A trajectory multi-source measurement data real-time slicing fusion method

Abstract

The present application relates to a kind of trajectory of exterior ballistic trajectory multi-source measurement data real-time slice fusion methods, comprising: the multiple measuring data of multiple exterior measuring equipment are respectively preprocessed, then carry out equal time interval slice processing;Linear fitting prediction, Kalman filtering prediction and Kalman correction processing are carried out respectively to each measuring data in slice interval using least square method and Kalman filtering, obtain the to-be-fused value corresponding to slice time;The to-be-fused value corresponding to slice time of multiple measuring data is carried out weighted fusion processing, and trajectory of fused trajectory is obtained.The trajectory of exterior ballistic trajectory multi-source data real-time slice fusion method of the present application effectively combines polynomial extrapolation and Kalman filtering technology, overcomes the problem in the fusion process using single technology, compared with existing slice fusion algorithm, not only the trajectory data precision obtained is higher, in realization also more meet real-time, have higher engineering technical application value.

Description

Technical Field

[0001] This invention belongs to the field of external ballistic trajectory measurement technology, specifically relating to a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectories. Background Technology

[0002] External ballistic trajectory measurement technology obtains motion information such as the target's position and velocity during flight through optical or radio means. This provides support for target tracking, monitoring, guidance, and control, and offers relevant ballistic measurement information for target flight performance evaluation and design improvement. In external ballistic trajectory measurement, the commonly used external measuring equipment for optical measurement is the photoelectric theodolite, while pulse radar and telemetry are commonly used for radio measurement.

[0003] In practical work, measurements are susceptible to random noise interference, resulting in abrupt changes and jumps in data. This leads to inaccurate information about the position of the flight target, large spikes and low smoothness in the fused external ballistic trajectory. If such trajectory data is used for target guidance measurement, it will cause the measurement and control equipment to start and stop suddenly, resulting in high operational risks and making it difficult to effectively and continuously track and measure.

[0004] Currently, multi-source data fusion technology for external ballistic trajectories mainly involves improvements and extensions to the least squares method and Kalman filtering. Existing fusion algorithms consist of three parts: determining predicted values, determining correction values, and determining fusion weights. While determining predicted values ​​solves the problem of inconsistent measurement time intervals between stations, it requires two least squares fitting extrapolations, resulting in high time complexity for the fusion calculation. When determining correction values, it fails to consider the problem of large linear fitting errors caused by sudden increases in the trajectory curvature during the target's stable flight phase. Furthermore, when determining fusion weights, due to significant differences in linear fitting accuracy between different stations, the determination of weights for different dimensions of external ballistic trajectory measurements fails to account for varying random noise during the measurement process, leading to inconsistent measurement accuracy and ultimately insufficient accuracy of the final fusion result.

[0005] In summary, existing research only applies least squares polynomial fitting or filtering techniques to multi-source data fusion, which results in problems such as long fusion time or insufficient fusion accuracy. Summary of the Invention

[0006] To address the aforementioned problems in existing slice fusion techniques, this invention provides a real-time slice fusion method for multi-source measurement data of external ballistic trajectories. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] This invention combines least squares polynomial fitting and Kalman filtering techniques to provide a real-time slice fusion method for multi-source measurement data of external ballistic trajectories, including:

[0008] Step 1: After preprocessing the multi-channel measurement data acquired by various external measuring devices, perform equal time interval slicing processing;

[0009] Step 2: Using the least squares method and Kalman filtering, linear fitting prediction, Kalman filtering prediction and Kalman correction are performed on each measurement data in the slice interval to obtain the value to be fused at the slice time.

[0010] Step 3: Perform weighted fusion processing on the values ​​to be fused corresponding to the multi-channel measurement data at the slice time to obtain the fused ballistic trajectory.

[0011] In one embodiment of the present invention, the multi-channel measurement data includes telemetry measurement data, radar measurement data, and photoelectric theodolite measurement data.

[0012] In one embodiment of the present invention, the preprocessing includes time alignment processing and coarse error processing.

[0013] In one embodiment of the present invention, step 2 includes:

[0014] Step 2.1: Use the least squares method to perform linear fitting on the data within the slice time period to obtain the initial predicted value at the corresponding slice time.

[0015] Step 2.2: Perform Kalman filtering on the slice time to obtain the Kalman prediction value at the slice time. Use the Kalman prediction value at the slice time to perform Kalman correction on the initial prediction value at the slice time to obtain the value to be fused at the corresponding slice time.

[0016] In one embodiment of the present invention, step 2.1 includes:

[0017] The least squares method is used to fit and extrapolate the data within the slice time period on the X, Y, and Z coordinate axes respectively to obtain the extrapolated value of the slice time. The extrapolated value is used as the initial predicted value of the slice time.

[0018] In one embodiment of the present invention, step 2.2 includes:

[0019] Step 2.2.1: Based on the Kalman time update equation, filter to obtain the Kalman prediction value at the current slice time;

[0020] Step 2.2.2: Using the Kalman prediction value at the current slice time as the correction value, perform Kalman correction processing on the initial prediction value at the current slice time according to the Kalman measurement update equation to obtain the value to be fused at the current slice time.

[0021] In one embodiment of the present invention, the Kalman time update equation is:

[0022]

[0023]

[0024] In the formula, k represents the slice time, and k-1 represents the time corresponding to the data preceding the existing slice time. F represents the Kalman prediction value at time k. k Represents the state transition matrix. B represents the Kalman prediction value at time k-1. k Represents the state control matrix, u k Represents the state control vector. Let k represent the covariance matrix at time k. Let w represent the covariance matrix at time k-1. k This represents the system state error, which follows a mean of 0 and a variance of Q. k Gaussian distribution;

[0025] The Kalman measurement update equation is as follows:

[0026]

[0027]

[0028]

[0029] In the formula, K represents the Kalman filter gain, and H... k Let R represent the observation matrix. k Let z represent the measurement covariance matrix. k X represents the initial predicted value. k Let P represent the corrected state matrix. k This represents the corrected covariance matrix.

[0030] In one embodiment of the present invention, step 3 includes:

[0031] Step 3.1: Calculate the measurement error corresponding to each type of external measuring device;

[0032] The measurement error is calculated as follows:

[0033]

[0034] in:

[0035]

[0036] In the formula, s represents the integer time preceding the slice time, i.e., s = ceil(Δk-1), ceil(s) represents rounding up s, and Δk represents the size of the slice time interval. This represents the measurement accuracy of the i-th external measuring device at time k. This represents the measurement data of the i-th external measuring device at the j-th time within the slice interval. Let represent the average value of the measurement data of the i-th external measuring device within the slice interval, n represent the number of measurement data within the slice interval, and m represent the number of external measuring devices;

[0037] Step 3.2: Assign corresponding weighting coefficients to the values ​​to be fused according to the measurement error, and then perform data weighted fusion to obtain fused ballistic trajectory data;

[0038] The calculation of the weighted data fusion is as follows:

[0039]

[0040] In the formula, x k This represents the weighted fused data at time k. This represents the value to be fused obtained from the measurement data acquired by the i-th external measuring device at time k after fitting extrapolation, Kalman prediction, and Kalman correction. This represents the weighting coefficient corresponding to the i-th external measuring device at time k.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] 1. The real-time slice fusion method for multi-source measurement data of external ballistic trajectory of the present invention uses a fitting extrapolation algorithm to determine the initial prediction value within a short slice time interval, and uses the least squares linear fitting method to complete both real-time time alignment and prediction of unbuffered data. Compared with the existing slice fusion algorithm, it reduces one fitting and one fusion in algorithm implementation and takes less time in data processing.

[0043] 2. The real-time slice fusion method for multi-source measurement data of external ballistic trajectory of the present invention uses Kalman filtering technology to determine the correction value. Combining three different types of station system noise and random noise in the measurement process, a consistent linear minimum variance unbiased estimate can be obtained. Compared with the existing slice fusion algorithm that uses the least squares fitting method, this method is more accurate in the correction value of the stable segment of the target flight.

[0044] 3. The real-time slice fusion method for multi-source measurement data of external ballistic trajectory of the present invention uses a statistical weighting method to determine the fusion weights, which can effectively suppress the interference of different random noises from different measurement devices and reflect the characteristics of the real ballistic trajectory. In addition, the fusion algorithm has good robustness compared with the existing slice fusion algorithm. When some ballistic data of low quality appears, it will not affect the accuracy of the final fusion result.

[0045] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0046] Figure 1 This is a flowchart of a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory provided by an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory provided in an embodiment of the present invention;

[0048] Figure 3 This is a flowchart of a slice fusion algorithm provided in an embodiment of the present invention. Detailed Implementation

[0049] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory proposed according to the present invention, in conjunction with the accompanying drawings and specific embodiments.

[0050] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0051] Please see Figures 1-3 , Figure 1 This is a flowchart of a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of a real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory provided in an embodiment of the present invention; Figure 3 This is a flowchart of a slice fusion algorithm provided in an embodiment of the present invention.

[0052] The real-time slicing and fusion method for multi-source measurement data of external ballistic trajectories in this embodiment includes:

[0053] Step 1: After preprocessing the multi-channel measurement data acquired by various external measuring devices, perform equal time interval slicing processing;

[0054] In this embodiment, the external measurement equipment used includes telemetry, radar, and photoelectric theodolite, and the corresponding multi-channel measurement data includes telemetry measurement data, radar measurement data, and photoelectric theodolite measurement data.

[0055] In an optional embodiment, preprocessing includes time alignment and coarse error processing. The coarse error processing employs existing coarse error processing algorithms, the specific process of which will not be detailed here.

[0056] Step 2: Using the least squares method and Kalman filtering, linear fitting prediction, Kalman filtering prediction and Kalman correction are performed on each measurement data in the slice interval to obtain the value to be fused at the slice time.

[0057] In an optional embodiment, step 2 includes:

[0058] Step 2.1: Use the least squares method to perform linear fitting on the data within the slice time period to obtain the initial predicted value at the corresponding slice time.

[0059] In this embodiment, for each measurement data, the least squares method is used to perform linear fitting on the data within the slice time period to obtain the initial predicted value of the slice time corresponding to that measurement data.

[0060] Optionally, the process of obtaining the initial predicted values ​​at each slice time includes:

[0061] The least squares method is used to fit and extrapolate the data within the slice time period on the X, Y, and Z coordinate axes respectively to obtain the extrapolated value of the slice time. This extrapolated value is used as the initial predicted value of the slice time.

[0062] In this embodiment, within a relatively short slice time interval, the initial prediction value is determined by a fitting extrapolation algorithm. The least squares linear fitting method is used to achieve both real-time time alignment and prediction of unbuffered data. Compared with existing slice fusion algorithms, this reduces one fitting and one fusion step in algorithm implementation and shortens the time required for data processing.

[0063] Step 2.2: Perform Kalman filtering on the slice time to obtain the Kalman prediction value at the slice time. Use the Kalman prediction value at the slice time to perform Kalman correction on the initial prediction value at the slice time to obtain the value to be fused at the corresponding slice time.

[0064] In this embodiment, assuming the slice time is k, the correction part fully considers that the three types of external measuring devices—telemetry, radar, and photoelectric theodolite—have different systematic and random measurement errors. Combining the measurement data of each telemetry, radar, and photoelectric theodolite within the slice interval and the initial predicted values ​​of the measurement data of the telemetry, radar, and photoelectric theodolite at slice time k, Kalman filtering is performed on the measurement data of the three types of external measuring devices during this time period to obtain the Kalman predicted values ​​of the measurement data of the three types of external measuring devices at time k. These predicted values ​​are then used as correction values ​​to correct the initial predicted values ​​of the three measurement data, resulting in the corresponding values ​​to be fused.

[0065] Optionally, step 2.2 includes:

[0066] Step 2.2.1: Filter the Kalman prediction value at the current slice time according to the Kalman time update equation; Step 2.2.2: Use the Kalman prediction value at the current slice time as the correction value, and perform Kalman correction processing on the initial prediction value at the current slice time according to the Kalman measurement update equation to obtain the value to be fused at the current slice time.

[0067] In this embodiment, the prediction equation for the flight target by each external measuring device is a linear fitting equation within each slice interval. The measurement of the flight target only considers its position and state, and the most recent observation data is replaced by data extrapolated from the linear fitting within the slice interval. When the flight trajectory of the flight target is linearly fitted using the CV model within each short-time slice interval (not applicable when the output frequency is high), the error is within a reasonable range, and the flight target within the slice interval is regarded as uniform motion.

[0068] The core function of Kalman filtering is to fuse predicted data and actual measurement data (in this embodiment, predicted data refers to the Kalman prediction data from each channel, and actual measurement data refers to the initial prediction data from each channel), fully utilizing the unknowns between the predicted and actual measurement data to obtain more accurate prediction results. In actual measurements, considering the complexity of the flight target's internal environment and the target range environment, external uncertainties may introduce errors to the system state, i.e., random noise from external environmental factors affecting the target state. This system state error w k Follows the pattern of mean 0 and variance Q k The distribution is Gaussian, therefore, the Kalman time update equation is as follows:

[0069]

[0070]

[0071] In the formula, k represents the slice time, and k-1 represents the time corresponding to the data preceding the existing slice time. F represents the Kalman prediction value at time k. k Represents the state transition matrix. B represents the Kalman prediction value at time k-1. k Represents the state control matrix, u k Represents the state control vector. Let k represent the covariance matrix at time k. Let represent the covariance matrix at time k-1.

[0072] The Kalman measurement update equation is as follows:

[0073]

[0074]

[0075]

[0076] The Kalman filter gain K reflects the degree of correction to the original measurement value after Kalman filtering, where H... k Let R represent the observation matrix. k Let z represent the measurement covariance matrix. k X represents the initial predicted value. k Let P represent the corrected state matrix. k This represents the corrected covariance matrix.

[0077] Kalman filtering is an iterative process. Each iteration occurs when a new observation (in this case, the initial prediction obtained through linear fitting using the least squares method) is obtained. Specifically, the iteration process uses the Kalman prediction at the slice time as a correction value to adjust the extrapolated measurement value (i.e., the initial prediction value), and obtains the optimal estimate at the slice time as the value to be fused.

[0078] In this embodiment, Kalman filtering technology is used to determine the correction value. By combining three different types of station system noise and random noise in the measurement process, a uniform linear minimum variance unbiased estimate can be obtained. Compared with the existing slice fusion algorithm that uses least squares fitting to determine the correction value, this method is more accurate in the stable segment of the flight target.

[0079] Step 3: Perform weighted fusion processing on the values ​​to be fused corresponding to the multi-channel measurement data at the slice time to obtain the fused ballistic trajectory.

[0080] In an optional embodiment, step 3 includes:

[0081] Step 3.1: Calculate the measurement error corresponding to each type of external measuring device;

[0082] The measurement error is calculated as follows:

[0083]

[0084] in:

[0085]

[0086] In the formula, s represents the integer time preceding the slice time, i.e., s = ceil(Δk-1), ceil(s) represents rounding up s, and Δk represents the size of the slice time interval. This represents the measurement accuracy of the i-th external measuring device at time k. This represents the measurement data of the i-th external measuring device at the j-th time within the slice interval. Let represent the average value of the measurement data of the i-th external measuring device within the slice interval, n represent the number of measurement data within the slice interval, and m represent the number of external measuring devices; in this embodiment, m = 3.

[0087] Step 3.2: Assign corresponding weighting coefficients to the values ​​to be fused based on the measurement error, and then perform data weighted fusion to obtain fused ballistic trajectory data;

[0088] The calculation for data weighting and fusion is as follows:

[0089]

[0090] In the formula, x k This represents the weighted fused data at time k. This represents the value to be fused obtained from the measurement data acquired by the i-th external measuring device at time k after fitting extrapolation, Kalman prediction, and Kalman correction. This represents the weighting coefficient corresponding to the i-th external measuring device at time k.

[0091] In this process, the data from all slice moments within the slice period are weighted and fused to form the fused ballistic trajectory.

[0092] In this embodiment, a statistical weighting method is used to determine the fusion weights, which can effectively suppress noise interference and reflect the characteristics of the real ballistics. In addition, this fusion algorithm has good robustness compared with the existing slice fusion algorithm. When some ballistic data of low quality appears, it will not affect the accuracy of the final fusion result.

[0093] Optionally, after weighted fusion of the data, the accuracy of the fused telemetry, radar, and photoelectric theodolite data at time k can be calculated using formula (9).

[0094]

[0095] The real-time slicing and fusion method for multi-source measurement data of external ballistic trajectories in this invention effectively solves the problem that accuracy decreases as the flight target moves further away from the measurement station. It not only more accurately reflects the characteristics of the actual ballistic trajectory but also effectively suppresses noise interference. Furthermore, the direct proportionality between the fusion weights and the accuracy of the ballistic measurement demonstrates the good robustness of this fusion algorithm.

[0096] It should be noted that, in this document, and, moreover, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the article or device that includes said element.

[0097] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for real-time slicing and fusing multi-source measurement data of external ballistic trajectories, characterized in that, include: Step 1: After preprocessing the multi-channel measurement data acquired by various external measuring devices, perform equal time interval slicing processing; Step 2: Using the least squares method and Kalman filtering, linear fitting prediction, Kalman filtering prediction, and Kalman correction are performed on each measurement data within the slice interval to obtain the value to be fused at the slice time; Step 2 includes: Step 2.1: Perform linear fitting on the data within the slice time period using the least squares method to obtain the initial predicted value for the corresponding slice time; Step 2.1 includes: The least squares method is used to fit and extrapolate the data within the slice time period on the three coordinate axes of X, Y, and Z respectively to obtain the extrapolated value of the slice time. The extrapolated value is used as the initial predicted value of the slice time. Step 2.2: Perform Kalman filtering on the slice time to obtain the Kalman prediction value at the slice time. Use the Kalman prediction value at the slice time to perform Kalman correction processing on the initial prediction value at the slice time to obtain the value to be fused at the corresponding slice time; Step 2.2 includes: Step 2.2.1: Based on the Kalman time update equation, filter to obtain the Kalman prediction value at the current slice time; Step 2.2.2: Using the Kalman prediction value at the current slice time as the correction value, perform Kalman correction processing on the initial prediction value at the current slice time according to the Kalman measurement update equation to obtain the value to be fused at the current slice time; The Kalman time update equation is as follows: In the formula, k represents the slice time, and k-1 represents the time corresponding to the data preceding the existing slice time. F represents the Kalman prediction value at time k. k Represents the state transition matrix. B represents the Kalman prediction value at time k-1. k Represents the state control matrix, u k Represents the state control vector. Let k represent the covariance matrix at time k. Let w represent the covariance matrix at time k-1. k This represents the system state error, which follows a mean of 0 and a variance of Q. k Gaussian distribution; The Kalman measurement update equation is as follows: In the formula, K represents the Kalman filter gain, and H... k Let R represent the observation matrix. k Let z represent the measurement covariance matrix. k X represents the initial predicted value. k Let P represent the corrected state matrix. k This represents the corrected covariance matrix; Step 3: Perform weighted fusion processing on the values ​​to be fused corresponding to the multi-channel measurement data at the slice time to obtain the fused ballistic trajectory.

2. The real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory according to claim 1, characterized in that, The multi-channel measurement data includes telemetry measurement data, radar measurement data, and photoelectric theodolite measurement data.

3. The real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory according to claim 1, characterized in that, The preprocessing includes time alignment and gross error handling.

4. The real-time slicing and fusion method for multi-source measurement data of external ballistic trajectory according to claim 1, characterized in that, Step 3 includes: Step 3.1: Calculate the measurement error corresponding to each type of external measuring device; The measurement error is calculated as follows: in: In the formula, s represents the integer time preceding the slice time, i.e., s = ceil(Δk-1), ceil(s) represents rounding up s, and Δk represents the size of the slice time interval. This represents the measurement accuracy of the i-th external measuring device at time k. This represents the measurement data of the i-th external measuring device at the j-th time within the slice interval. Let represent the average value of the measurement data of the i-th external measuring device within the slice interval, n represent the number of measurement data within the slice interval, and m represent the number of external measuring devices; Step 3.2: Assign corresponding weighting coefficients to the values ​​to be fused according to the measurement error, and then perform data weighted fusion to obtain fused ballistic trajectory data; The calculation of the weighted data fusion is as follows: In the formula, x k This represents the weighted fused data at time k. This represents the value to be fused obtained from the measurement data acquired by the i-th external measuring device at time k after fitting extrapolation, Kalman prediction, and Kalman correction. This represents the weighting coefficient corresponding to the i-th external measuring device at time k.

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