally, the optimizing model for the intersection target track parameter estimation (i.e. the intersection target track parameter estimation model) is:
wherein p is 0 Representing the initial position of the object to be measured, v representing the velocity of the object to be measured,and K represents the kth observation time slot, and the K observation time slots are all formed by a Doppler discrete change sequence reconstructed by unknown track parameters of a measured target, an array response vector and a complex baseband discrete sampling sequence.
Finally, the invention utilizes the grid search method to make the track parameter { p } of the high-speed meeting target 0 Reasonable meshing of the v-possible existence domain is carried out, and the cost function value corresponding to each mesh node is calculated by combining a formula (27) so as to obtain a track parameter estimation resultI.e. the mesh node corresponding to the largest cost function value.
According to the passive high-speed intersection target direct orbit determination method, the problem that a traditional algorithm for target orbit positioning based on Doppler frequency and phase difference is limited by priori knowledge is solved by positioning the trajectories of the high-speed intersection targets, and the accuracy of target orbit positioning in a passive high-speed intersection scene is improved.
On the basis of the above embodiment, the obtaining, according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model, the track parameter estimation result of the measured target includes:
and estimating the motion trail of the detected target to obtain an estimated trail of the detected target.
Respectively carrying out grid division on the estimated existence domain of the initial position and the estimated existence domain of the speed of the detected target according to the estimated track by a grid search method, and obtaining a cost function value corresponding to each grid node by the intersection target track parameter estimation model;
and taking the track parameter corresponding to the grid node when the cost function value is the maximum as the track parameter estimation result of the measured target.
In the invention, motion track parameters of a detected target are estimated based on other priori information, a grid search method is combined to carry out grid division on a possible existence domain (namely, an estimated existence domain) of the initial position and the speed of the detected target, a track parameter estimation model of the intersection target is utilized to calculate a cost function value corresponding to each grid point, and finally, track parameters corresponding to grid nodes when the value of the cost function is maximum are selected to be used as track parameter estimation results of the detected target. The specific algorithm flow is as follows:
step 201, orthogonal receiving the telemetry signal according to the nominal carrier frequency, and combining and arranging the sampling sequence of each observation time slot through formulas (10) to (19) to obtain a complex baseband discrete sampling sequence r k ；
Step 202, partitioning a search grid. In particular, trajectory parameter p for high-speed meeting target 0 V may have domain reasonable grid division, and grid nodes consisting of six-dimensional parameters are respectively marked as g 1 ，…g i ,…g I Let i=1;
step 203, calculating the grid node g by using the formulas (9) to (15) i Array response vector α at the kth observation time slot, respectively k (p 0 V) and Doppler shift
Step 204, combining equation (18), equation (24) andequation (26), calculate
Step 205, computing grid node g according to equation (27) i Is set according to the objective function value of (1);
step 206, if I is less than I, let i=i+1, and return to step 203; otherwise, go to step 207;
step 207, obtaining an objective function Γ (p 0 V) maximum value, wherein the maximum value point corresponds to six-dimensional parameters of the grid node, namely the estimation result of the track parameters of the high-speed intersection target
In order to verify the performance of the algorithm provided by the invention, in an embodiment, the root mean square error and the Lower boundary of the Kramer of 200 Monte Carlo simulation results of target motion parameter estimation under different signal-to-noise ratio conditions are given in comparison, wherein the deriving process of the Lower boundary of the Kramer-Rao Lower Bound (CRLB) of the target track parameter estimation variance under the Gaussian noise distribution condition is specifically as follows:
in the case of unknown signal waveforms, an unknown parameter vector is defined in conjunction with equation (17)Wherein:
re and Im represent the real and imaginary operations, respectively. Thus, the fischer information matrix (Fischer Information Matrix, FIM) under the observation model of the present invention can be expressed as:
in the present invention, the noise and signal phase are observedIndependent of each other, the signal complex envelope s of each snapshot k [n]Independent of each other, the complex propagation coefficient beta between the observation gaps k Independent of each other, then [ i, j ] of the FIM matrix]The following elements:
wherein [ (x)] i Representing the taken vector [ x ]]Is the i-th element of (c). In a block matrixThe derivation process of (2) is as example:
wherein,
combining equations (4) through (9) and equations (11) through (16) may be derived:
for velocity v= [ v x v y v z ] T The bias derivation process of (a) is similar to the formulae (a.4) to (a.6), and will not be repeated. In addition, according to the formulas (a.1) to (a.3), the complex envelope s k [n]Complex propagation coefficient beta k The bias derivatives can be obtained by respectively:
bringing formulas (a.3) to (a.7) into formula (a.2) can obtain each element of the FIM matrix J, thereby obtaining the CRLB lower bound of the estimation variance of the target track parameter in the observation scene of the invention:
wherein [ (x)] lu6 Representative matrix]The upper left 6 main diagonal elements operate as row vectors.
After the completion of the above-described derivation of the lower bound of the cladoceram, further simulation verification was performed. Signal to noise ratio snr=a of the present invention B 2 /(2σ 2 ) The statistical root mean square error (Root Mean Square Error, abbreviated RMSE) is defined as:
wherein, the true value x epsilon { p } 0 Estimated value of each Monte Carlo simulation experimentC is the Monte Carlo simulation times.
The simulation scenario can be shown with reference to FIG. 2, in which the initial position p of the object under test 0 ＝[-225 440 315] T Target speed v= [ 1175-2250-1575 ]] T Telemetry carrier wave f c =2.3 GHz, carrier deviation Δf=1 kHz, sampling frequencyThe number of observation gaps k=7, and the number of shots n=100 in each observation gap.
FIG. 3 is a schematic diagram of the estimation result of the position vector parameter provided by the present invention, the position vector p 0 The three-dimensional distance-wise estimation of root mean square error as a function of signal-to-noise ratio is shown with reference to fig. 3. Fig. 4 is a schematic diagram of a speed vector parameter estimation result provided by the present invention, and the root mean square error of the speed vector v estimation is changed along with the signal to noise ratio, which can be referred to as fig. 4. FIG. 5 is a schematic diagram of the scalar parameter estimation result provided by the present invention, and the scalar position distance p 0 || 2 And scalar speed v 2 The estimated root mean square error as a function of signal to noise ratio is shown with reference to fig. 5. As can be seen from fig. 3 to 5, when SNR is less than or equal to-5 dB, the root mean square error of the six-dimensional parameter estimation with respect to the target track positioning deviates far from CRLB, indicating that the accuracy of the target track positioning by using DPD algorithm in combination with Shan Zhanchang scene is poor when the signal-to-noise ratio is low. Generally, as the signal-to-noise ratio increases, the performance of the DPD algorithm gradually approaches the CRLB, and when the SNR is more than or equal to 0dB, the performance of the DPD algorithm is basically consistent with the CRLB.
Further, the miss distance of the present invention is defined herein as the Euclidean distance from the intersection of the target trajectory and the observation station plane to the reference element. In order to verify the applicability of the algorithm, three tracks are respectively given for comparison simulation according to different miss distance and different speeds, and track parameters are shown in table 1:
TABLE 1
| Project | Initial position p 0 (m) | Velocity vector v (m/s) | Scalar speed v 2 (m/s) | Scalar miss distance (m) |
| Track one | [-135；325；240] | [780；-1400；-1200] | 2002 | 50 |
| Track two | [-200；260；150] | [1120；-800；-600] | 1501 | 100 |
| Track three | [-165；595；345] | [1200；-2250；-1575] | 2997 | 141 |
Other simulation conditions are unchanged, FIG. 6 is a schematic diagram of a simulation result of a track one provided by the invention, FIG. 7 is a schematic diagram of a simulation result of a track two provided by the invention, FIG. 8 is a schematic diagram of a simulation result of a track three provided by the invention, scalar position distances P corresponding to different tracks 0 || 2 And scalar speed v 2 The estimated root mean square error statistics are referred to in fig. 6, 7 and 8, respectively. Therefore, the CRLB is sensitive to the track parameters, but the track parameter estimation can be obtained accurately in theory as long as the track determination is carried out by utilizing the intersection section observation data with obvious fluctuation of Doppler frequency change. Meanwhile, under the condition of small signal-to-noise ratio, the estimation accuracy of the algorithm for track parameters under the condition of high speed and large off-target amount can be reduced, and when the SNR is more than or equal to 2dB, the estimation performance of the algorithm is close to CRLB under the condition of different off-target amounts and different speeds, and the algorithm has good applicability.
Likewise, three sets of telemetry parameters are given in Table 2, respectively, according to different telemetry parameters:
TABLE 2
| Project | Code rate (Mbps) | Frequency offset deltaf (kHz) | Modulation index |
| Telemetry parameter one | 10 | 1 | 0.7 |
| Telemetry parameter two | 5 | 10 | 0.3 |
| Telemetry parameter three | 2 | 10 | 0.7 |
The track parameters and other simulation conditions are unchanged, fig. 9 is a schematic diagram of a simulation result of a telemetry parameter one provided by the invention, fig. 10 is a schematic diagram of a simulation result of a telemetry parameter two provided by the invention, fig. 11 is a schematic diagram of a simulation result of a telemetry parameter three provided by the invention, and scalar position distances p corresponding to different telemetry parameters are shown as follows 0 || 2 And scalar speed v 2 The estimated root mean square error statistics are shown in fig. 9, 10 and 11, respectively. As can be seen, CRLB is insensitive to telemetry parameters, and meanwhile, when SNR is more than or equal to 0dB, the track performance of the algorithm is close to CRLB for different telemetry parameter conditions, and the algorithm has strong robustness.
The invention provides a method for realizing track positioning of high-speed intersection target motion by combining with a DPD (digital video) concept, and solves the problem that a traditional algorithm for positioning the target track based on Doppler frequency and phase difference is limited by priori knowledge. By combining with the actual engineering problem, the CRLB for target track six-dimensional parameter estimation under the unknown condition of the signal waveform is theoretically deduced, and simulation verifies that the performance of the algorithm provided by the invention is basically consistent with that of the CRLB under the condition that the SNR is more than or equal to 2dB, so that the algorithm can be used for solving the target track positioning problem under the passive high-speed intersection scene, and simultaneously, a better estimation result can be obtained.
Fig. 12 is a schematic structural diagram of a passive high-speed intersection target direct orbit determination system provided by the present invention, as shown in fig. 12, the present invention provides a passive high-speed intersection target direct orbit determination system, which includes a signal processing module 1201, a signal sampling module 1202 and an orbit determination module 1203, wherein the signal processing module 1201 is configured to obtain a complex baseband signal in each observation time slot based on PCM-FM signals transmitted by a telemetry transmitter on a measured target; the signal sampling module 1202 is configured to perform snapshot sampling on a complex baseband signal to obtain a complex baseband discrete sampling sequence in each observation time slot; the orbit determination module 1203 is configured to obtain an estimation result of the track parameter of the measured object according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
According to the passive high-speed intersection target direct orbit determination system, the problem that a traditional algorithm for target orbit positioning based on Doppler frequency and phase difference is limited by priori knowledge is solved by positioning the trajectories of the high-speed intersection targets, and the accuracy of target orbit positioning in a passive high-speed intersection scene is improved.
On the basis of the above embodiment, the signal processing module includes:
the signal receiving unit is used for acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal;
and the signal orthogonal processing unit is used for carrying out orthogonal receiving processing on the telemetry receiving array vector signals through nominal telemetry carrier frequency to obtain complex baseband signals in each observation time slot.
The system provided in the embodiment of the present invention is used for executing the above method embodiments, and specific flow and details refer to the above embodiments, which are not repeated herein.
Fig. 13 is a schematic structural diagram of an electronic device according to the present invention, as shown in fig. 13, the electronic device may include: processor 1301, communication interface (communication interface) 1302, memory 1303 and communication bus 1304, wherein processor 1301, communication interface 1302, memory 1303 complete communication with each other through communication bus 1304. Processor 1301 may invoke logic instructions in memory 1303 to perform a passive high-speed rendezvous target direct tracking method, the method comprising: obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target; performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot; and obtaining a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
Further, the logic instructions in the memory 1303 described above may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-only memory (ROM), a random access memory (RAM, randomAccessMemory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the passive high-speed intersection target direct-tracking method provided by the above methods, the method comprising: obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target; performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot; and obtaining a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
In yet another aspect, the present invention further provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the passive high-speed rendezvous target direct tracking method provided in the above embodiments, the method comprising: obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target; performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot; and obtaining a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. A passive high-speed meeting target direct orbit determination method, which is characterized by comprising the following steps:
obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured target;
performing snapshot sampling on the complex baseband signals to obtain complex baseband discrete sampling sequences in each observation time slot;
acquiring a track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model;
the obtaining the track parameter estimation result of the measured target according to the complex baseband discrete sampling sequence and the intersection target track parameter estimation model comprises the following steps:
estimating the motion trail of the detected target to obtain an estimated trail of the detected target;
respectively carrying out grid division on the estimated existence domain of the initial position and the estimated existence domain of the speed of the detected target according to the estimated track by a grid search method, and obtaining a cost function value corresponding to each grid node by the intersection target track parameter estimation model;
taking the track parameter corresponding to the grid node when the cost function value is the maximum as the track parameter estimation result of the measured object;
the intersection target track parameter estimation model is as follows:
r k ＝β k A k (p 0 ,v)s k +n k k＝0,...,K-1；
wherein p is 0 Representing the initial position of the object to be measured, v representing the velocity of the object to be measured,the method comprises the steps of representing a cost function formula constructed by a Doppler discrete change sequence reconstructed by unknown track parameters of a measured target, an array response vector and a complex baseband discrete sampling sequence, wherein K represents a kth observation time slot, and the K observation time slots are altogether; r is (r) k Representing the complex baseband discrete sample sequence, beta, in the kth observation time slot k Representing the complex propagation coefficient of the signal arriving at the observation station in the kth observation time slot, A k (p 0 V) an array response vector representing the arrival of a signal at an observation station in the kth observation time slot, s k A complex envelope representing the arrival of the signal at the observation station in the kth observation time slot, n k Representing observed noise.
2. The method for direct tracking of a passive high-speed rendezvous target according to claim 1, wherein the obtaining a complex baseband signal in each observation time slot based on PCM-FM signals transmitted by telemetry transmitters on the target under test comprises:
acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal;
and carrying out quadrature receiving processing on the telemetry receiving array vector signals through the nominal telemetry carrier frequency to obtain complex baseband signals in each observation time slot.
3. The passive high-speed meeting target direct-tracking method according to claim 1, further comprising:
PCM-FM signals transmitted by telemetry transmitters of the object under test are received by a single observation station.
4. A passive high-speed meeting target direct-track-fixing system, comprising:
the signal processing module is used for obtaining a complex baseband signal in each observation time slot based on the PCM-FM signal transmitted by the telemetry transmitter on the measured object;
the signal sampling module is used for carrying out snapshot sampling on the complex baseband signal to obtain a complex baseband discrete sampling sequence in each observation time slot;
the orbit determination module is used for obtaining the orbit parameter estimation result of the measured object according to the complex baseband discrete sampling sequence and the intersection object orbit parameter estimation model;
the rail fixing module is specifically used for:
estimating the motion trail of the detected target to obtain an estimated trail of the detected target;
respectively carrying out grid division on the estimated existence domain of the initial position and the estimated existence domain of the speed of the detected target according to the estimated track by a grid search method, and obtaining a cost function value corresponding to each grid node by the intersection target track parameter estimation model;
taking the track parameter corresponding to the grid node when the cost function value is the maximum as the track parameter estimation result of the measured object;
the intersection target track parameter estimation model is as follows:
r k ＝β k A k (p 0 ,v)s k +n k k＝0,...,K-1；
wherein p is 0 Representing the initial position of the object to be measured, v representing the velocity of the object to be measured,the method comprises the steps of representing a cost function formula constructed by a Doppler discrete change sequence reconstructed by unknown track parameters of a measured target, an array response vector and a complex baseband discrete sampling sequence, wherein K represents a kth observation time slot, and the K observation time slots are altogether; r is (r) k Representing the complex baseband discrete sample sequence, beta, in the kth observation time slot k Representing the complex propagation coefficient of the signal arriving at the observation station in the kth observation time slot, A k (p 0 V) an array response vector representing the arrival of a signal at an observation station in the kth observation time slot, s k A complex envelope representing the arrival of the signal at the observation station in the kth observation time slot, n k Representing observed noise.
5. The passive high-speed meeting target direct-tracking system of claim 4, wherein the signal processing module comprises:
the signal receiving unit is used for acquiring a telemetry receiving array vector signal in each observation time slot according to the PCM-FM signal;
and the signal orthogonal processing unit is used for carrying out orthogonal receiving processing on the telemetry receiving array vector signals through nominal telemetry carrier frequency to obtain complex baseband signals in each observation time slot.
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the passive high-speed rendezvous target direct tracking method as claimed in any one of claims 1 to 3 when the computer program is executed by the processor.
7. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor performs the steps of the passive high-speed rendezvous target direct tracking method as claimed in any one of claims 1 to 3.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106507953B (en) * | 2006-05-12 | 2012-03-07 | 中国科学院国家天文台 | The passive Orbit determination of satellite and system |
| CN104270713A (en) * | 2014-09-09 | 2015-01-07 | 西北大学 | Passive type moving target track mapping method based on compressed sensing |
| CN110297234A (en) * | 2018-03-22 | 2019-10-01 | 西安航通测控技术有限责任公司 | A kind of big region passive type air target intersection measuring method of networking and system |
| CN209462366U (en) * | 2019-02-18 | 2019-10-01 | 西安汉华防务电子科技有限公司 | A kind of telemetering digital if receiver |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106507953B (en) * | 2006-05-12 | 2012-03-07 | 中国科学院国家天文台 | The passive Orbit determination of satellite and system |
| CN104270713A (en) * | 2014-09-09 | 2015-01-07 | 西北大学 | Passive type moving target track mapping method based on compressed sensing |
| CN110297234A (en) * | 2018-03-22 | 2019-10-01 | 西安航通测控技术有限责任公司 | A kind of big region passive type air target intersection measuring method of networking and system |
| CN209462366U (en) * | 2019-02-18 | 2019-10-01 | 西安汉华防务电子科技有限公司 | A kind of telemetering digital if receiver |
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