A joint trajectory fault-tolerant positioning method of photoelectric theodolite and remote radar

Abstract

The present invention discloses a joint trajectory fault-tolerant positioning method of an optoelectronic theodolite and a remote-site radar, which specifically comprises the following steps: firstly, a third-order difference model of trajectory parameters is established, and abnormal parameters and normal parameters in the trajectory parameters are identified according to a threshold principle; a trajectory fault-tolerant positioning method is established according to the identified normal parameters. B spline model; determine the spline coefficient estimate in the model by the least square method and obtain the spline fault-tolerant model; then obtain the correction value of the abnormal parameter by the abnormal parameter and the spline fault-tolerant model; finally, replace the abnormal parameter in the original trajectory parameter with the abnormal parameter correction value, update the trajectory parameter, and obtain accurate positioning results. By processing the abnormal data in the trajectory parameter, the located trajectory parameter is closer to the true value, which is more conducive to evaluating and improving the accuracy and performance of the guidance system, and can avoid the huge loss of benefits caused by the inaccurate trajectory parameters of the light-mine off-site positioning method.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace data processing, and in particular relates to a joint trajectory fault-tolerant positioning method of an optoelectronic theodolite and a remote-site radar. Background Art

[0002] In the post-measurement data processing of spacecraft, due to the influence of various factors such as station layout, it is often necessary to jointly locate the photoelectric theodolite and the radar at a different location, so as to give full play to the advantages of the high accuracy of the photoelectric theodolite angle measurement and the radar distance measurement, and to achieve positioning at a different location. For a long time, it has been highly valued and widely used in spacecraft positioning methods. However, due to the influence of inherent systematic errors and random errors in the measurement data of the photoelectric theodolite and the radar, and the fact that the two are in different coordinates constrained by different locations, the trajectory parameters located will produce some abnormal data, making it difficult to obtain a relatively satisfactory positioning result. However, the analysis, evaluation and identification of the post-measurement trajectory are important information bases for evaluating and improving the accuracy and performance of the guidance system, so the trajectory measured by the external measurement equipment must be high-precision and low-error. When the dynamic accuracy of the hardware measurement equipment is difficult to meet the actual needs, the high-precision trajectory fault-tolerant positioning method is a powerful supplement to the hardware. Summary of the invention

[0003] The purpose of the present invention is to provide a joint trajectory fault-tolerant positioning method of an optoelectronic theodolite and a remote-site radar, which can identify abnormal data in trajectory parameters, thereby improving the positioning accuracy of the entire trajectory.

[0004] The technical solution adopted by the present invention is a method for joint trajectory fault-tolerant positioning of an optoelectronic theodolite and a remote-site radar, which is specifically implemented according to the following steps:

[0005] Step 1: Establish a third-order difference model of ballistic parameters, and identify abnormal parameters and normal parameters in the ballistic parameters according to the threshold principle;

[0006] Step 2: Establish a ballistic cubic B-spline model based on the normal parameters identified in step 1;

[0007] Step 3, determine the spline coefficient estimation in the model of step 2 by the least square method and obtain the spline fault-tolerant model;

[0008] Step 4, obtaining a correction value of the abnormal parameter based on the abnormal parameter identified in step 1 and the spline fault tolerance model determined in step 3;

[0009] Step 5: Replace the abnormal parameters in the original trajectory parameters with the abnormal parameter correction values ​​obtained in step 4, update the trajectory parameters, and obtain accurate positioning results.

[0010] The present invention is also characterized in that:

[0011] In step 1, specifically: in the trajectory parameters in the X, Y or Z direction, {A i}i=1,2,L,n is a ballistic parameter data sequence sampled at equal intervals, where n is the data length. i} Make a third-order forward difference and get the third-order difference sequence, as shown in formula (1);

[0012] Δ 3 A i =Δ 2 A i+1 -Δ 2 A i (1);

[0013] In formula (1), Δ 2 A i =ΔA i+1 -ΔA i , Δ 2 A i+1 =ΔA i+2 -ΔA i+1 ; ΔA i =A i+1 -A i , ΔA i+1 =A i+2 -A i+1 ;

[0014] After obtaining the third-order difference sequence of trajectory parameters {Δ 3 A i}, i = 1, 2, L, n-3, the mean square error σ of the third-order difference sequence can be obtained, as shown in formula (2);

[0015]

[0016] In formula (2), m is the starting point of the data, l is the data length, σ is the corresponding mean square error, if σ>λ, λ is the judgment threshold, the ballistic data corresponding to this part of the differential data in the ballistic parameter is regarded as the abnormal parameter A abnormal ; If σ≤λ, then this part of the ballistic parameters is regarded as normal parameters A normal ,

[0017] In step 2, the specific process is as follows:

[0018] The normal trajectory parameters obtained from step 1 It is expressed by piecewise cubic B-spline function, as shown in formula (3);

[0019]

[0020] In formula (3), is the normal ballistic parameter, t i is the sampling time of the trajectory parameters, L is the data length; p is the number of segments, α j is the unknown spline coefficient of each segment, j = 0, L, p; ε i is the random error vector of trajectory parameters without abnormality; T0, T p are the two time endpoints of the trajectory parameter interval being processed, namely, T p =t L ,T0=t1,T j is the time corresponding to each trajectory parameter, and T j =T0+jh; h is the time length of each segment interval,

[0021] is the third-order standard B-spline function, let Then B(t) is as shown in formula (4);

[0022]

[0023] If you

[0024]

[0025] And let ε=[ε1,L,ε L ] T , then we get the cubic B-spline model, as shown in formula (5);

[0026] A normal =Tα+ε (5);

[0027] in,

[0028] In step 3, the specific process is as follows:

[0029] Assume that the random error vector ε is independent and has the same variance σ in the time series 2 , the spline coefficients are estimated by the least squares method As shown in formula (6);

[0030]

[0031] Further get the spline fault-tolerant model

[0032] In the formula, is the data sequence to be estimated, is the spline basis function of the data sequence to be estimated, and,

[0033]

[0034] N is the length of the data sequence to be estimated, P is the number of spline segments, and h is the time length of each segment interval.

[0035] In step 4, specifically: Calculating the spline basis function of abnormal area data in trajectory parameters Then the correction value of the abnormal area data is obtained by the spline fault tolerance model, as shown in formula (7);

[0036]

[0037] The beneficial effects of the present invention are that, since the third-order difference can separate the nonlinear trend in the trajectory parameters, and through the threshold principle, abnormal data can be identified, and because the 3rd order B-spline curve can well meet the characteristics of the trajectory curve, the abnormal data can be corrected and processed by establishing a 3rd order B-spline fault-tolerant model, thereby obtaining an accurate positioning result. Errors are inevitable in the actual external ballistic measurement process. The existence of measurement errors in the measurement data is taken into account, and the abnormal data in the trajectory parameters are processed, so that the located ballistic parameters are closer to the true values, which is more conducive to evaluating and improving the accuracy and performance of the guidance system. The ballistic parameters obtained by the ballistic fault-tolerant positioning method of the photoelectric theodolite and the remote radar of the present invention can avoid the huge loss of benefits caused by the inaccurate ballistic parameters of the light-thunder remote positioning method. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a method for joint trajectory fault-tolerant positioning of an optoelectronic theodolite and a remote-site radar according to the present invention;

[0039] Figure 2 It is the relationship diagram of the joint positioning between the photoelectric theodolite and the radar;

[0040] Figure 3 It is a relationship diagram when the measurement information of the photoelectric theodolite and radar intersect;

[0041] Figure 4 It is a relationship diagram when the measurement information of the photoelectric theodolite and radar are tangent;

[0042] Figure 5 It is a comparison diagram of the trajectory parameter results of the joint trajectory fault-tolerant positioning method of the photoelectric theodolite and the off-site radar of the present invention, as well as the light-radar off-site positioning results and the GPS trajectory parameter X direction;

[0043] Figure 6 It is a comparison diagram of the trajectory parameter results of the joint trajectory fault-tolerant positioning method of the photoelectric theodolite and the off-site radar of the present invention, as well as the light-radar off-site positioning results and the GPS trajectory parameter Y direction;

[0044] Figure 7It is a comparison diagram of the trajectory parameter results of the joint trajectory fault-tolerant positioning method of the photoelectric theodolite and the off-site radar of the present invention, as well as the light-radar off-site positioning results and the GPS trajectory parameter Z direction;

[0045] Figure 8 It is the ballistic parameter result of the joint ballistic fault-tolerant positioning method of the photoelectric theodolite and the remote radar of the present invention, as well as the difference diagram of the light-radar remote positioning result and the GPS ballistic parameter X direction;

[0046] Fig. 9 It is the ballistic parameter result of the joint ballistic fault-tolerant positioning method of the photoelectric theodolite and the remote radar of the present invention, as well as the difference diagram of the light-radar remote positioning result and the GPS ballistic parameter Y direction;

[0047] Fig.10 It is the ballistic parameter result of the joint ballistic fault-tolerant positioning method of the photoelectric theodolite and the remote radar of the present invention, as well as the difference diagram of the light-radar remote positioning result and the GPS ballistic parameter Z direction. DETAILED DESCRIPTION

[0048] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] like Figure 2 As shown in the figure, assuming that the coordinates of the target in the launch system are (X, Y, Z), and the station location of the photoelectric theodolite in the launch system is (X g ,Y g ,Z g ), the radar station in the transmitting system is (X l ,Y l ,Z l ), the distance measurement information of the radar is R, and the angle measurement information of the photoelectric theodolite transmission system is A and E. The light-radar location method is through Figure 2 The joint positioning relationship between the optoelectronic theodolite and the off-site radar is used to establish the positioning model of the target and the measuring station to obtain the target trajectory parameters. As shown in the following formula

[0050]

[0051] For the above positioning model, one or two sets of target trajectory parameters can be solved. Figure 3 As shown in the figure, when the ray formed by the measurement information of the photoelectric theodolite intersects the sphere formed by the measurement information of the radar, two sets of target trajectory parameters (X1, Y1, Z1) and (X2, Y2, Z2) can be solved. Then, the true solution (X, Y, Z) can be determined by whether the direction vector between the measuring station and the target is consistent with the direction of the ray formed by the measurement information of the photoelectric theodolite. Figure 4As shown in the figure, when the ray formed by the measurement information of the photoelectric theodolite is tangent to the sphere formed by the measurement information of the radar, a set of target trajectory parameters (X, Y, Z) can be solved in theory. However, the exterior ballistic measurement data contains certain errors, large or small. At this time, due to the influence of the measurement information error, two sets of trajectory position parameters (X′1, Y′1, Z′1) and (X′2, Y′2, Z′2) will be solved. If the direction vector of the space straight line is continued, the true solution (X, Y, Z) can also be determined, but this is bound to produce errors. Research has found that abnormal data with jumps will be generated in this nearby area.

[0052] The present invention discloses a method for joint ballistic fault-tolerant positioning of photoelectric theodolite and off-site radar. Firstly, a third-order difference model of trajectory parameters is established for the result of the light-radar off-site positioning method, and abnormal data in the trajectory parameters is identified according to the threshold principle. Finally, a cubic B-spline fault-tolerant model is established to correct the abnormal data, thereby obtaining an accurate positioning result.

[0053] like Figure 1 As shown, the specific implementation steps are as follows:

[0054] Step 1: Establish a third-order difference model of trajectory parameters for the light-radar off-site positioning results, and identify abnormal parameters and normal parameters in the trajectory parameters according to the threshold principle;

[0055] Specifically: In the trajectory parameters of the X, Y or Z direction, {A i}i=1,2,L,n is a ballistic parameter data sequence sampled at equal intervals, where n is the data length. i} Make a third-order forward difference and get the third-order difference sequence, as shown in formula (1);

[0056] Δ 3 A i =Δ 2 A i+1 -Δ 2 A i (1);

[0057] In formula (1), Δ 2 A i =ΔA i+1 -ΔA i , Δ 2 A i+1 =ΔA i+2 -ΔA i+1 ; ΔA i =A i+1 -A i , ΔA i+1 =A i+2 -A i+1

[0058] After obtaining the third-order difference sequence of trajectory parameters {Δ 3 A i}, i = 1, 2, L, n-3, since the difference can eliminate the trend term in the trajectory parameters, the mean square error σ of the third-order difference sequence can be obtained, as shown in formula (2);

[0059]

[0060] In formula (2), m is the starting point of the data, l is the data length, and σ is the corresponding mean square error. According to the threshold principle, if σ>λ, the ballistic data corresponding to this part of the differential data in the ballistic parameter is regarded as the abnormal parameter A. abnormal ; If σ≤λ, then this part of the ballistic parameters is regarded as normal parameters A normal ,

[0061] λ is the judgment threshold, which is 3 to 5 times the measurement accuracy. To reduce the amount of calculation, the third-order difference data {Δ 3 A i}, i=1,2,L,n-3, any 30-point data can be taken to calculate the measurement accuracy, as shown in the following formula;

[0062]

[0063] Where δ is the measurement accuracy, m′ is the starting point of the third-order difference data, and l′ is the data length.

[0064] Step 2: Establish a ballistic cubic B-spline model based on the normal parameters identified in step 1; the specific process is as follows:

[0065] The cubic B-spline curve is generalized based on the Bezier curve. It solves many shortcomings of the Bezier curve and has many important properties: geometric invariance, convex hull, convexity preservation, variation reduction, and local support.

[0066] The normal trajectory parameters obtained from step 1 It can be expressed by a piecewise cubic B-spline function, as shown in formula (3);

[0067]

[0068] In formula (3), is the normal ballistic parameter, t i is the sampling time of the trajectory parameters, L is the data length; p is the number of segments, α j is the unknown spline coefficient of each segment, j = 0, L, p; ε i is the random error vector of trajectory parameters without abnormality; T0, T pare the two time endpoints of the trajectory parameter interval being processed, namely, T p =t L ,T0=t1,T j is the time corresponding to each trajectory parameter, and T j =T0+jh; h is the time length of each segment interval,

[0069] is the third-order standard B-spline function, let Then B(t) is as shown in formula (4);

[0070]

[0071] If you

[0072]

[0073] And let ε=[ε1,L,ε L ] T , then we can get the cubic B-spline model, as shown in formula (5);

[0074] A normal =Tα+ε (5);

[0075] in,

[0076] Step 3: Determine the spline coefficient estimate in the model of step 2 by the least square method and obtain the spline fault-tolerant model; the specific process is as follows:

[0077] For the unknown spline coefficient α in step 2, assume that the random error vector ε is independent and has the same variance σ in the time series. 2 , the spline coefficients can be estimated by the least squares method, as shown in formula (6);

[0078]

[0079] Further, we can get the spline fault-tolerant model

[0080] In the formula, is the data sequence to be estimated, is the spline basis function of the data sequence to be estimated, and,

[0081]

[0082] N is the length of the data sequence to be estimated, P is the number of spline segments, and h is the time length of each segment interval. is an estimate of the spline coefficients.

[0083] Step 4, obtaining a correction value of the abnormal parameter based on the abnormal parameter identified in step 1 and the spline fault tolerance model determined in step 3;

[0084] From step 3 Calculating the spline basis function of abnormal area data in trajectory parameters Then, the spline fault-tolerant model The correction value of the abnormal area data is obtained, as shown in formula (7);

[0085]

[0086] Step 5: Replace the abnormal parameters in the original trajectory parameters with the abnormal parameter correction values ​​obtained in step 4, update the trajectory parameters, and obtain accurate positioning results.

[0087] After the photoelectric theodolite and the off-site radar jointly locate the target trajectory, according to the continuity of the trajectory change, when the sampling frequency of the measurement data is high enough, the gap between adjacent observations will be very small, and as long as the target trajectory parameters do not change, the trajectory position curve will not change suddenly. Therefore, the third-order difference model can be used to separate the nonlinear trend, and then the abnormal data can be identified according to the threshold principle. The advantage of the difference is that it can transform a non-stationary sequence into a stationary sequence, especially when the time series contains a significant linear trend, the trend term can be extracted by the first-order difference. Theoretical and practical results have shown that the Taylor expansion of the trajectory with respect to time t is at most a 4th-order polynomial. Therefore, for the trend in the trajectory data, low-order (second-order or third-order) differences can usually extract the influence of the curve trend.

[0088] After identifying the abnormal data, considering that the ballistic curve will not change suddenly, the data set with the abnormal data removed can be used to establish a cubic B-spline fault-tolerant model of the trajectory. In addition to the fault-tolerant function of the trajectory parameters, the model can also ensure high positioning accuracy by correcting the abnormal data. The reason is that the cubic B-spline is developed based on the Bezier curve, which has many excellent properties such as geometric invariance, reduced variation, and local support. Moreover, it is a smooth curve with continuous second-order derivatives, which can well meet the characteristics of the ballistic curve. On the other hand, the ballistic curve model established by the cubic B-spline requires much fewer identification parameters than the polynomial model.

[0089] The present invention uses the external ballistic measurement data of a rocket launch mission for experimental analysis, selects the data of a photoelectric theodolite and a radar for the experiment, uses the data between 11.3s and 130s of the two devices, and the sampling frequency is 20HZ. First, the trajectory position parameters are obtained according to the light-ray off-site positioning method, and then the abnormal area in the trajectory parameters is identified by the third-order difference model, and the data of the abnormal area is corrected and processed by the third-order B-spline fault-tolerant model, and the results of the light-ray off-site positioning method and the method of the present invention are compared with the GPS data of this mission. Figure 5 , Figure 6 , Figure 7 The figure is a comparison diagram of the trajectory position parameters obtained by the light-radar off-site positioning method and the method of the present invention and the GPS trajectory parameters, which are the X-direction trajectory parameters, the Y-direction trajectory parameters, and the Z-direction trajectory parameters in sequence. Figure 8 , Fig. 9 , Fig.10 It is a difference diagram between the trajectory position parameters obtained by the light-radar off-site positioning method and the method of the present invention and the GPS trajectory parameters, which are the trajectory parameter difference in the X direction, the trajectory parameter difference in the Y direction, and the trajectory parameter difference in the Z direction.

[0090] from Figures 5 to 10 It can be seen from the comparison chart and difference chart of the ballistic parameter results that if the ballistic parameters obtained by the light-radar off-site positioning method are used, abnormal data with jumps will appear in the area of ​​25s to 45s. However, the data in the jump area of ​​the ballistic parameters obtained by the method of the present invention will be obviously corrected, and the corrected results are greatly close to the GPS ballistic parameters. This result illustrates the correctness and reliability of the method of the present invention.

[0091] Table 1 shows the root mean square error between the results of the light-radar off-site positioning method and the method of the present invention and the GPS trajectory parameters.

[0092] Table 1 Error comparison between the two methods

[0093]

[0094] It can be seen from the above table that the ballistic parameters obtained by the method of the present invention are significantly different from those obtained by the light-radar off-site positioning method, especially the root mean square errors of the Y-direction ballistic parameters and the Z-direction ballistic parameters are reduced by more than 60%. However, the abnormal data area is only about 20s, accounting for about 16.7% of the total data time length, which shows that the positioning result of the method of the present invention is better than that of the light-radar positioning method.

[0095] Through the above simulation analysis, it can be seen that the joint ballistic fault-tolerant positioning method of the photoelectric theodolite and the remote-site radar proposed in the present invention can locate the target trajectory parameters more effectively and accurately when there are errors in the measurement data, compared with the light-radar remote-site positioning method.

Claims

1. A method for joint trajectory fault-tolerant positioning of an optoelectronic theodolite and a remote radar, characterized in that: Follow the steps below to implement it: Step 1: Establish a third-order difference model of ballistic parameters, and identify abnormal parameters and normal parameters in the ballistic parameters according to the threshold principle; specifically: in the ballistic parameters in the X, Y or Z direction, {A i }| i＝1，2，…，n is a ballistic parameter data sequence sampled at equal intervals, where n is the data length. i } Make a third-order forward difference and get the third-order difference sequence, as shown in formula (1); D 3 A i =D 2 A i+1 -D 2 A i (1); In formula (1), Δ 2 A i = ΔA i+1 - ΔA i , Δ 2 A i+1 = ΔAi i+2 - ΔA i+1 ; ΔA i = A i+1 - A i , ΔA i+1 = A i+2 - A i+1 ; After obtaining the third-order difference sequence of trajectory parameters {Δ 3 A i }, i = 1, 2, ..., n-3, the mean square error σ of the third-order difference sequence can be obtained, as shown in formula (2); In formula (2), m is the starting point of the data, l is the data length, σ is the corresponding mean square error, if σ>λ, λ is the judgment threshold, the ballistic data corresponding to this part of the differential data in the ballistic parameter is regarded as the abnormal parameter A abnormal ; If σ≤λ, then this part of the ballistic parameters is regarded as normal parameters A normal , A normal , λ is 3 to 5 times the measurement accuracy. To reduce the amount of calculation, the third-order difference data {Δ 3 A i }, i=1, 2, ..., n-3, any 30 points of data can be selected to calculate the measurement accuracy, as shown in the following formula; In the formula, δ is the measurement accuracy, m′ is the starting point of the third-order difference data, and l′ is the data length; Step 2: Establish a ballistic cubic B-spline model based on the normal parameters identified in step 1; the specific process is as follows: The normal trajectory parameters obtained from step 1 It is expressed by piecewise cubic B-spline function, as shown in formula (3); In formula (3), is the normal ballistic parameter, t i is the sampling time of the trajectory parameters, L is the data length; p is the number of segments, α j is the unknown spline coefficient of each segment, j = 0, ..., p; ε i is the random error vector of trajectory parameters without abnormality; T0, T p are the two time endpoints of the trajectory parameter interval being processed, namely, T p =t L ,T0=t1,T j is the time corresponding to each trajectory parameter, and T j =T0+jh; h is the time length of each segment interval, is the third-order standard B-spline function, let Then B(t) is as shown in formula (4); If you And let ε=[ε1,…,ε L ] T , then we get the cubic B-spline model, as shown in formula (5); A normal =Tα+ε (5); in, Step 3: Determine the spline coefficient estimate in the model of step 2 by the least square method and obtain the spline fault-tolerant model; the specific process is as follows: Assume that the random error vector ε is independent and has the same variance σ in the time series 2 , the spline coefficients are estimated by the least squares method As shown in formula (6); Further get the spline fault-tolerant model In the formula, is the data sequence to be estimated, is the spline basis function of the data sequence to be estimated, and, N is the length of the data sequence to be estimated, P is the number of spline segments, and h is the time length of each segment interval; Step 4: Obtain a correction value of the abnormal parameter from the abnormal parameter identified in step 1 and the spline fault tolerance model determined in step 3; specifically: Calculating the spline basis function of abnormal area data in trajectory parameters Then the correction value of the abnormal area data is obtained by the spline fault tolerance model, as shown in formula (7); Step 5: Replace the abnormal parameters in the original trajectory parameters with the abnormal parameter correction values ​​obtained in step 4, update the trajectory parameters, and obtain accurate positioning results.

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