Arrow-carried phased array antenna arrow-satellite pointing angle calculation method based on Kalman filtering

Abstract

The present invention discloses a method for calculating the arrow-satellite pointing angle of an arrow-borne phased array antenna based on Kalman filtering, belonging to the field of communication of relay satellite systems, and comprising the steps of: introducing the azimuth angle, elevation angle of the arrow-satellite beam of the phased array antenna pointing to the relay satellite, the vector of the rocket pointing to the satellite in the rocket body coordinate system, and the motion attitude angle of the rocket to construct a state vector; constructing a state equation based on the Kalman filtering model and in combination with the state vector; using the optimal estimated values of the azimuth angle and elevation angle at the known time t and the motion control instructions of the rocket and the satellite or the preset motion trajectory to obtain the motion increment from time t to time t + 1, and calculating the prior values of the azimuth angle and elevation angle at time t + 1; and then in combination with the observed values at time t + 1, calculating the posterior values of the azimuth angle and elevation angle at time t + 1. Compared with the traditional method for calculating the arrow-satellite beam pointing of a phased array antenna, the method of the present invention has higher filtering accuracy and stronger anti-interference ability.

Description

Technical Field

[0001] The present invention relates to the field of communication of relay satellite systems, and more specifically, to a method for calculating the arrow-satellite pointing angle of an on-arrow phased array antenna based on Kalman filtering. Background Art

[0002] The relay satellite space-based TT&C system is a TT&C communication system that uses geostationary satellites (Tianlian satellites), ground stations, and user terminals for data relay. It mainly realizes two major functions: one is to track, telemeter, and remotely control the aircraft; the other is data relay. The telemetry data and application data that the aircraft wants to transmit to the ground are first sent to the relay satellite via the S-band and Ku / Ka-band inter-satellite links. The relay satellite then forwards them to the ground terminal station in the Ku / Ka band and performs RF demodulation and decoding processing at the terminal station. The video signal is sent to the ground user terminal or the payload control center in its original format through the communication satellite link or other broadband links. Information such as commands, voice, data, and TV that the ground wants to send to the aircraft is first collected at the ground terminal, modulated onto the Ku / Ka-band link, sent to the relay satellite, and then sent by the relay satellite to the aircraft user terminal. The communication link of ground station-relay satellite-aircraft user terminal is called the forward link (uplink), and the communication link of aircraft user terminal-relay satellite-ground station is called the return link (downlink).

[0003] The relay satellite space-based TT&C system mainly completes the following functions: 1. Transmit the telemetry information of the aircraft to the ground through the relay satellite; 2. Upload the ground safety control command to the aircraft through the relay satellite; 3. Upload the ground remote control command to the arrow through the relay satellite; 4. Conduct flight trajectory measurement and transmit the measurement results to the ground.

[0004] The relay satellite system requires that the user terminal can track the signals of the ground station and extract data during both the free flight segment and the powered flight segment of the aircraft. During the powered segment, the acceleration of the aircraft is very large, causing the carrier Doppler to reach MHz. Carrier frequency acquisition is an important part of the signal acquisition process in phase-locked tracking. Only on the premise of locking the carrier frequency acquisition can range acquisition be achieved.

[0005] The on-board user terminal of the relay satellite system is an important part of the relay satellite system. It not only has functions such as remote control, telemetry, ranging, and velocity measurement, but also can perform data relay transmission. Therefore, the quality of its performance will directly affect the system's orbit determination and tracking of the spacecraft and the quality of data communication. The main functions of the on-board user terminal of the relay satellite system are as follows: receiving and demodulating the remote control commands, ranging signals, and data transmission signals sent by the ground station; coherently forwarding the forward velocity measurement and ranging signals sent by the ground station; transmitting the data transmission signals and telemetry data of the user spacecraft back to the ground station; and being able to accept the monitoring of equipment such as data processing. The on-board user terminal of the relay satellite system usually consists of a low-gain omnidirectional antenna suitable for transmitting low data rates, a medium-gain patch array antenna for transmitting medium data rates, and a high-gain parabolic antenna or phased array antenna with beam control for transmitting high data rates. The on-board user terminal of the relay satellite system generally consists of an antenna, a receiving channel, a transmitting channel, a local oscillator source, and baseband signal processing, etc. The receiving channel includes a low-noise amplifier, a down-converter, an amplifier, a filter, and an AGC circuit to complete the down-conversion of the received signal. The transmitting channel includes an up-converter, an amplifier, a filter, and a power amplifier link to complete the up-conversion and power amplification of the forwarded signal. The local oscillator source consists of multiple phase-locked loops to provide multiple local oscillator signals required by the receiving channel and the transmitting channel. The baseband signal processing completes functions such as pseudo-code acquisition and tracking, carrier recovery, information demodulation, generation of various reverse-mode signals, and digital modulation. At the same time, the baseband signal processing also has an extremely important function: to realize the beam pointing control of the phased array antenna of the on-board user terminal of the relay satellite system. Only when the main beam of the phased array antenna is aligned with the relay satellite can the communication function of spacecraft-satellite-ground be realized.

[0006] With the development of space technology, electronic technology, and the continuous expansion of application fields, the demand for the user terminal of the relay satellite system is also increasing and improving. For each function, the volume, weight, and power consumption of the equipment should be minimized as much as possible. The usual user terminal of the relay satellite system should achieve the following: ensure stable and reliable pointing to the relay satellite, realize multi-functional integration, including the transmission of TT&C information and application data, and realize various functions of orbit determination. In addition to meeting the above functions, the user terminal of the relay satellite system also faces a complex electronic countermeasure environment, so it should have strong anti-jamming capabilities.

[0007] With the continuous development of relay satellite technology, using the on-board user terminal of the relay satellite to solve the transmission of various signals between the rocket and the ground station, forward the telecommand mission information and other data transmitted by the ground station, etc., is an ideal communication means to achieve ultra-long-distance communication and measurement and control tasks. The on-board user terminal of the relay satellite is a device installed on the rocket and serves as a direct interface between external signals and the internal equipment of the rocket. During the rocket flight, it establishes forward and backward links with the ground station through the relay satellite of the relay satellite system to complete the reception and forwarding of signals beyond the line of sight. It is connected to the command subsystem, data subsystem, and telemetry subsystem of the launch vehicle through the bus interface to complete the measurement and control and data transmission functions of the launch vehicle. In the application scenario of the on-board user terminal of the relay satellite, the capture and tracking of the relay satellite by the on-board user terminal of the relay satellite is the primary prerequisite for establishing the data link between the rocket and the satellite. The on-board user terminal of the relay satellite uses the received rocket telemetry data stream to select routes for the full-frame data as required, form the backward link data stream, and extract real-time takeoff, rocket position, and attitude information from it. According to the above information and the bound pointing constant information, calculate the beam pointing angle information of the phased array antenna to align its beam with the relay satellite and complete the two-way capture of the antenna. At the same time, it can also receive the telecommand sent by the relay satellite ground station.

[0008] The deficiency of the existing beam pointing algorithm for the on-board user terminal of the relay satellite is: low anti-interference ability. The current method is to use the real-time measured rocket position and attitude information to calculate the required beam pointing angle of the phased array antenna through coordinate transformation. Since the rocket's flight trajectory itself is not theoretical under the influence of various factors such as engine thrust deviation and wind speed during flight, there are certain deviations; theoretically, the relay satellite is in a geostationary orbit and moves synchronously with the earth, but the satellite orbit also has fluctuations; moreover, the position, attitude, and other parameters used for beam pointing calculation are measured by sensors, and there are certain measurement errors. If the error is too large, it will cause a large deviation in the calculated beam pointing angle of the phased array antenna, resulting in misalignment with the relay satellite, and ultimately leading to the inability to establish the transmission link from the rocket to the relay satellite and communication failure. In summary, due to the influence brought by the deviation of the motion orbits of the rocket and the satellite and the measurement of the rocket position and attitude parameters, using the traditional calculation method for the phased array antenna arrow-satellite pointing of the on-board user terminal will cause pointing angle deviation and may lead to the inability to establish the arrow-satellite communication link. Summary of the Invention

[0009] The purpose of the present invention is to overcome the deficiencies of the existing technology and provide a method for calculating the arrow-satellite pointing angle of the on-board phased array antenna based on Kalman filtering, which has higher filtering accuracy, stronger anti-interference ability, is easy to expand, and has good universality.

[0010] The purpose of the present invention is achieved through the following solutions:

[0011] A method for calculating the pointing angle of an on - arrow phased array antenna between the rocket and the satellite based on Kalman filtering, comprising the following steps:

[0012] S1, introduce the azimuth angle α, elevation angle β of the phased array antenna beam pointing from the rocket to the relay satellite, the vector P of the rocket pointing to the satellite in the rocket body coordinate system, and the motion attitude angle T of the rocket r , and construct the following state vector X:

[0013]

[0014] S2, based on the Kalman filter model and combined with X, construct the following state equation:

[0015]

[0016] In the formula, t is the time, is the prior estimate, is the optimal estimate of the previous moment, U(t) is the motion increment from the moment t to the moment t + 1 obtained from the motion control command of the rocket and the satellite or the preset motion trajectory, and

[0017]

[0018] In the formula, Δα is the increment of α from the moment t to the moment t + 1, Δβ is the increment of β from the moment t to the moment t + 1, ΔP is the vector increment of the rocket pointing to the satellite in the rocket body coordinate system from the moment t to the moment t + 1, and ΔT r is the increment of the rocket attitude angle from the moment t to the moment t + 1;

[0019] S3, use the known optimal estimated values of α and β at the moment t and use the motion control command of the rocket and the satellite at the moment t or the preset motion trajectory to obtain the motion increment U(t) from the moment t to the moment t + 1, and calculate the prior values of α and β at the moment t + 1 and

[0020] S4, combined with the observed values at the moment t + 1, calculate the posterior values of α and β at the moment t + 1.

[0021] Furthermore, in step S2, Δα is calculated by constructing the following state transition equation:

[0022] α(t + 1) = α(t) + Δα

[0023]

[0024] where, t is the time, α(t) is the azimuth angle at the current moment, α(t + 1) is the azimuth angle at the next moment, P z$\vec{P}(t)$ is the vector of the rocket pointing to the satellite in the Z direction in the rocket system at time $t$. y $\vec{Q}(t)$ is the vector of the rocket pointing to the satellite in the Y direction in the rocket system at time $t$. y $\Delta\vec{Q}$ is the increment of the vector of the rocket pointing to the satellite in the Y direction in the rocket system from time $t$ to the next time. z $\Delta\vec{P}$ is the increment of the vector of the rocket pointing to the satellite in the Z direction in the rocket system from time $t$ to the next time.

[0025] Furthermore, in step S2, $\Delta\beta$ is calculated by constructing the following state transition equation:

[0026] $\beta(t + 1)=\beta(t)+\Delta\beta$

[0027]

[0028] where $\beta(t)$ is the pitch angle at the current time, $\beta(t + 1)$ is the pitch angle at the next time, $\vec{P}$ z $(t)$ is the vector of the rocket pointing to the satellite in the Z direction in the rocket system at time $t$. y $\vec{Q}(t)$ is the vector of the rocket pointing to the satellite in the Y direction in the rocket system at time $t$. x $\vec{R}(t)$ is the vector of the rocket pointing to the satellite in the X direction in the rocket system at time $t$. z $\Delta\vec{P}$ is the increment of the vector of the rocket pointing to the satellite in the Z direction in the rocket system from time $t$ to the next time. y $\Delta\vec{Q}$ is the increment of the vector of the rocket pointing to the satellite in the Y direction in the rocket system from time $t$ to the next time. x $\Delta\vec{R}$ is the increment of the vector of the rocket pointing to the satellite in the X direction in the rocket system from time $t$ to the next time.

[0029] Furthermore, in step S2, $\Delta\vec{P}$ is calculated by constructing a recurrence formula for the vector $\vec{P}$:

[0030] $\vec{P}(t + 1)=\vec{P}(t)+\Delta\vec{P}$,

[0031] $\Delta\vec{p}=Rot(T(t + 1))Rot(T(t))$ -1 $\cdot\vec{P}(t)-\vec{P}(t)+Rot(T(t + 1))\cdot\Delta\vec{P}$ l

[0032] where $\vec{P}(t)$ is the direction vector of the rocket pointing to the satellite in the rocket system at time $t$, $\vec{P}(t + 1)$ is the direction vector of the rocket pointing to the satellite in the rocket system at time $t + 1$, $\Delta\vec{P}$ l is the relative motion increment between the satellite and the rocket in the launch inertial system, $Rot(T(t))$ is the rocket attitude angle rotation transformation matrix at time $t$, and $Rot(T(t + 1))$ is the rocket attitude angle rotation transformation matrix at time $t + 1$.

[0033] Further, in step S2, ΔT r is obtained from the rocket kinematic equation.

[0034] Further, in step S3, calculating the prior values of α and β at time t+1 and specifically, it is calculated by using the established state transition equation of α and the established state transition equation of β.

[0035] Further, it includes the update steps of the direction vector P and the Kalman gain K:

[0036] Update the direction vector P of the rocket pointing to the satellite and the Kalman gain K in the rocket coordinate system according to the following formula:

[0037]

[0038]

[0039] In the formula, is the prior estimation covariance, P(t) is the posterior estimation covariance at the previous moment, Q is the process noise covariance, R is the measurement noise covariance, and both the process noise and the measurement noise are Gaussian white noise; K(t+1) is the Kalman gain, and H is the observation matrix;

[0040] The optimal estimation is:

[0041]

[0042] is the optimal estimation at the current moment, Z(t+1) is the measurement value at the current moment, i.e., the observation value; finally, update the posterior estimation covariance:

[0043]

[0044] Further, for the observation matrix, H takes:

[0045] H = [I 2×2 0 2×6

[0046] where H is a 2×8 matrix, I 2×2 is a 2×2 identity matrix, and 0 2×6 is a matrix of all zeros.

[0047] Further, the calculation of the azimuth angle α and the elevation angle β of the phased array antenna's arrow-satellite beam pointing to the relay satellite includes the following steps:

[0048] By the actual installation angles α of the phased array antenna m 、β m ​Constraints are imposed and, in combination with the quadrants and directions of α and β, the specific calculation formulas for α and β from the rocket body coordinate system to the antenna coordinate system are given as follows:

[0049] Suppose the three coordinate values of the direction vector P of the rocket pointing to the satellite in the rocket coordinate system are P(x), P(y), and P(z),

[0050]

[0051]

[0052]

[0053]

[0054] From this, the theoretical calculation function of the phased array antenna rocket-satellite beam pointing angle is obtained:

[0055]

[0056] Among them, P(x), P(y), and P(z) are the direction vectors of the rocket pointing to the satellite in the rocket coordinate system. R s (x s , y s , z s ) is the satellite motion trajectory equation in the launch inertial coordinate system, and R r (x r , y r , z r ) is the rocket motion trajectory equation in the launch inertial coordinate system, is the rocket motion attitude angle equation, x s , y s , z s are the coordinates of the satellite in the launch inertial coordinate system, and x r , y r , z r are the coordinates of the rocket in the launch inertial coordinate system, are the pitch angle, yaw angle, and roll attitude angle in the rocket launch inertial coordinate system.

[0057] Furthermore, the actual installation angle β of the phased array antenna m is constrained, that is, β m is installed at 90°.

[0058] The beneficial effects of the present invention include:

[0059] (1) The method of the present invention filters out the Gaussian noise contained in the rocket and satellite motions and sensor measurements. Therefore, compared with the traditional phased array antenna rocket-satellite beam pointing calculation method, the filtering accuracy is higher and the anti-interference ability is stronger.

[0060] (2) For the method of the present invention, for different satellite and rocket motion models, the adaptability of the calculation method can be changed only by changing the input of its motion increment.

[0061] (3) If you want to filter out the Gaussian error of a higher-level model, such as the dynamic model error of a rocket, you only need to add the dynamic model of the rocket. Therefore, the method of the present invention is easy to expand and has good universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings.

[0063] Figure 1 It is the representation of each vector in the launch inertial coordinate system under the traditional method;

[0064] Figure 2 It is a schematic diagram of the specific definition of α and β under the traditional method;

[0065] Figure 3 It is the representation of each vector in the launch inertial coordinate system in the method of the embodiment of the present invention;

[0066] Figure 4 It is the flow chart of the Kalman filter system involved in the present invention;

[0067] Figure 5 、 Figure 6 It is the comparison of the measured values, true values and filtered values of the α and β angles under the Kalman filter system process. DETAILED DESCRIPTION OF THE INVENTION

[0068] All the features disclosed in all the embodiments in this specification, or all the steps in the methods or processes implicitly disclosed, except for mutually exclusive features and / or steps, can be combined and / or expanded and replaced in any way.

[0069] Kalman filtering is an algorithm that uses the state equation of a linear system to optimally estimate the system state through the system input and output observation data. Since the observation data includes the influence of noise and interference in the system, the optimal estimate can also be regarded as a filtering process. Data filtering is a data processing technique for removing noise and restoring real data. Kalman filtering can estimate the state of a dynamic system from a series of data with measurement noise when the measurement variance is known. Because it is easy to implement by computer programming and can update and process the data collected on-site in real time, Kalman filtering is currently the most widely used filtering method and has been well applied in many fields such as communication, navigation, guidance, and control.

[0070] State estimation is an important part of Kalman filtering. Generally speaking, quantitatively inferring a random quantity based on observation data is an estimation problem. Especially for the state estimation of dynamic behavior, it can realize the functions of estimating and predicting the real-time operating state. The state quantity affected by noise interference is a random quantity and its exact value cannot be measured, but a series of observations can be made on it, and based on a set of observation values, it can be estimated from a certain statistical perspective. Making the estimated value as accurately close to the real value as possible is the optimal estimate. The difference between the real value and the estimated value is called the estimation error. If the mathematical expectation of the estimated value is equal to the real value, this kind of estimation is called unbiased estimation. The recursive optimal estimation theory proposed by Kalman uses the state space description method, and the algorithm is in a recursive form. Kalman filtering can handle multi-dimensional and non-stationary random processes.

[0071] The idea of Kalman filtering can be understood as: predicting the current value using the previous optimal result, and at the same time using the observed value to correct the current value to obtain the optimal result. The Kalman filtering process can be summarized into 5 formulas, as follows.

[0072] System prediction:

[0073]

[0074]

[0075] Among them, represents the prior estimate of the system state at time K, A represents the state transition matrix, X(K - 1) represents the optimal estimate at time K - 1, B represents the control matrix, and U(K) represents the system control quantity at time K. represents the prior estimate covariance at time K, P(K - 1) represents the posterior estimate covariance at time K - 1, and Q represents the system process noise variance.

[0076] Optimal estimate:

[0077] Now that the prediction result of the current state is available, the measurement value of the current state is then collected. By combining the predicted value and the measurement value, the optimal estimated value X(K) of the current state can be obtained:

[0078]

[0079] where Kg is the Kalman gain:

[0080]

[0081] Z(K) is the measurement value at time K, H is the measurement system parameter, and R is the measurement noise covariance. So far, we have obtained the optimal estimated value X(K) in the k state. However, in order to keep the Kalman filter running continuously until the end of the system process, the covariance P(K) of X(K) in the k state also needs to be updated:

[0082]

[0083] Equations (1) to (5) are the five basic formulas of the Kalman filter.

[0084] The technical solution of the present invention aims to provide a method for calculating the arrow satellite pointing angle of an arrow-borne phased array antenna based on the Kalman filter to solve the technical problem of weak anti-interference ability of the traditional method. This method is implemented through the following steps: theoretically solving the α (azimuth angle) and β (elevation angle) of the phased array antenna beam pointing to the relay satellite; constructing a state transition matrix and establishing a Kalman filter system model based on α and β; Kalman filtering.

[0085] (1) Theoretical solution of α and β

[0086] As Figure 1 shown, given the motion equation of the rocket and the motion trajectory equation of the satellite, it can be regarded that the rocket and the satellite move strictly according to the predetermined motion trajectory equation in a short period of time.

[0087] R s (x s , y s , z s ) = s(t)

[0088] R r (x r , y r , z r ) = r(t)

[0089] And the motion attitude angle equation of the rocket:

[0090]

[0091] The satellite coordinates in the inertial system are R s, the rocket coordinates are R r , then the direction vector P of the rocket pointing to the satellite in the rocket system can be calculated through this satellite-rocket model as follows:

[0092]

[0093] where is the attitude angle rotation transformation matrix

[0094]

[0095] are respectively the pitch, yaw, and roll attitude angles of the rocket in the inertial launch state.

[0096] The specific definitions of α and β are as Figure 2 shown. α is the angle in the cross-section of the rocket, and the α angle rotates counterclockwise. The value of α is related to the rocket installation position α m . Usually, the installation position of the phased array antenna on the rocket is such that its beam normal is perpendicular to the flight direction of the rocket, and the 0° of the β angle coincides with the longitudinal axis of the rocket in the flight direction, that is, 0° to 180° is measured from the positive direction of the longitudinal axis of the rocket. In the process of solving the inverse trigonometric function (α, β) = arctg(P), the obtained results only need to be added or subtracted from the installation angle α m of the phased array antenna on the rocket to obtain the final theoretical values of α and β.

[0097] The above is the theoretical calculation process of the α and β angles by the traditional method. There are also records in the existing literature about the specific derivation process of the α and β angles. In the theoretical calculation, the difference in the technical solution of the present invention is that it combines the actual application situation and constrains the actual installation angle of the phased array antenna, that is, β m is installed at 90°. And by combining the quadrant and direction problems of the α and β angles, the specific calculation formulas of α and β from the rocket body coordinate system to the antenna coordinate system are finally given, as shown in Formulas (6) to (9).

[0098] Let the three coordinate values of the P vector be P(x), P(y), and P(z) respectively.

[0099]

[0100]

[0101]

[0102]

[0103] Thus, the calculation function of the phased array antenna satellite-rocket beam pointing angle is obtained:

[0104]

[0105] In addition, to solve the technical problem of the weak anti-interference ability of traditional methods, the inventive concept of the technical solution of the present invention also lies in: filtering the system calculation model. The following is the key content of the technical solution of the present invention.

[0106] (2) Construct a Kalman filter system model based on α and β

[0107] For the calculation models of α and β, Kalman filtering is required. A state transition equation for α and β needs to be established as a prediction model. Since the calculation of α and β involves inverse trigonometric functions, after creative thinking, the inventors of the present invention adopted the following method to construct a prediction model to obtain the corresponding state transition equation for easy calculation and error reduction:

[0108] Let the positions of the current rocket and satellite be R r (t) and R s (t) respectively. Then the positions at the next moment are R r (t + 1) and R s (t + 1). Given the exact motion equations of the rocket and satellite, the prediction of the motion increments of the rocket and satellite can be obtained:

[0109]

[0110]

[0111] From the addition and subtraction operations of vectors, the vector from the rocket to the satellite at the next moment

[0112]

[0113] Let (Δs - Δr) = ΔP l , which is called the relative motion increment of the satellite and the rocket, and further derivation:

[0114] P(t + 1) = Rot(T(t + 1)) · (P l (t) + ΔP l )

[0115] P(t + 1) = Rot(T(t + 1)) · P l (t) + Rot(T(t + 1)) · ΔP l

[0116] For the right side of the equation, since

[0117] Rot(T(t + 1)) · P l (t)

[0118] = Rot(T(t + 1)) · P l(t) - Rot(T(t))·P l (t) + Rot(T(t))·P l (t)

[0119] Thus

[0120] Rot(T(t + 1))·P l (t)

[0121] = (Rot(T(t + 1)) - Rot(T(t)))·P l (t) + Rot(T(t))·P l (t)

[0122] Then

[0123] P(t + 1) = Rot(T(t))·P l (t) + (Rot(T(t + 1)) - Rot(T(t)))·P l (t) + Rot(T(t + 1))·ΔP l (10)

[0124] Given P(t) = Rot(T(t))·P l (t), then P l (t) = Rot(T(t)) -1 ·P(t),

[0125] Let

[0126] ΔP = (Rot(T(t + 1)) - Rot(T(t)))·P l (t) + Rot(T(t + 1))·ΔP l

[0127] ΔP = Rot(T(t + 1))Rot(T(t)) -1 ·P(t) - P(t) + Rot(T(t + 1))·ΔP l (11)

[0128] By combining (10) and (11), the recurrence formula for vector P is obtained:

[0129] P(t + 1) = P(t) + ΔP, ΔP = Rot(T(t + 1))Rot(T(t)) -1 ·P(t) - P(t) + Rot(T(t + 1))·ΔP l (12)

[0130] Next, calculate the angle conversion. Considering that the value of α0 is between [-90, 90], and the sign of α0 can be determined by the signs of P(y) and P(z). After creative thinking, for the convenience of subsequent calculations, the calculation formulas of α and β in the method of the present invention can be further simplified as follows.

[0131] Referring to equations (6)-(9), we can obtain

[0132]

[0133] Thus

[0134]

[0135] Furthermore, we get

[0136]

[0137] From equations (6) and (13), in summary,

[0138]

[0139] Similarly:

[0140]

[0141] Furthermore, we can obtain:

[0142]

[0143]

[0144] It should be noted that if α m ≤180, at this time

[0145]

[0146] After creative thinking, by finding the first-order Taylor expansion of P z (t) and P y (t) at time t to calculate their increments (higher precision can be obtained by solving higher-order Taylor expansions), a recurrence formula for the state transition equation is constructed.

[0147] The first-order Taylor expansion of α(t + 1) at α(t) is:

[0148]

[0149] Furthermore

[0150]

[0151] So

[0152]

[0153] Similarly, the state transition equation of β can be obtained as follows:

[0154] β(t + 1) = β(t) + Δβ

[0155]

[0156] (3) Kalman filter

[0157] Returning to the construction of the Kalman filter system for the actual problem, the inventor of the present invention considered that in the actual situation, the optimal estimated value at time t is Given the motion control commands (or preset motion trajectories) of the rocket and the satellite at time t, the motion increment from time t to time t + 1 can be obtained. Substituting it into the foregoing formula gives the prior Combined with the observed value at time t + 1, the posterior The specific formulas are as follows:

[0158] When only α, β, the motion increment, and the attitude angle increment are known, the α and β at the next moment cannot be deduced (only the direction of the vector is known, not the length of the vector). Therefore, when constructing the state vector, after creative thinking again, the present invention not only introduces the phased array antenna rocket-satellite beam pointing angles α and β required finally, but also introduces the vector P pointing from the rocket to the satellite in the body coordinate system and the motion attitude angle T of the rocket r .

[0159] Construct the following state vector:

[0160]

[0161] From the derivation formula for constructing the Kalman filter model in step (2), combined with the state vector, the state equation can be constructed as:

[0162]

[0163] is the prior estimate, is the optimal estimate (posterior estimate) at the previous moment, U(t) is the motion increment from time t to time t + 1 obtained from the motion control commands (or preset motion trajectories) of the rocket and the satellite as mentioned above

[0164]

[0165] Among them, Δα is obtained from the derivation formula (13), Δβ is obtained from the derivation formula (14), ΔP is obtained from the derivation formula (12), and ΔT r can be obtained from the rocket kinematic equation.

[0166] On this basis, in order to make the Kalman filter continuously run until the end of the system process, the inventor of the present invention, through creative thinking, proposed to update the vector P and the Kalman gain K in the above steps in the following manner:

[0167]

[0168]

[0169] Wherein, is the prior estimate covariance, P(t) is the posterior estimate covariance at the previous moment, Q is the process noise covariance, R is the covariance of the measurement noise, and both the process noise and the measurement noise are Gaussian white noises. K(t + 1) is the Kalman gain, H is the observation matrix. Since this problem only involves the observation of α and β,

[0170] H = [I 2×2 0 2×6

[0171] Optimal estimate:

[0172]

[0173] is the optimal estimate at the current moment, and Z(t + 1) is the measurement value (observation value) at the current moment.

[0174] Finally, update the posterior estimate covariance:

[0175]

[0176] Verification of the beneficial technical effects of the method of the present invention compared with the prior art:

[0177] For the filtering method described in the present invention, a set of motion data (R r (x r , y r , z r ) containing Gaussian noise w(n) is substituted into this method. After filtering by this method, the optimal estimated value, compared with the observed value with respect to the theoretical true value, the error of the α angle is reduced from a maximum of 6.47° to below 0.66°, and the error of the β angle is reduced from a maximum of 7.73° to below 1.44°. Its accuracy is improved by nearly an order of magnitude. For specific simulation curves, see Figure 5 、 Figure 6 . It can also be seen from the figure that the filtering effect is obvious.

[0178] The flow chart of the method of the present invention is as shown in Figure 4 ​As shown, although certain transformations are taken for simplified calculation, it can be seen from this figure that this method filters out the Gaussian noise contained in the rocket and satellite movements and sensor measurements. Therefore, compared with the traditional phased array antenna rocket-satellite beam pointing method, the filtering method described in the present invention has higher accuracy and stronger anti-interference ability. Moreover, this method has two main advantages:

[0179] 1) For different satellite and rocket motion models, the adaptability of this method can be achieved simply by changing the input of their motion increments.

[0180] 2) If you want to filter out higher-level model Gaussian errors, such as the dynamic model error of the rocket, you only need to add the rocket dynamic model. Therefore, this method is easy to expand and has good universality.

[0181] The units involved in the embodiments described in the present invention can be implemented in software or in hardware, and the described units can also be set in a processor. Among them, the names of these units do not constitute a limitation to the unit itself in some cases.

[0182] According to one aspect of the present application, there is provided a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the methods provided in the above various optional implementation manners.

[0183] As another aspect, the present application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist alone without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the methods described in the above embodiments.

[0184] The parts not involved in the present invention are the same as the prior art or can be implemented by the prior art.

[0185] The above technical solution is only one implementation manner of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is very easy to make various types of improvements or deformations, not limited to the methods described in the above specific implementation manners of the present invention. Therefore, the above-described manner is only preferred and does not have a restrictive meaning.

[0186] In addition to the above examples, those skilled in the art can obtain inspiration based on the above disclosure or make modifications by using the knowledge or technology in related fields to obtain other embodiments. The features of each embodiment can be interchanged or replaced. As long as the modifications and changes made by those skilled in the art do not depart from the spirit and scope of the present invention, they should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for calculating the arrow-satellite pointing angle of an arrow-borne phased array antenna based on Kalman filtering, characterized in that, Including the following steps: S1. Introduce the azimuth angle α, elevation angle β of the phased array antenna's arrow star beam pointing to the relay satellite, the vector P of the rocket pointing to the satellite in the rocket body coordinate system, and the motion attitude angle of the rocket , and construct the following state vector : ； S2, based on the Kalman filter model and combined with construct the following state equation: where \(t\) is the time, is the prior estimate, is the optimal estimate at the previous time, is obtained from the motion control command of the rocket and the satellite or the preset motion trajectory from time to time, and In the formula, is the increment from moment to is the increment from moment to is the increment of the vector from the rocket pointing to the satellite in the body coordinate system from moment is the increment of the rocket attitude angle from moment; S3, using the known optimal estimated values of α and β at time t , , and using the known motion control instructions or preset motion trajectories of the rocket and the satellite at a certain time to obtain the motion increment from a certain time to a certain time , and calculate the prior values of α and β at a certain time and ; S4, combine the observed values at each moment and calculate the posterior values of α and β at each moment; In step S2, it is calculated by constructing the following state transition equation: where t is the moment, is the azimuth angle at the current moment, is the azimuth angle at the next moment, is the vector of the rocket pointing to the satellite in the Z direction in the rocket system at moment t, is the vector of the rocket pointing to the satellite in the Y direction in the rocket system at moment t, is the vector increment of the rocket pointing to the satellite in the Y direction in the rocket system from moment t to the next moment, is the vector increment of the rocket pointing to the satellite in the Z direction in the rocket system from moment t to the next moment; In step S2, it is calculated by constructing the following state transition equation: Among them, is the pitch angle at the current moment, is the pitch angle at the next moment, is the vector of the rocket pointing to the satellite in the Z direction in the rocket system at time t, is the vector of the rocket pointing to the satellite in the Y direction in the rocket system at time t, is the vector of the rocket pointing to the satellite in the X direction in the rocket system at time t, is the increment of the vector of the rocket pointing to the satellite in the Z direction in the rocket system from time t to the next moment, is the increment of the vector of the rocket pointing to the satellite in the Y direction in the rocket system from time t to the next moment, is the increment of the vector of the rocket pointing to the satellite in the X direction in the rocket system from time t to the next moment; In step S2, It is calculated by constructing a recurrence formula for vector P: ， Among them, is the direction vector of the rocket pointing to the satellite in the arrow system at moment, is the direction vector of the rocket pointing to the satellite in the arrow system at +1 moment, is the relative motion increment of the satellite and the rocket in the inertial system, is the rocket attitude angle rotation transformation matrix at time t, is the rocket attitude angle rotation transformation matrix at time t + 1; In step S2, obtained from the rocket kinematic equation; including the direction vector and the Kalman gain Update step: Update the direction vector of the rocket pointing to the satellite in the arrow system according to the following formula and the Kalman gain : In the formula, is the prior estimate covariance, is the posterior estimate covariance at the previous moment, is the process noise covariance, Measurement noise covariance, both the process noise and the measurement noise are Gaussian white noise; is the Kalman gain, is the observation matrix; The optimal estimate is: is the optimal estimate at the current moment, is the measured value at the current moment, i.e., the observed value; finally update the posterior estimate covariance: 。 2. The method for calculating the arrow-satellite pointing angle of the arrow-borne phased array antenna based on Kalman filtering according to claim 1, wherein In step S3, the calculation of the prior values of α and β at the moment and specifically is obtained by using the established state transition equation of and the established state transition equation of β.

3. The method for calculating the arrow-satellite pointing angle of the arrow-borne phased array antenna based on Kalman filtering according to claim 1, characterized in that, The observation matrix, Take: Among them, H is a 2×8 matrix, is a 2×2 identity matrix, is a zero matrix.

4. The method for calculating the arrow-satellite pointing angle of the arrow-borne phased array antenna based on Kalman filtering according to claim 1, wherein, The calculation of the azimuth angle α and elevation angle β of the phased array antenna's arrow-star beam pointing to the relay satellite includes the following steps: By constraining the actual installation angle of the phased array antenna and combining with the quadrant and direction, the specific calculation formula for from the rocket body coordinate system to the antenna coordinate system is as follows: The direction vector of the rocket pointing to the satellite in the arrow system The three coordinate values are respectively , , , Thus, the theoretical calculation function of the phased array antenna's arrow-star beam pointing angle is obtained: Wherein, is the satellite motion trajectory equation in the launch inertial coordinate system, is the rocket motion trajectory equation in the launch inertial coordinate system, is the rocket motion attitude angle equation, is the satellite coordinate in the launch inertial coordinate system, is the rocket pitch angle, yaw angle, and roll attitude angle of.

5. The method for calculating the arrow-satellite pointing angle of the arrow-borne phased array antenna based on Kalman filtering according to claim 4, characterized in that, The actual installation angle of the phased array antenna is constrained, that is, is installed at 90°.

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