阅读说明：本技术 一种基于位置指纹和二步多项式拟合的卫星位置预测跟踪方法 (Satellite position prediction tracking method based on position fingerprint and two-step polynomial fitting ) 是由 马琳 黄鹏飞 韩飞 王兆龙 于 2020-04-14 设计创作，主要内容包括：本发明是一种基于位置指纹和二步多项式拟合的卫星位置预测跟踪方法。所述方法为设置时间窗,通过基于位置指纹的卫星分级定位方法确定时间窗内成员星的N个离散位置构成的轨迹；将时间窗内的N个离散位置作为历史定位结果,根据二步多项式拟合方法确定出N个离散位置的二步多项式拟合值；确定成员星历史定位结果的轨迹吻合度,根据轨迹吻合度确定分级定位轨迹与真实轨迹的偏移程度；计算指纹定位结果,并对指纹定位结果进行卡尔曼滤波,得到成员星最终定位结果。本发明预测跟踪的定位结果的定位误差小于5m的概率为90％,定位误差小于10m的概率约为95％,定位误差小于30m的概率超过95％。定位精度远远高于未跟踪的定位结果。(The invention discloses a satellite position prediction tracking method based on position fingerprints and two-step polynomial fitting. Setting a time window, and determining a track formed by N discrete positions of member satellites in the time window by a satellite hierarchical positioning method based on position fingerprints; taking N discrete positions in a time window as a historical positioning result, and determining a two-step polynomial fitting value of the N discrete positions according to a two-step polynomial fitting method; determining the track goodness of fit of the member ephemeris history positioning result, and determining the deviation degree of the hierarchical positioning track and the real track according to the track goodness of fit; and calculating a fingerprint positioning result, and performing Kalman filtering on the fingerprint positioning result to obtain a final positioning result of the member satellite. The probability that the positioning error of the positioning result of the prediction tracking is less than 5m is 90%, the probability that the positioning error is less than 10m is about 95%, and the probability that the positioning error is less than 30m exceeds 95%. The positioning accuracy is much higher than the untracked positioning result.)

1. A satellite position prediction tracking method based on position fingerprints and two-step polynomial fitting is characterized by comprising the following steps of: the method comprises the following steps:

step 1: setting a time window, and carrying out N times of continuous positioning on member satellites at a certain time by a satellite hierarchical positioning method based on position fingerprints from the starting time of the time window to determine a track formed by N discrete positions of the member satellites in the time window;

step 2: taking N discrete positions in a time window as a historical positioning result, and determining a two-step polynomial fitting value of the N discrete positions according to a two-step polynomial fitting method;

and step 3: determining the track goodness of fit of the member ephemeris history positioning result, and determining the deviation degree of the hierarchical positioning track and the real track according to the track goodness of fit;

and 4, step 4: calculating a fingerprint positioning result, and performing Kalman filtering on the fingerprint positioning result to obtain a final positioning result of the member satellite;

and 5: sliding the time window to the movement direction of the member satellite by 1 unit, judging whether the member satellite has the maneuver rail change at the current moment according to the member satellite receiving signaling, and repeating the step 2 to the step 4 when the maneuver rail change does not exist; and when the maneuvering orbital transfer exists, resetting the time window, taking the orbital transfer moment as the starting moment of the time window, and repeating the steps 1 to 4.

2. The method of claim 1, wherein the method comprises: continuously positioning member stars for N times in a certain time by a satellite hierarchical positioning method based on position fingerprints, determining a track formed by N discrete positions of the member stars in a time window, and representing the track formed by the N discrete positions of the member stars in the time window by the following formula:

L＝[l₁l₂…l_N]^T

l_i＝(x_i,y_i,z_i),i＝1,2,…,N

wherein L is a track formed by N discrete positions, L_NIs the ith position in L.

3. The method of claim 1, wherein the method comprises: the step 2 specifically comprises the following steps:

step 2.1: fitting and calculating the X-axis data, the Y-axis data and the Z-axis data of N discrete positions in the time window to obtain a polynomial fitting track equation, and expressing the one-step polynomial fitting track equation by the following formula:

wherein p is_n(t) is the X-axis one-step polynomial fitting trajectory equation, q_n(t) is a Y-axis one-step polynomial fitting trajectory equation, r_n(t) is a Z-axis one-step polynomial fitting trajectory equation; n is the degree of the one-step fitting polynomial, k is the number of the degree of the one-step fitting polynomial, a_kFitting polynomial coefficients to the X-axis in one step, b_kFitting polynomial coefficients to the Y-axis in one step, c_kFitting polynomial coefficients, t, for the Z-axis in one step^kIs the corresponding time;

determining a trajectory of the one-step polynomial fit, the trajectory of the one-step polynomial fit being represented by:

wherein the content of the first and second substances,for the trajectory of the one-step polynomial fit,is t_iA one-step polynomial fit value of the trajectory of the time;

step 2.2: determining the difference value between the historical positioning result and the one-step polynomial fitting value according to the track fitted by the one-step polynomial, and expressing the difference value between the historical positioning result and the one-step polynomial fitting value by the following formula:

wherein the content of the first and second substances,the difference value of the historical positioning result and the one-step polynomial fitting value is obtained;

determining a two-step polynomial fitting threshold value according to the difference value between the historical positioning result and the one-step polynomial fitting value, and expressing the two-step polynomial fitting threshold value by the following formula:

wherein, mean (-) represents the median, k is a proportionality constant, and η is a two-step polynomial fitting threshold;

step 2.3: fitting the polynomial fitting process again to obtain a two-step polynomial fitting trajectory equation, and expressing the two-step polynomial fitting trajectory equation by the following formula:

wherein the content of the first and second substances,fitting a trajectory equation for an X-axis two-step polynomial,fitting polynomial coefficients for the X-axis two-step,fitting a trajectory equation for a two-step polynomial of the Y axis,fitting polynomial coefficients for the Y-axis two-step,fitting a trajectory equation for a Z-axis two-step Z polynomial,fitting polynomial coefficients for the Z axis in two steps;

determining a two-step polynomial fitting value of the historical positioning result of the member star according to a polynomial function, and representing the two-step polynomial fitting value by the following formula:

wherein the content of the first and second substances,a two-step polynomial fit value of the member ephemeris history positioning result,is at the t_iA two-step polynomial fit value of the trajectory of the time of day.

4. The method of claim 3, wherein the method comprises: determining the track goodness of the member ephemeris history positioning result, and expressing the track goodness of fit through the following formula:

wherein w is the track goodness of fit of the member satellite historical positioning result, I (·) is an indication function, v is the running speed of the member satellite, and c is a proportionality constant;

points with large deviation in the historical positioning result are increased, the fitting position cannot represent the real position, and the goodness of fit is reduced.

5. A location based fingerprint according to claim 1And a satellite position prediction tracking method of two-step polynomial fitting, which is characterized in that: the calculation of the fingerprint positioning result specifically comprises the following steps: determining a threshold value sigma of the track goodness of fit, wherein sigma is 0.8, and when the track goodness of fit w of the member satellite historical positioning result is less than sigma, obtaining t by a satellite grading positioning method based on position fingerprints_N+1The time fingerprint positioning result is represented by the following formula t_N+1And (3) fingerprint positioning result at moment:

wherein the content of the first and second substances,is t_N+1The result of the fingerprint positioning at the moment,is t_N+1The X-axis coordinate of the fingerprint positioning result at the moment,is t_N+1The Y-axis coordinate of the fingerprint positioning result at the moment,is t_N+1The Z-axis coordinate of the moment fingerprint positioning result;

when w is more than or equal to sigma, obtaining a polynomial function pair t according to two-step fitting_N+1Predicting the positions of the member stars at the moment to obtain t_N+1A predicted location of a time member star, the predicted location represented by:

wherein the content of the first and second substances,is t_N+1The predicted location of the time member star;

with t_N+1Predicted location of a time member starEstablishing a tracking area with the side length of l as a center, dividing the tracking area into a plurality of microcubes with the side length of l', taking the center of each microcube as a reference point, and obtaining t by utilizing a KNN algorithm_N+1The time fingerprint positioning result is represented by the following formula t_N+1And (3) fingerprint positioning result at moment:

6. the method of claim 1, wherein the method comprises: the final positioning result of the member satellite is determined as follows:

step 4.1: passing through t_NThe state of the moment is t_N+1Kalman prediction of time statesBy the following formula t_N+1Representation Kalman prediction value of time state

X_N＝[l_Nv]^T

Wherein A is a state transition matrix, X_NIs t_NState of the moment,/_NIs t_NThe positioning result of the member star at the moment,

calculating t_N+1The predicted value of the state covariance matrix at the time is represented by the following equation_N+1Prediction of state covariance matrix at time:

wherein the content of the first and second substances,is t_N+1Prediction value of the state covariance matrix at a time, P_NRepresents t_NA time state covariance matrix, Q representing a process noise covariance matrix;

step 4.2: will t_N+1Using the fingerprint positioning result of the moment as an observed value and using t_N+1Correcting the Kalman predicted value of the current state by the observation value at the moment so as to obtain t_N+1Time correction state X_N+1：

Where K is the Kalman gain, l_N+1Is member star at t_N+1A final positioning result at the moment, H is an observation matrix, R represents a measurement noise covariance matrix, and Z is an observation value;

step 4.3: according to t_N+1Time correction state X_N+1Determining member star at t_N+1And (4) the final positioning result of the moment represents the member star at t by the following formula_N+1And (3) a final positioning result at the moment:

l_N+1＝(x_N+1,y_N+1,z_N+1)

wherein l_N+1Is t_N+1And finally positioning the result at the moment.

Technical Field

The invention relates to the technical field of satellite position prediction tracking, in particular to a satellite position prediction tracking method based on position fingerprints and two-step polynomial fitting.

Background

A satellite constellation refers to a distributed satellite system consisting of a plurality of satellites. Wherein, one or a plurality of satellites are selected as reference satellites, and the other satellites are member satellites. The reference star flies along a preset orbit, and the member star follows the reference star to accompany flying. The purpose of autonomous positioning of the satellite cluster is to position the member satellites by using the information of the reference satellite. Conventional satellite constellation autonomous positioning is mainly aimed at two satellites or small scale satellite constellations. With the continuous development of the task demand of the space mission, the number of the satellite cluster members is continuously increased, and the functions tend to be specialized, so that a fast and low-cost positioning technology with cluster autonomy needs to be researched. The positioning method based on the position fingerprint is a mature positioning method, and the fingerprint positioning system has the characteristics of low cost and simple structure, so that the fingerprint positioning method is expanded to satellite cluster positioning, the development cost can be effectively reduced, and the method has important significance on the cooperative control of a satellite cluster and the development of a satellite technology.

However, because the satellite cluster range is large, the positions of the member satellites at any time cannot be guaranteed to be within a range close to the reference satellite, so that the positioning results of some member satellites are greatly deviated from the real positions, and the positioning accuracy is rapidly reduced. Secondly, the reference stars are in periodic operation all the time, and the topology formed between the reference stars also shows periodic changes. When the topology of the reference star at a certain moment is poor, especially when the reference stars are located on the same plane, the signal distribution in the space will present symmetry, which also results in that the positioning result at that moment deviates too much from the actual situation. Member stars need to be tracked to improve positioning accuracy.

Disclosure of Invention

The invention provides a satellite position prediction tracking method based on position fingerprints and two-step polynomial fitting for improving positioning accuracy, and the invention provides the following technical scheme:

a satellite position prediction tracking method based on position fingerprints and two-step polynomial fitting comprises the following steps:

step 1: setting a time window, and carrying out N times of continuous positioning on member satellites at a certain time by a satellite hierarchical positioning method based on position fingerprints from the starting time of the time window to determine a track formed by N discrete positions of the member satellites in the time window;

step 2: taking N discrete positions in a time window as a historical positioning result, and determining a two-step polynomial fitting value of the N discrete positions according to a two-step polynomial fitting method;

and step 3: determining the track goodness of fit of the member ephemeris history positioning result, and determining the deviation degree of the hierarchical positioning track and the real track according to the track goodness of fit;

and 4, step 4: calculating a fingerprint positioning result, and performing Kalman filtering on the fingerprint positioning result to obtain a final positioning result of the member satellite;

and 5: sliding the time window to the movement direction of the member satellite by 1 unit, judging whether the member satellite has the maneuver rail change at the current moment according to the member satellite receiving signaling, and repeating the step 2 to the step 4 when the maneuver rail change does not exist; and when the maneuvering orbital transfer exists, resetting the time window, taking the orbital transfer moment as the starting moment of the time window, and repeating the steps 1 to 4.

Preferably, the member satellite is continuously positioned for N times in a certain time by a satellite hierarchical positioning method based on the position fingerprint, the track formed by the N discrete positions of the member satellite in the time window is determined, and the track formed by the N discrete positions of the member satellite in the time window is represented by the following formula:

L＝[l₁l₂… l_N]^T

l_i＝(x_i,y_i,z_i),i＝1,2,…,N

wherein L is a track formed by N discrete positions, L_NIs the ith position in L.

Preferably, the step 2 specifically comprises:

step 2.1: fitting and calculating the X-axis data, the Y-axis data and the Z-axis data of N discrete positions in the time window to obtain a polynomial fitting track equation, and expressing the one-step polynomial fitting track equation by the following formula:

wherein p is_n(t) is the X-axis one-step polynomial fitting trajectory equation, q_n(t) is a Y-axis one-step polynomial fitting trajectory equation, r_n(t) is a Z-axis one-step polynomial fitting trajectory equation; n is the degree of the one-step fitting polynomial, k is the number of the degree of the one-step fitting polynomial, a_kFitting polynomial coefficients to the X-axis in one step, b_kFitting polynomial coefficients to the Y-axis in one step, c_kFitting polynomial coefficients, t, for the Z-axis in one step^kIs the corresponding time;

determining a trajectory of the one-step polynomial fit, the trajectory of the one-step polynomial fit being represented by:

wherein the content of the first and second substances,for the trajectory of the one-step polynomial fit,is t_iA one-step polynomial fit value of the trajectory of the time;

step 2.2: determining the difference value between the historical positioning result and the one-step polynomial fitting value according to the track fitted by the one-step polynomial, and expressing the difference value between the historical positioning result and the one-step polynomial fitting value by the following formula:

wherein the content of the first and second substances,locating results and one-step-multiple-item for historyDifference of the fitting values of the formulae;

determining a two-step polynomial fitting threshold value according to the difference value between the historical positioning result and the one-step polynomial fitting value, and expressing the two-step polynomial fitting threshold value by the following formula:

wherein, mean (-) represents the median, k is a proportionality constant, and η is a two-step polynomial fitting threshold;

step 2.3: fitting the polynomial fitting process again to obtain a two-step polynomial fitting trajectory equation, and expressing the two-step polynomial fitting trajectory equation by the following formula:

wherein the content of the first and second substances,fitting a trajectory equation for an X-axis two-step polynomial,fitting polynomial coefficients for the X-axis two-step,fitting a trajectory equation for a two-step polynomial of the Y axis,fitting polynomial coefficients for the Y-axis two-step,fitting a trajectory equation for a Z-axis two-step Z polynomial,fitting polynomial coefficients for the Z axis in two steps;

determining a two-step polynomial fitting value of the historical positioning result of the member star according to a polynomial function, and representing the two-step polynomial fitting value by the following formula:

wherein the content of the first and second substances,a two-step polynomial fit value of the member ephemeris history positioning result,is at the t_iA two-step polynomial fit value of the trajectory of the time of day.

Preferably, the track goodness of the member ephemeris history positioning result is determined, and is expressed by the following formula:

wherein w is the track goodness of fit of the member satellite historical positioning result, I (·) is an indication function, v is the running speed of the member satellite, and c is a proportionality constant;

points with large deviation in the historical positioning result are increased, the fitting position cannot represent the real position, and the goodness of fit is reduced.

Preferably, the calculating the fingerprint positioning result specifically includes: determining a threshold value sigma of the track goodness of fit, wherein sigma is 0.8, and when the track goodness of fit w of the member satellite historical positioning result is less than sigma, obtaining t by a satellite grading positioning method based on position fingerprints_N+1The time fingerprint positioning result is represented by the following formula t_N+1And (3) fingerprint positioning result at moment:

wherein the content of the first and second substances,is t_N+1The result of the fingerprint positioning at the moment,is t_N+1The X-axis coordinate of the fingerprint positioning result at the moment,is t_N+1The Y-axis coordinate of the fingerprint positioning result at the moment,is t_N+1The Z-axis coordinate of the moment fingerprint positioning result;

when w is more than or equal to sigma, obtaining a polynomial function pair t according to two-step fitting_N+1Predicting the positions of the member stars at the moment to obtain t_N+1A predicted location of a time member star, the predicted location represented by:

wherein the content of the first and second substances,is t_N+1The predicted location of the time member star;

with t_N+1Predicted location of a time member starEstablishing a tracking area with the side length of l as a center, dividing the tracking area into a plurality of microcubes with the side length of l', taking the center of each microcube as a reference point, and obtaining t by utilizing a KNN algorithm_N+1The time fingerprint positioning result is represented by the following formula t_N+1And (3) fingerprint positioning result at moment:

preferably, the determination of the final positioning result of the member satellite specifically comprises:

step 4.1: passing through t_NThe state of the moment is t_N+1Kalman prediction of time statesBy the following formula t_N+1Representation Kalman prediction value of time state

X_N＝[l_Nv]^T

Wherein A is a state transition matrix, X_NIs t_NState of the moment,/_NIs t_NThe positioning result of the member star at the moment,

calculating t_N+1The predicted value of the state covariance matrix at the time is represented by the following equation_N+1Prediction of state covariance matrix at time:

wherein the content of the first and second substances,is t_N+1Prediction value of the state covariance matrix at a time, P_NRepresents t_NA time state covariance matrix, Q representing a process noise covariance matrix;

step 4.2: will t_N+1Using the fingerprint positioning result of the moment as an observed value and using t_N+1Correcting the Kalman predicted value of the current state by the observation value at the moment so as to obtain t_N+1Time correction state X_N+1：

Where K is the Kalman gain, l_N+1Is member star at t_N+1A final positioning result at the moment, H is an observation matrix, R represents a measurement noise covariance matrix, and Z is an observation value;

step 4.3: according to t_N+1Time correction state X_N+1Determining member star at t_N+1And (4) the final positioning result of the moment represents the member star at t by the following formula_N+1And (3) a final positioning result at the moment:

l_N+1＝(x_N+1,y_N+1,z_N+1)

wherein l_N+1Is t_N+1And finally positioning the result at the moment.

The invention has the following beneficial effects:

according to the method, whether the historical positioning result meets the tracking condition or not is identified and judged in a mode of performing two-step fitting on the historical positioning result and calculating the track goodness of fit, and when the tracking condition is met, the predicted positions of the member satellites at the current moment are obtained by using the tracks fitted in the two steps; and then, determining a tracking area according to the predicted position, establishing a tracking RadioMap in the tracking area, performing fingerprint positioning again, determining a fingerprint positioning result of the member satellite, and performing Kalman filtering on the fingerprint positioning result to obtain a final positioning result.

The experimental result shows that the probability that the positioning error of the positioning result of the prediction tracking is less than 5m is 90%, the probability that the positioning error is less than 10m is about 95%, and the probability that the positioning error is less than 30m exceeds 95%. The positioning accuracy is much higher than the untracked positioning result. Therefore, the algorithm provided by the invention can greatly improve the positioning precision.

Drawings

FIG. 1 is a schematic diagram of setting a time window;

FIG. 2 is a schematic view of a tracking area;

FIG. 3 is a flow chart of a method for predicting and tracking satellite positions based on position fingerprints and two-step polynomial fitting;

FIG. 4 is a diagram illustrating a real track;

FIG. 5 is a diagram illustrating a hierarchical positioning result;

FIG. 6 is a diagram illustrating predicted trace results;

fig. 7 is a CDF graph of positioning error before and after correction.

Detailed Description

The present invention will be described in detail with reference to specific examples.