CN110779532B - Geomagnetic navigation system and method applied to near-earth orbit satellite - Google Patents
Geomagnetic navigation system and method applied to near-earth orbit satellite Download PDFInfo
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Abstract
The invention discloses a geomagnetic navigation system and a geomagnetic navigation method applied to a near-earth orbit satellite, wherein the system comprises a geomagnetic field intensity measurement system and a navigation information processing system; the geomagnetic field intensity measurement system comprises a high-precision magnetic resistance magnetometer, a flexible extension rod, an international geomagnetic field model, a measurement error compensation system and a geomagnetic field error comparison module; the navigation information processing system comprises an extended Kalman filter, a track dynamics module under a ground-fixed coordinate system, a geomagnetic field intensity measurement module and an information processing module. The method is based on an extended Kalman filtering algorithm, takes an orbit dynamics equation and a geomagnetic field measurement equation under a geostationary coordinate system as mathematical models, and obtains filtering updating data by analyzing a theoretical calculation value of a geomagnetic reference model and an actual measurement value of a magnetometer; and then inputting the model and the updated data into a filter, and finally achieving the purposes of spacecraft orbit determination and navigation through iteration.
Description
Technical Field
The invention belongs to the technical field of satellite autonomous navigation, and particularly relates to a geomagnetic navigation system and a geomagnetic navigation method applied to a near-earth orbit satellite.
Background
Satellite navigation systems provide information on the spatial location of a receiver by receiving signals from different satellites. There are four satellite navigation positioning systems in orbit in the world today: the Global Positioning System (GPS) in the United states, the Global navigation satellite System (GLONASS) in Russia, the Galileo Global navigation System (Galileo) in Europe, and the Beidou satellite navigation System (BD/BD-2) in China. Although the satellite navigation system can provide high-precision navigation information for the low earth orbit spacecraft, the navigation mode has the inherent defect that the satellite navigation signal has low receiving power and is very easy to be interfered by the outside world, so that the positioning navigation service is limited or even interrupted; in severe cases, the whole satellite navigation system may be paralyzed, and the consequences are not reasonable. Although the traditional ground measurement and control navigation mode can complete the navigation task, the tasks of the measurement and control station are increased continuously due to the increasing number of on-orbit spacecrafts, and the data transmission task is very heavy. Therefore, the research on the autonomous navigation mode independent of satellite navigation has important significance.
FIG. 1 is a 500 km orbit altitude space, the variation curve of the earth magnetic field intensity with geographical latitude and longitude. It can be seen that, for a certain point in the near-earth space, the determined geomagnetic intensity corresponds to the certain point, so that the orbit parameters of the satellite can be determined by using the measurement data of the on-satellite magnetometer. Meanwhile, the geomagnetic intensity is directional, and parameters such as satellite position, speed and attitude and the like are determined by using a theoretical geomagnetic intensity vector calculated by an international geomagnetic reference model IGRF and a geomagnetic intensity vector measured by a magnetometer. Compared with active navigation modes such as traditional ground measurement and control navigation, beidou navigation and the like, the geomagnetic navigation has the advantages of strong anti-jamming capability and high concealment; in contrast to inertial navigation, such navigation errors do not accumulate over time. Meanwhile, due to the characteristics of small volume, light weight, low power consumption and the like of the magnetometer, the occupied resources on the satellite are few, so that the research on the geomagnetic navigation method of the low-earth orbit satellite can effectively improve the autonomous ability and the survival ability of the satellite and meet the autonomous navigation performance requirement of the satellite.
Technical parameters of the geomagnetic navigation system are as follows:
(1) Input and output:
inputting: magnetometer and magnetic measuring digital quantity
And (3) outputting: real-time position of satellite, etc
(2) Precision and processing speed:
orbit determination precision: when the residual magnetic moment of the satellite is less than 0.5Am2 and the measurement precision of the magnetometer is superior to 5nT, the orbit of the near-earth satellite is superior to 1km.
Processing speed: the way of determining the track in real time is adopted.
(3) Weight volume power consumption:
weight: less than 2.5kg
Volume: less than 250mm 180mm 50mm
Power consumption: less than 10W
Disclosure of Invention
The invention aims to provide a geomagnetic navigation system and a geomagnetic navigation method applied to a near-earth orbit satellite based on task indexes of on-satellite autonomous navigation, such as autonomous observation and planning, sensor information processing, navigation settlement and the like. The invention can process data in real time and rapidly, and has enough space for data storage. In addition, based on a geomagnetic navigation related optimization algorithm, the aircraft can realize autonomous orbit determination, and the position and speed information of the spacecraft can be given in real time. Therefore, the geomagnetic navigation system with simple structure, strong anti-interference capability, small volume, good stability and high cost performance is provided for the near-earth orbit satellite, and reference are provided for the application of geomagnetic navigation in engineering.
The invention is realized by adopting the following technical scheme:
a geomagnetic navigation system applied to a near-earth orbit satellite comprises a geomagnetic field intensity measurement system and a navigation information processing system; wherein the content of the first and second substances,
the geomagnetic field intensity measurement system comprises a high-precision magnetic resistance magnetometer, a flexible extension rod, an international geomagnetic field model, a measurement error compensation system and a geomagnetic field error comparison module; in order to reduce the interference of magnetic materials on a carrier to measurement, a high-precision magnetic resistance magnetometer is arranged at the tail end of a flexible extension rod and used for obtaining a magnetic field intensity vector under a body coordinate system at the position of a satellite as a magnetic field measurement value in navigation information processing; in the measuring process, because the zero deviation, the sensitivity error, the quadrature error and the residual magnetism error of the magnetometer interfere with the measuring precision, the measuring result is compensated in real time through a measuring error compensation system; the international geomagnetic field model is used for outputting an estimated value of a geomagnetic field intensity vector according to the navigation estimation information; in a geomagnetic field error comparison module, comparing an actual measurement value of a magnetometer with an output value of an international geomagnetic field model to obtain a geomagnetic field measurement error value, wherein the geomagnetic field measurement error value comprises correction data and is used for being input into a navigation information processing system;
the navigation information processing system comprises an extended Kalman filter, a track dynamics module under a ground-fixed coordinate system, a geomagnetic field intensity measurement module and an information processing module; the orbit dynamics module under the earth fixed coordinate system is used as a state equation of the navigation information processing system, the geomagnetic field intensity measurement module is used as a measurement module of the navigation information processing system, the geomagnetic field intensity measurement module and the geomagnetic field intensity error are jointly input into the extended Kalman filter, and satellite orbit data are estimated and corrected in real time by using a data fusion algorithm; and finally, the orbit data is sent to an information processing module to achieve the purpose of determining the satellite orbit.
A geomagnetic navigation method applied to a low-earth orbit satellite is based on the geomagnetic navigation system applied to the low-earth orbit satellite, and comprises the following steps of:
1) Establishing a state equation and a measurement equation of a navigation system
Defining the state quantity of the navigation system as X = (X, y, z, v) x ,v y ,v z ) T And the quantity is measured as Z = [ Bx, by, bz =] T ，(x,y,z)、(v x ,v y ,v z ) Respectively representing the position and the speed of the satellite in three directions under a ground-fixed coordinate system, and Bx, by and Bz respectively representing the vector components of the geomagnetic field of the ground-fixed coordinate system; the linear discretized state equation and the measurement equation are as follows:
wherein k is a discrete point; Φ (k, k-1) represents a state transition matrix; h (k) represents a measurement matrix; w and ν are respectively a system noise matrix and a measurement noise matrix, and respectively satisfy the following relational expressions:
E[w(k)]＝0,E[w(k)w(l)]＝Q k ·δ kl (2)
E[ν(k)]＝0,E[ν(k)ν(l)]＝R k ·δ kl (3)
in the formula, l is a discrete time point; q k And R k Respectively representing a system noise covariance matrix and a measured noise covariance matrix which are positive definite matrixes; delta. For the preparation of a coating kl Representing a Kronecker symbol;
2) Estimating state quantities based on extended Kalman filter
The extended Kalman filter establishes a state equation of the navigation system by using the orbit dynamics equation in the step 1), and establishes the navigation system by using the measurement equation in the step 1)The observation model of (2); taking an error value between an actual measurement value of the magnetometer and an output value of the international geomagnetic field model as updating information, and performing optimal estimation on the orbit parameters of the satellite according to the state updating characteristic of Kalman filtering; setting initial input parameters of filtering including initial value of state quantity, filtering time and system noise covariance matrix Q k Measuring the noise covariance matrix R k And the sampling frequency and the actual measurement value of the magnetometer are input into a filter together for state quantity estimation, and finally the orbit determination parameter of the satellite is obtained.
The further improvement of the invention is that the specific implementation method of the step 1) is as follows:
101 Equation of state for the building system
Defining the state quantity of the navigation system as X = (X, y, z, v) x ,v y ,v z ) T Considering only the J2 perturbation term, the orbital dynamics equation of the satellite in the earth-fixed coordinate system is as follows:
wherein (x, y, z), (v) x ,v y ,v z ) Respectively represents X of the satellite under the earth-fixed coordinate system e 、Y e 、Z e Position and velocity in three directions; r represents the geocentric distance; μ represents a gravitational constant; t represents time; f represents a function; j is a unit of 2 =0.00108263 is a second-order harmonic coefficient of the earth gravitation; r e Is the earth mean radius; omega e Vectors representing rotational angular velocities of the earth in the earth-fixed coordinate system, i.e. ω e ＝[0,0,ω e ]；
The extended Kalman filter requires linearization and discretization of a system state equation; therefore, the orbit dynamics equation is firstly estimated at the optimal value
And performing Taylor series expansion, and taking a first-order approximate term as shown in the following formula:
wherein, the first and the second end of the pipe are connected with each other,
representing the linearized partial differential matrix; according to equation (5), solving the partial differential of the state quantity for the right term of the equation, M can be expressed in the form of a block matrix as follows:
in the formula I 3×3 An identity matrix representing 3 × 3 dimensions; let the matrix F [ X (t), t)]＝[F 1 ,F 2 ,F 3 ,F 4 ,F 5 ,F 6 ] T Then, each element in N, L is as follows:
assuming that the sampling period of the system is T, when approximate calculation is carried out, the discretized system state transition matrix phi (k, k-1) is expressed as follows:
Φ(k,k-1)＝I+M×T (10)
through the analysis, the linear discretization state equation of the navigation system is obtained as follows:
X(k)＝Φ(k,k-1)X(k-1)+w(k-1) (11)
102 To establish a measurement equation for a navigation system
The measurement value in the navigation system is the earth magnetic field intensity vector, and the measurement quantity is defined as Z = [ Bx, by, bz =] T ；
In the formula, the scalar magnetic potential U satisfies laplace's equation, and the spherical harmonics thereof are expressed as follows:
wherein: bx, by and Bz respectively represent geomagnetic field vector components of a ground-fixed coordinate system; a represents the average radius of the earth;
the magnetic field is a geomagnetic model Gaussian spherical harmonic coefficient and is provided by an earth main magnetic field model; r is the earth center distance, theta is the earth center weft allowance, and lambda is the earth center longitude; n is the maximum truncation order of the spherical harmonic series; />
Is an order normalized associated legendre polynomial;
optimal estimation value of measurement equation
And performing Taylor series expansion, and taking a first-order approximate term as shown in the following formula:
in the formula (I), the compound is shown in the specification,
is an observation matrix, is a function of the geocentric distance r, the geographic latitude theta and the geographic precision lambda; and solving after expansion to obtain: />
By combining the above, the measurement equation of the navigation system is obtained as follows:
Z B (k)＝H B (k)X(k)+ν B (k) (16)。
the further improvement of the invention is that when the EKF algorithm is adopted, the specific implementation method of the step 2) is as follows:
201 Setting initial parameters of the filter at zero time
The parameters are as follows: state quantity containing errors
Initial error covariance matrix>
A system noise covariance matrix Q, a measurement noise covariance matrix R and observation information Z of a measurement sensor, wherein the sampling time T =1; obtaining an estimated value of the state quantity at a sampling point k, wherein k =1,2, \ 8230, through time updating and measurement updating of a filter; wherein I represents an identity matrix;
202 Time update
Prediction information of state quantity
Comprises the following steps: />
Prediction information for error covariance matrix
Comprises the following steps: />
Filter gain matrix K k Comprises the following steps:
203 Measurement update
Estimation value of satellite state quantity at current moment
Comprises the following steps: />
At the current time, the error covariance matrix
Comprises the following steps:
the invention has at least the following beneficial technical effects:
the invention provides a geomagnetic navigation system applied to a near-earth orbit satellite, wherein a hardware part mainly comprises a high-precision magnetic resistance magnetometer, a flexible extension rod and an information processing module. A traditional GPS navigation system mainly comprises an on-orbit satellite, a ground main control station, a monitoring station and a GPS signal receiver. Compared with a GPS navigation system, the geomagnetic navigation system provided by the invention has the advantages of simple and compact structure composition, good concealment, no interference of navigation signals from the outside and capability of realizing the continuity of navigation information. Compared with an inertial navigation system, the geomagnetic navigation system provided by the invention has low equipment cost. The navigation method is used immediately, navigation accumulation errors cannot be generated, and the navigation method is a navigation mode with higher economical efficiency for the low earth orbit satellite.
The software control program comprises an FPGA program and a DSP program. The FPGA is mainly responsible for interfacing with an upper computer, namely receiving geomagnetic data in the upper computer and storing the geomagnetic data in the FPGA. The DSP is mainly responsible for a navigation algorithm program, namely when navigation is started, geomagnetic data is read from the FPGA and applied to navigation operation to obtain a navigation result, the navigation operation is performed every 1s, namely the DSP is required to start a timer to interrupt every 1s, the timer is interrupted every 1s, navigation solution is correspondingly performed, and the navigation result is output. All programs are compiled and debugged in the DSP-specific tool CCS (Code Composer Studio). The navigation control module software flow chart is shown in fig. 5.
The innovation points are as follows: the design and development of the geomagnetic navigation system promote the application conversion of the geomagnetic navigation method, and provide reliable guarantee for autonomous navigation of the spacecraft under the condition of meeting the requirement of navigation precision.
The invention takes a single geomagnetic navigation algorithm as a core, designs a geomagnetic navigation control module based on a DSP + FPGA architecture, and forms a geomagnetic navigation system together with an upper computer and a high-precision magnetic resistance magnetometer.
The method is characterized in that: high navigation precision, strong anti-interference capability and wide engineering application prospect
1. High navigation precision
The method optimizes the traditional terrestrial magnetic navigation algorithm. The debugging result based on the measured data of the geomagnetic field of the satellite shows that the geomagnetic navigation system can respectively improve the position and speed accuracy of single navigation by 63 percent and 58 percent. (simulation tests show that under the same conditions, the navigation precision of the invention is 2.72km and 3.26m/s, and the traditional geomagnetic navigation precision is 4.43km and 5.15 m/s)
2. Strong anti-interference ability
Conventional GPS and Beidou navigation signals are weak and are easily interfered by external signals, so that the reliability of navigation is reduced. The invention belongs to a passive navigation mode, and the ground interference signal has no influence on navigation equipment, thereby improving the anti-interference capability of a navigation system.
3. Has wide engineering application prospect
The method provided by the invention can realize the navigation of the near-earth orbit satellite by only utilizing a single magnetometer and processing equipment without adding other measuring equipment, has the advantages of small volume, light weight, low power consumption and high cost performance compared with a GPS/Beidou/inertial navigation mode, has very strong engineering value, and further promotes the application transformation research of the geomagnetic navigation.
The system can independently complete the navigation task of the spacecraft by applying the system to the satellite, and meanwhile, the system can provide high-precision satellite navigation parameters on the premise of ensuring stable work due to the adoption of a geomagnetic navigation optimization method, thereby laying a solid foundation for in-orbit control of the spacecraft.
According to the geomagnetic navigation method applied to the near-earth orbit satellite, an orbit kinetic equation under an earth fixed connection coordinate system is taken as a state equation, and compared with the orbit kinetic equation under an earth center inertia coordinate system, the geomagnetic navigation method reduces the conversion between different coordinate systems and reduces the complex coordinate conversion between observed quantity and state quantity. In addition, in the geomagnetic navigation method, constructing a measurement equation with higher linearization degree is an important means for ensuring navigation accuracy, and in the traditional navigation method, the linearization from the earth fixed coordinate system to the inertial coordinate system needs four processes to be completed, so that great error accumulation exists. The navigation method provided by the invention can adopt a quantitative estimation method in the linearization process. Therefore, compared with the traditional navigation method, the navigation method can not only effectively improve the navigation precision (the position precision can be improved from 4.43km to 2.72km, the speed precision can be improved from 5.15m/s to 3.26ms, and respectively improved by 63 percent and 58 percent), but also reduce the navigation calculation time (the single resolving time is improved from 4.7ms to 1.3 ms).
Drawings
FIG. 1 is a graph of the variation of the magnetic field strength of the earth in a 500 km altitude space with geographical latitude and longitude; wherein FIG. 1 (a) is a three-dimensional perspective view of a variation curve, and FIG. 1 (b) is a contour diagram of a variation graph;
FIG. 2 is a schematic diagram of a geomagnetic navigation method;
FIG. 3 is a system block diagram of a geomagnetic navigation system;
FIG. 4 is a hardware schematic of the navigation control module;
FIG. 5 is a software flow diagram of a navigation control module;
FIG. 6 is a diagram illustrating a position error curve of a geomagnetic navigation method;
FIG. 7 is a velocity error graph of a geomagnetic navigation method.
Detailed Description
The invention is further described below with reference to the following figures and examples.
The invention provides a geomagnetic navigation system applied to a near-earth orbit satellite, which comprises a geomagnetic field intensity measuring system and a navigation information processing system; the geomagnetic field intensity measurement system comprises a high-precision magnetic resistance magnetometer, a flexible extension rod, an international geomagnetic field model, a measurement error compensation system and a geomagnetic field error comparison module; in order to reduce the interference of magnetic materials on a carrier to measurement, the high-precision magnetic resistance magnetometer is arranged at the tail end of the flexible extension rod and used for obtaining a magnetic field intensity vector under a body coordinate system at the position of a satellite as a magnetic field measurement value in navigation information processing; in the measuring process, because the zero deviation, the sensitivity error, the quadrature error and the residual magnetism error of the magnetometer interfere the measuring precision, the measuring result is compensated in real time through a measuring error compensation system; the international geomagnetic field model is used for outputting an estimated value of a geomagnetic field intensity vector according to the navigation estimation information; in the geomagnetic field error comparison module, the actual measurement value of the magnetometer is compared with the output value of the international geomagnetic field model to obtain a geomagnetic field measurement error value, and the geomagnetic field measurement error value comprises correction data and is used for being input into the navigation information processing system.
The navigation information processing system comprises an extended Kalman Filter (EKF for short), a track dynamics module under a geostationary coordinate system, a geomagnetic field intensity measurement module and an information processing module; the orbit dynamics module under the earth-fixed coordinate system is used as a state equation of the navigation information processing system, the geomagnetic field intensity measurement module is used as a measurement module of the navigation information processing system, the measurement module and the geomagnetic field intensity error are jointly input into the extended Kalman filter, and satellite orbit data are estimated and corrected in real time by using a data fusion algorithm; and finally, the orbit data is sent to an information processing module to achieve the purpose of determining the satellite orbit. The information processing module is the core of the system and can autonomously complete the functions of receiving and storing geomagnetic field strength information, resolving navigation information, outputting information and the like.
The working principle diagram is shown in fig. 2. The navigation process comprises the following steps: firstly, a state equation and an observation equation of a system are respectively established on the basis of a satellite orbit dynamics equation and a mathematical model of a magnetometer. Through a state equation of the system, a state transfer matrix of the state quantity of the system can be obtained and used for predicting state forecast information at a given moment; by using the geomagnetic field model, the measurement information corresponding to the predicted value can be output. And comparing the output value of the model with the geomagnetic field intensity measured by the sensor, and inputting the navigation correction information and the predicted value into a filter. And after comprehensively considering the system model error and the sensor measurement error, continuously updating and correcting the filter to obtain the optimal estimation value of the position and speed information, thereby completing the navigation purpose.
The invention provides a geomagnetic navigation method applied to a near-earth orbit satellite, which comprises the following steps:
1. establishing a system equation
And deducing an orbital dynamics equation under the earth fixed connection coordinate system according to the relative motion relation of the particles. Let the absolute acceleration of the satellite be a i The acceleration of the drag is a e Coriolis acceleration of a c The moving velocity vector of the centroid of the satellite relative to the earth is V e And V is e ＝[v x ,v y ,v z ]. The absolute acceleration is equal to the sum of the relative acceleration, the involved acceleration and the coriolis acceleration, as shown in the following equation:
in the formula, the acceleration a is involved e And Coriolis acceleration a c Respectively as follows:
a e ＝ω e ×(ω e ×r) (1.2)
a c ＝2ω e ×V e (1.3)
in the formula, omega e Representing the vector of the rotational angular velocity of the earth in the earth's fixed-relation coordinate system, i.e. omega e ＝[0,0,ω e ]；r＝(x,y,z) T The position vector is under the earth fixed connection coordinate system.
From the two-body orbit motion model, the absolute acceleration can be expressed as:
wherein μ is the gravitational constant;
representing the earth-center distance of the satellite. Combining the above equations, an expression for the relative acceleration is obtained as follows:
the above equation is expanded by using the vector cross product relation:
simplifying the above formula, and obtaining the orbital dynamics equation of the satellite under the earth fixed coordinate system as follows:
considering only the J2 perturbation term, the orbital dynamics equation of the satellite in the earth-fixed coordinate system is expressed as follows:
wherein X = (X, y, z, v) x ,v y ,v z ) T ，(x,y,z)、(v x ,v y ,v z ) Respectively representing the position and the speed of the satellite in three directions under a ground-fixed coordinate system; j2=0.00108263 is a harmonic coefficient of a second order band of the earth gravitation; r e =6371.2km for earth mean radius.
When a computer is used for solving the state equation of the linear system, a discretization process is required for a model of the linear system. The purpose of discretization is to output a model that is equivalent to the continuous system state at the sampling instant. The samples are typically equally spaced. When calculating approximately, the discretized system model can be expressed as follows:
X(k)＝Φ(k,k-1)X(k-1)+w(k-1) (1.9)
in the formula: k is a sampling point, w is the random interference noise of the system, and the statistical characteristics of the random interference noise meet the following conditions:
E[w(k)]＝0,E[w(k)w(l)]＝Q k ·δ kl (1.10)
the state transition matrix Φ (k, k-1) has a large relationship with the sampling time. The closer the approximate solution to the exact value of phi (k, k-1) the smaller the sampling time, the closer the discrete system is to the continuous system. Otherwise, the larger the error between the state transition matrix and the accurate value is, the worse the discretization effect of the linear system is, and the accuracy of the navigation result is directly influenced.
2. Establishing magnetometer observation model
The magnetometer is used as a measurement sensor of the satellite and can provide geomagnetic field intensity information of the satellite at any point in space, wherein the geomagnetic field intensity information comprises vector information and total intensity information. The autonomous navigation method based on geomagnetic information provides navigation correction information by using a difference value between a measurement value of a magnetometer and a geomagnetic field model, and finally obtains the position and the speed of the satellite at each moment through filtering. The orbit determination is carried out by taking geomagnetic field vector information as observed quantity. The orbit dynamics equation is established under a ground-fixed coordinate system, a reference coordinate system of the geomagnetic vector is an observation point coordinate system, the conversion process between the two coordinates is simple, and the precision is very high; on the other hand, compared with a one-dimensional geomagnetic field total intensity observation value, the state quantity information contained in the geomagnetic vector is richer, so that compared with geomagnetic navigation in an inertial coordinate system, the navigation method in the earth fixed connection coordinate system can obtain higher precision.
The form of the observation equation for the assumed autonomous navigation system is:
Z＝B+v(t) (2.1)
v is the random interference noise measured, which is the superposition of the error caused by the measurement error of the magnetometer and the change of the external environment, and can be approximate to Gaussian white noise, and the statistical characteristics meet the following requirements:
E[v(k)]＝0,E[v(k)v(l)]＝R k ·δ kl (2.2)
z = [ Bx, by, bz ] vector observed values of three directions of geomagnetism, and the expression thereof is as follows:
wherein, a represents the average radius of the earth;
the magnetic field is a geomagnetic model Gaussian spherical harmonic coefficient and is provided by an earth main magnetic field model; r is the earth center distance, theta is the earth center weft allowance, and lambda is the earth center longitude; n is the maximum truncation order of the spherical harmonic order; />
Is an order normalized associated legendre polynomial.
Referring to the system model, carrying out first-order Taylor series expansion and discretization on the observation model to finally obtain the observation model of the magnetometer:
Z(k)＝H(k)X(k)+ν(k) (2.4)
wherein, H (k) is a system measurement matrix, v (k) is measurement noise, and the statistical characteristics thereof satisfy:
E[v(k)]＝0,E[v(k)v(l)]＝R k ·δ kl (2.5)
3. designing extended Kalman filter
The extended Kalman filter is a state estimation method of a nonlinear system which is most widely applied, and the method comprises the steps of firstly utilizing Taylor series expansion to carry out linearization processing on the nonlinear system at a nominal state, and then utilizing a basic Kalman filtering method to carry out state quantity estimation. And (3) taking the state equation shown in the formula (1.9) and the observation equation shown in the formula (2.4) as system models, designing an extended Kalman filter, and carrying out filtering updating on the state quantity. The working process of the extended Kalman filter can be divided into two parts of time sequence updating and measurement sequence updating, and a filtering recursion formula is respectively expressed as follows:
(1) Time series update
(2) Measurement sequence update
In the formula:
the optimal estimated value of the current time state is obtained; />
The predicted value of the state quantity at the next moment is obtained; />
An error covariance matrix which is an estimated value at the current time; phi (k, k-1) is a state transition matrix; q (k-1) is a system noise covariance matrix; />
An error covariance matrix representing a predicted value at a next time; k is k Is a gain matrix, representing the weight of state quantity correction; h (k) is a measurement matrix; r (k) is a measured noise covariance matrix; />
The optimal estimated value of the state quantity at the next moment is obtained; z (k) is a measurement value of the magnetometer; />
Is the error covariance matrix of the estimates at the next time instant.
So, given the initial parameters of the filter: state quantity containing errors
Initial error covariance matrix
The system noise covariance matrix Q, the measurement noise covariance matrix R and the observation information of the measurement sensor are recurred by a Kalman filter, and the estimation value of the state quantity X (k) at each sampling time kT (k =1,2, \ 8230;) can be obtained
4. Geomagnetic navigation system design
As shown in fig. 3, after the navigation system is started, firstly, the geomagnetic actual measurement data of the satellite is read as the observation information of the geomagnetic navigation. And then, data are transmitted to a processor and temporarily stored by using a data interface between the upper computer and the navigation principle model machine. Obtaining a predicted value of the track parameter through a track dynamics model and a track integrator; inputting the predicted value into a geomagnetic field model to obtain geomagnetic intensity estimation information; obtaining an observation equation of navigation by using the relation between the observed quantity and the state quantity; and finally, estimating the state quantity by a filtering method. And sending the navigation result to an upper computer.
5. Navigation control module hardware part design
The hardware of the navigation system is required to meet the following design requirements: the data acquisition can be completed rapidly; (2) real-time data processing; (3) Sufficient storage space for storing measurement data and programs; (4) a sufficient number of interactive interfaces; (5) The requirements of small volume, low power and modularized production of the navigation system are met. By integrating the design requirements, considering the excellent performance of the DSP chip and the maturity and reliability of the DSP + FPGA architecture in engineering application, the invention designs and develops the navigation control module based on the DSP + FPGA architecture. The FPGA is mainly used for data transmission, storage and the like due to the strong logic control capability of the FPGA, and the DSP chip is used for completing the core function of the geomagnetic navigation system, namely navigation solution and outputting a navigation result due to the high-speed computing capability of the DSP chip.
The DSP is mainly used for finishing the functions of geomagnetic field model calculation, orbit integration, state quantity estimation and the like. The invention adopts a floating-point DSP chip, 8 parallel processing units are arranged in the chip, the word length of a single byte is 32 bits, 8 instructions of 32 bits can be executed in each period, and the invention has strong peripheral support capability and supports interfaces such as HPI, EMIF, EDMA and the like. The EMIF interface (external memory interface) with 32 bits can be seamlessly connected with synchronous and asynchronous memories such as SRAM, SDRAM, EPRAM and the like, so that data transmission is realized.
The FPGA mainly transmits the geomagnetic actual measurement data to the navigation control module from the upper computer and stores the data. And meanwhile, data are continuously transmitted to the DSP according to requirements, data from the DSP are received, and finally, a navigation result is output to an upper computer. The invention adopts a product with Flash architecture of Actel company. The FPGA has 1.5-300 ten thousand system gates, a maximum 504Kbit double-port RAM and a maximum 1Kbit FlashROM; a maximum of 616 user available IOs can be provided; meanwhile, the flash Lock with 128bit and the AES with 128bit encrypt the design well to protect the design from being stolen.
In addition, both the floating-point DSP processor and the FPGA are provided with Flash chips for realizing the automatic power-on starting of the system. The data transmission interface adopts an RS422 interface, can complete the transmission of 10 million data per second, and has more application in space engineering and high reliability.
6. Navigation control module programming
The embedded software of the geomagnetic navigation control module comprises the following programs:
(1) Satellite orbit dynamics integration program: acquiring a predicted value of a satellite orbit parameter by adopting a Runge Kutta 4-order algorithm based on an orbit dynamics equation under an earth fixed connection coordinate system;
(2) Geomagnetic field model calculation program: the conventional Gaussian spherical harmonic function calculation method obtains geomagnetic field intensity information by using spherical harmonic coefficients and Legendre polynomials;
(3) And (3) satellite information storage: for storing position and velocity data of the satellites;
(4) Extended kalman filter program: in order to realize the autonomy and real-time performance of geomagnetic navigation, an extended Kalman filter is adopted for estimating navigation parameters;
(5) And (3) observation data storage: the device is used for storing the measurement data of the on-satellite magnetometer;
(6) Initializing a DSP program: the system is used for initializing the hardware configuration of the DSP and initializing the navigation parameters;
(7) The multitask management program comprises the following steps: the method mainly utilizes hardware resources of a floating-point DSP chip of a C6713 model to effectively manage a geomagnetic navigation algorithm, and finally achieves the purpose of improving the running efficiency of a navigation program;
(8) RS422 interface program: the device is used for reading geomagnetic field intensity measurement data in the upper computer.
Examples
The invention designs a terrestrial magnetic navigation system which can realize the orbit determination task of near-earth orbit spaceflight. The workflow of the geomagnetic navigation system can be briefly described as follows: after the navigation system is started, firstly, geomagnetic actual measurement data of the satellite is read as observation information of geomagnetic navigation. And then, data are transmitted to a processor and temporarily stored by using a data interface between the upper computer and the navigation principle model machine. Obtaining a predicted value of the track parameter through a track dynamics model and a track integrator; inputting the predicted value into a geomagnetic field model to obtain geomagnetic intensity estimation information; obtaining an observation equation of navigation by using the relation between the observed quantity and the state quantity; and finally, estimating the state quantity by a filtering method. And sending the navigation result to an upper computer. Therefore, the geomagnetic navigation system designed by the invention mainly comprises the following two implementation steps: data receiving and transmitting, and navigation resolving.
1. Data reception
The magnetometer can measure the geomagnetic component in the vector direction of the position of the carrier, then transmits the geomagnetic component to the navigation control module, and the FPGA receives geomagnetic measurement data in the upper computer through the RS422 according to the flowchart of the upper graph 6. The RS422 uses 8-bit data bits, 1-bit stop bits, and a baud rate of 115200bps to transmit data, and the sync word of the data is D5 35. After receiving the data, the FPGA firstly judges whether the synchronous words are correct or not, if so, the data are received and stored in the received geomagnetic data, otherwise, the data are continuously received until the conditions are met. And then the FPGA receives a data reading instruction of the DSP and transmits the read data to the DSP through the EMIF interface.
Since RS422 transmits 16-ary data and the actual measurement value of the magnetometer is floating point data, the floating point data is first converted into 16-ary data before the data is used. Each set of measured values is composed of four columns of data, the first column of data represents sampling time in seconds, and the last three columns of data represent three basic elements Bx, by and Bz in the geomagnetic field intensity respectively. Wherein, the sampling time is an integer and is expressed by 4 Byte; the integer part of the three geomagnetic elements is represented by 2 bytes, and the decimal part is represented by 4 bytes, so that each set of measured data has 22 bytes, and the transmission data format is as follows.
2. Navigation solution
The DSP is mainly responsible for a navigation algorithm program, namely when navigation is started, geomagnetic data is read from the FPGA and applied to navigation operation to obtain a navigation result, the navigation operation is performed every 1s, namely the DSP is required to start a timer to interrupt every 1s, the timer is interrupted every 1s for 1 time, corresponding navigation calculation is performed, and the navigation result is output.
The designed geomagnetic navigation system is utilized to set the initial conditions of the experiment, and the debugging and verification tests are carried out by combining the magnetic measurement data.
The initial conditions were as follows:
(1) The observation data is magnetic vector data of a magnetic survey satellite 2015, 5 months and 22 days, the sampling time is 1s, and the simulation time is 45000s
(2) The measuring range of the magnetometer is +/-66000 nT, and the precision is 0-30nT;
(3) Taking the initial value of the nominal position of the satellite in the earth fixed connection coordinate system as follows: (-5320.079636, -2784.946333, 3177.993263) km, nominal initial velocity value of (2.956729486, 1.903501916, 6.538071903) km/s;
(4) Initial error of state quantity: taking the errors of the satellite position in three directions as 20km, and the errors of the speed in the three directions as 0.2km/s;
(5) Setting parameters: system noise covariance matrix
Q = diag ([ 1 × 10-8,1 × 10^ -8,1 × 10-10 ]); the noise covariance matrix R = diag ([ 1202,802,1002 ]).
The position and speed precision calculation results are shown in the following fig. 6 and fig. 7:
based on two implementation steps of a geomagnetic navigation algorithm, data transmission and navigation resolving, the experimental result shows that the geomagnetic navigation position error is about 2km by using the geomagnetic navigation principle prototype designed by the text, which is willing to be seen from the error curves of the two navigation results. In addition, a single navigation takes 4.7ms, which is much lower than the current 67ms for a single simulation on a computer. The navigation precision and the real-time performance are improved.
Claims (4)
1. A geomagnetic navigation system applied to a near-earth orbit satellite is characterized by comprising a geomagnetic field intensity measurement system and a navigation information processing system; wherein, the first and the second end of the pipe are connected with each other,
the geomagnetic field intensity measurement system comprises a high-precision magnetic resistance magnetometer, a flexible extension rod, an international geomagnetic field model, a measurement error compensation system and a geomagnetic field error comparison module; in order to reduce the interference of magnetic materials on a carrier to measurement, a high-precision magnetic resistance magnetometer is arranged at the tail end of a flexible extension rod and used for obtaining a magnetic field intensity vector under a body coordinate system at the position of a satellite as a magnetic field measurement value in navigation information processing; in the measuring process, because the zero deviation, the sensitivity error, the quadrature error and the residual magnetism error of the magnetometer interfere the measuring precision, the measuring result is compensated in real time through a measuring error compensation system; the international geomagnetic field model is used for outputting an estimated value of a geomagnetic field intensity vector according to the navigation estimation information; in a geomagnetic field error comparison module, comparing an actual measurement value of a magnetometer with an output value of an international geomagnetic field model to obtain a geomagnetic field measurement error value, wherein the error value comprises correction data and is used for being input into a navigation information processing system;
the navigation information processing system comprises an extended Kalman filter, a track dynamics module under a ground-fixed coordinate system, a geomagnetic field intensity measurement module and an information processing module; the orbit dynamics module under the earth-fixed coordinate system is used as a state equation of the navigation information processing system, the geomagnetic field intensity measurement module is used as a measurement module of the navigation information processing system, the measurement module and the geomagnetic field intensity error are jointly input into the extended Kalman filter, and satellite orbit data are estimated and corrected in real time by using a data fusion algorithm; and finally, the orbit data is sent to an information processing module to achieve the purpose of determining the satellite orbit.
2. A geomagnetic navigation method applied to a low earth orbit satellite, wherein the method is based on the geomagnetic navigation system applied to the low earth orbit satellite of claim 1, and the method comprises the following steps:
1) Establishing a state equation and a measurement equation of a navigation system
Defining the state quantity of the navigation system as X = (X, y, z, v) x ,v y ,v z ) T And the quantity is measured as Z = [ Bx, by, bz =] T ，(x,y,z)、(v x ,v y ,v z ) Respectively representing the position and the speed of the satellite in three directions under a ground-fixed coordinate system, and Bx, by and Bz respectively representing the vector components of the geomagnetic field of the ground-fixed coordinate system; the linear discretized state equation and the measurement equation are as follows:
wherein k is a discrete point; Φ (k, k-1) represents a state transition matrix; h (k) represents a measurement matrix; w and v are respectively a system noise matrix and a measurement noise matrix, and respectively satisfy the following relational expressions:
E[w(k)]＝0,E[w(k)w(l)]＝Q k ·δ kl (2)
E[ν(k)]＝0,E[ν(k)ν(l)]＝R k ·δ kl (3)
in the formula, l is a discrete time point; q k And R k Respectively representThe system noise covariance matrix and the measured noise covariance matrix are positive definite matrixes; delta kl Representing a Kronecker symbol;
2) Estimation of state quantities based on extended Kalman filter
The extended Kalman filter establishes a state equation of the navigation system by using the orbit dynamics equation in the step 1), and establishes an observation model of the navigation system by using the measurement equation in the step 1); taking an error value between an actual measurement value of the magnetometer and an output value of the international geomagnetic field model as updating information, and performing optimal estimation on the orbit parameters of the satellite according to the state updating characteristic of Kalman filtering; setting initial input parameters of filtering including initial value of state quantity, filtering time and system noise covariance matrix Q k Measuring the noise covariance matrix R k And the sampling frequency and the actual measurement value of the magnetometer are jointly input into the filter for state quantity estimation, and finally the orbit determination parameter of the satellite is obtained.
3. A geomagnetic navigation method applied to a low earth orbit satellite according to claim 2, wherein the specific implementation method in the step 1) is as follows:
101 Equation of state for the system being built
Defining the state quantity of the navigation system as X = (X, y, z, v) x ,v y ,v z ) T Considering only the J2 perturbation term, the orbital dynamics equation of the satellite in the earth-fixed coordinate system is as follows:
wherein (x, y, z), (v) x ,v y ,v z ) Respectively representing the X of the satellite in the earth-fixed coordinate system e 、Y e 、Z e Position and velocity in three directions; r represents the geocentric distance; μ represents a gravitational constant; t represents time; f represents a function; j. the design is a square 2 =0.00108263 is a second-order harmonic coefficient of the earth gravitation; r e Is the earth mean radius;ω e representing the vector of the rotational angular velocity of the earth in the earth's fixed-relation coordinate system, i.e. omega e ＝[0,0,ω e ]；
The extended Kalman filter requires linearization and discretization of a system state equation; therefore, the orbital dynamics equation is first estimated at the optimum value
The process is subjected to Taylor series expansion, and a first-order approximate term is taken, which is shown as the following formula:
wherein, the first and the second end of the pipe are connected with each other,
representing the linearized partial differential matrix; according to equation (5), solving the partial differential of the state quantity for the right-end term of the equation, M can be expressed in the form of a block matrix as follows:
in the formula I 3×3 An identity matrix representing 3 × 3 dimensions; let matrix F [ X (t), t)]＝[F 1 ,F 2 ,F 3 ,F 4 ,F 5 ,F 6 ] T Then, the elements in N and L are as follows:
assuming that the sampling period of the system is T, when approximate calculation is carried out, the discretized system state transition matrix phi (k, k-1) is expressed as follows:
Φ(k,k-1)＝I+M×T (10)
through the analysis, the linear discretization state equation of the navigation system is obtained as follows:
X(k)＝Φ(k,k-1)X(k-1)+w(k-1) (11)
102 To establish a measurement equation for a navigation system
The measurement value in the navigation system is the earth magnetic field intensity vector, and the measurement quantity is defined as Z = [ Bx, by, bz =] T ；
In the formula, the scalar magnetic potential U satisfies laplace's equation, and the spherical harmonics thereof are expressed as follows:
wherein: bx, by and Bz respectively represent geomagnetic field vector components of a ground-fixed coordinate system; a represents the average radius of the earth;
the magnetic field is a geomagnetic model Gaussian spherical harmonic coefficient and is provided by an earth main magnetic field model; r is the earth center distance, theta is the earth center weft allowance, and lambda is the earth center longitude; n is the maximum truncation order of the spherical harmonic order; />
Is an order normalized associated legendre polynomial;
optimal estimation value of measurement equation
And performing Taylor series expansion, and taking a first-order approximate term as shown in the following formula:
in the formula (I), the compound is shown in the specification,
is an observation matrix, is a function of the geocentric distance r, the geographic latitude theta and the geographic precision lambda; and solving after expansion to obtain:
by combining the above, the measurement equation of the navigation system is obtained as follows:
Z B (k)＝H B (k)X(k)+ν B (k)(16)。
4. a geomagnetic navigation method applied to a low earth orbit satellite according to claim 3, wherein when the EKF algorithm is adopted, the specific implementation method of the step 2) is as follows:
201 Initial parameter for setting the zero time of the filter
The parameters are as follows: state quantity containing errors
Initial error covariance matrix->
The method comprises the following steps of (1) measuring observation information Z of a sensor, a system noise covariance matrix Q, a measurement noise covariance matrix R and a measurement noise covariance matrix R, wherein the sampling time T =1; obtaining an estimated value of the state quantity at a sampling point k, wherein k =1,2, \ 8230, through time updating and measurement updating of a filter; wherein I represents an identity matrix;
202 Time update
Prediction information of state quantity
Comprises the following steps: />
Prediction information for error covariance matrix
Comprises the following steps: />
Filter gain matrix K k Comprises the following steps:
203 Measurement update
Estimation value of satellite state quantity at current moment
Comprises the following steps: />
Current time, error covariance matrix
Comprises the following steps: />
/>
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