An interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF

Abstract

The present invention discloses an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF, which obtains the measurement noise information of the target at the (k-1) moment in the UKF and calculates the theoretical innovation covariance P of the target at the k moment. ZZ,j (k); Calculate the actual innovation covariance C of the target based on the target measurement information at time k j (k); with P ZZ,j (k) and C j (k) is the input information, and a fuzzy reasoning method is used to determine the adaptive adjustment factor of the measurement noise information at time k; the measurement noise information of the target at time k is calculated based on the adaptive adjustment factor and the state information of the target at time k. The present invention adopts the principle of consistency between the actual innovation covariance and the theoretical innovation covariance, and adopts fuzzy parameters of normalized input and output. This enables the FIS to more comprehensively reflect the degree of deviation between the actual value of the innovation covariance and the theoretical value, thereby increasing the speed at which the measurement noise covariance converges to its true value, thereby improving the tracking performance of the maneuvering target.

Description

Technical Field

[0001] The present invention belongs to the technical field of target tracking, and in particular relates to an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF. Background Art

[0002] Target tracking is a technique that uses measurements of a moving target, such as its position and altitude, combined with tracking algorithms to estimate its motion state. Depending on the target's motion state, target tracking can be categorized as either maneuvering or non-maneuvering. In modern warfare, military aircraft are becoming increasingly maneuverable. Reliably and accurately tracking maneuvering aerial targets is crucial for gaining information control on the battlefield and is a current research focus in the field of maneuvering target tracking.

[0003] Target tracking methods are mainly categorized into single-model and multi-model approaches. When a target maneuvers, single-model approaches, using a single motion model, struggle to accurately describe the target's maneuvering state. Consequently, they often fail to accurately track the target and may even lose the target due to large estimation errors. Multi-model approaches, such as the interactive multi-model (IMM) method, overcome the shortcomings of single-model algorithms by employing different motion models to match the target's maneuvering state. IMM methods use two or more models to describe the target's motion state, with the weights between the models determined by a Markov probability transition matrix. IMM methods can achieve adaptive variable structures by varying model probabilities, improving target tracking performance. Furthermore, these methods are modular, parallelizable, and computationally efficient.

[0004] Filtering is a key supporting technology for the implementation of the IMM method. For the problem of maneuvering target tracking, radar is usually used to measure the distance and direction of the target. This measurement model is nonlinear. Commonly used nonlinear filtering methods include the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The EKF requires a Taylor series expansion of the nonlinear state or measurement equation and truncation of its high-order terms, which will introduce large linearization errors. The UKF uses an unscented transformation to approximate the probability density distribution of the nonlinear function, without ignoring the high-order terms. The filtering accuracy and stability are better than the EKF.

[0005] Filtering methods require prior knowledge of the system model and noise statistics. However, when the external environment produces significant interference, the measurement noise statistics will change. Since the standard UKF cannot adjust for the measurement noise statistics, the estimation accuracy of the parallel filters in the IMM method decreases, which in turn causes the error in the weighted fusion estimate of the system state to increase or even diverge. Summary of the Invention

[0006] The purpose of the present invention is to provide an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF, which uses normalized fuzzy parameters to perform real-time correction on the system measurement noise statistics of UKF, thereby improving the tracking accuracy of IMM-UKF for maneuvering targets when the measurement noise statistics change.

[0007] The present invention adopts the following technical solution: an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF, which includes the following steps when using the IMM-UKF method to track the target:

[0008] Obtain the measurement noise information of the target at time (k-1) in UKF And according to Calculate the theoretical innovation covariance P of the target at time k ZZ,j (k);

[0009] Calculate the actual innovation covariance C of the target based on the target measurement information at time k j (k);

[0010] P ZZ,j (k) and C j (k) is the input information, and the fuzzy reasoning method is used to determine the adaptive adjustment factor of the measurement noise information at time k;

[0011] Based on the adaptive adjustment factor and Calculate the measurement noise information of the target at time k

[0012] based on Calculate the state information of the target at time k.

[0013] Furthermore, the adaptive adjustment factor of the measurement noise information at time k is determined by using a fuzzy inference method, including:

[0014] according to Generate the input parameter matrix q of the fuzzy inference method j (k);

[0015] in, Indicates C j The i-th element on the main diagonal of (k), Indicates P ZZ,j The i-th element on the main diagonal of (k).

[0016] Furthermore, the adjustment rules in the fuzzy reasoning method are:

[0017]

[0018] in, η j(k) is the output parameter matrix of the fuzzy inference method, is η j The nth element on the main diagonal of (k), ξ j (k) is the adaptive adjustment factor of the measurement noise information at time k, for ξ j (k) The nth element on the main diagonal of

[0019] Furthermore, it also includes:

[0020] Obtain the state estimation value and covariance estimation value of each model for the target at time (k-1), and calculate the state estimation input value and covariance estimation input value of each model at time k in combination with the Markov probability transfer matrix;

[0021] In each model, the state estimation input value and covariance estimation input value at time k are combined with the measurement noise information Determine the state estimate and covariance estimate of the target at time k in each model;

[0022] The target's mixed state estimate and mixed covariance are calculated based on the target's state estimate and covariance estimate at time k.

[0023] Furthermore, calculating the target's mixed state estimate based on the target's state estimate and covariance estimate at time k includes:

[0024]

[0025] in, is the mixed state estimate of the target at time k, is the state estimate of the jth model at time k, μ j (k) is the model probability of the jth model at time k.

[0026] Furthermore, the update method of the model probability is:

[0027]

[0028] Among them, Λ j (k) is the maximum likelihood function of the j-th model at time k, is the normalization constant when calculating the probability of input interaction from model i to model j, and c is the normalization constant when calculating the probability of model j.

[0029] Furthermore, the state estimation input value and covariance estimation input value of each model at time k are calculated in combination with the Markov probability transition matrix, including:

[0030]

[0031]

[0032] in, is the state estimation input value of the j-th model at time k, is the state estimate of the i-th model at time (k-1), μ ij (k-1|k-1) is the input interaction probability from the i-th model to the j-th model at time (k-1), r is the total number of models, is the covariance estimation input value of the j-th model at time k, is the covariance estimate of the i-th model at time (k-1).

[0033] Furthermore, determining the state estimate and covariance estimate of the target at time k in each model includes:

[0034]

[0035]

[0036] in, is the state estimate of the target at time k of the j-th model, K is the one-step prediction value of the target state at the jth model k moment, j (k) is the Kalman filter gain of the jth model at time k during filtering, Z(k) is the observed value of the target at time k, is the mean of the observation prediction of the jth model at time k, P j (k|k) is the covariance estimate of the target at time k for the jth model.

[0037] Furthermore, the kinematic model in the IMM-UKF method includes a uniform motion model, a uniform acceleration motion model and a current statistical model.

[0038] Another technical solution of the present invention: an interactive multi-model maneuvering target tracking device based on fuzzy adaptive UKF, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, it implements the above-mentioned interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF.

[0039] The beneficial effects of the present invention are: the present invention does not need to set a priori input parameter value range. When the system measurement noise statistics change, the present invention adopts the fuzzy parameters of normalized input and output based on the principle of consistency between the actual innovation covariance and the theoretical innovation covariance. This enables the FIS to more comprehensively reflect the degree of deviation between the actual value and the theoretical value of the innovation covariance, thereby improving the speed at which the measurement noise covariance converges to its true value, thereby improving the tracking performance of the maneuvering target, and improving the tracking accuracy of the IMM-UKF for the maneuvering target when the measurement noise statistics change. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of a flow chart of an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF in an embodiment of the present invention;

[0041] Figure 2 Schematic diagram of the structure of the fuzzy adaptive noise regulator in an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of the membership function of the input and output of the FIS in an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of the motion trajectory of a maneuverable target in the verification embodiment of the present invention;

[0044] Figure 5 This is a comparison chart of the position root mean square error simulation results of the method of the present invention and the IMM-UKF method in the embodiment of the present invention;

[0045] Figure 6 This is a comparison diagram of the velocity root mean square error simulation results of the method of the present invention and the IMM-UKF method in the embodiment of the present invention;

[0046] Figure 7 This is a comparison result diagram of the mean RMS error of position and velocity between the method of the present invention and the IMM-UKF method in the verification embodiment of the present invention. DETAILED DESCRIPTION

[0047] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] To address the problem of tracking maneuvering targets subject to changes in system measurement noise statistics, this paper proposes an interactive multi-model maneuvering target tracking method based on a fuzzy adaptive UKF. Considering the advantage of fuzzy inference methods in rapidly responding to external input information, this paper introduces a fuzzy inference system (FIS) based on the Interacting Multi-Model Unscented Kalman Filter (IMM-UKF) method to construct a new noise estimator. This method uses normalized fuzzy parameters to perform real-time corrections to the UKF's system measurement noise statistics, thereby improving the IMM-UKF's tracking performance for maneuvering targets when measurement noise statistics change.

[0049] Specifically, the present invention discloses an interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF, which includes the following steps when using the IMM-UKF method to track the target: obtaining the measurement noise information of the target at time (k-1) in the UKF And according to Calculate the theoretical innovation covariance P of the target at time k ZZ,j (k); Calculate the actual innovation covariance C of the target based on the target measurement information at time k j (k); with P ZZ,j (k) and C j (k) is the input information, and the fuzzy reasoning method is used to determine the adaptive adjustment factor of the measurement noise information at time k; based on the adaptive adjustment factor and Calculate the measurement noise information of the target at time k based on Calculate the state information of the target at target time k.

[0050] The present invention does not need to set a priori input parameter value range. When the system measurement noise statistics change, the fuzzy parameters of normalized input and output are adopted based on the principle of consistency between the actual innovation covariance and the theoretical innovation covariance. This enables the FIS to more comprehensively reflect the degree of deviation between the actual value and the theoretical value of the innovation covariance, thereby improving the speed at which the measurement noise covariance converges to its true value, thereby improving the tracking performance of the maneuvering target and improving the tracking accuracy of the IMM-UKF for the maneuvering target when the measurement noise statistics change.

[0051] In an embodiment of the present invention, the number of prior models of the system is first set, and the corresponding maneuvering target state equation is established. This embodiment uses three motion models to match different maneuvering states of the maneuvering target, namely, a uniform velocity motion model (CV model), a uniform acceleration motion model (CA model) and a "current" statistical model (CS model).

[0052] The uniform velocity model (CV model) and the uniform acceleration model (CA model) are commonly used to describe target motion. However, when a target maneuvers, the CV and CA models alone are insufficient to describe the target's motion. The Singer model and the "current" statistical model (CS model), in which acceleration is a variable, offer greater maneuverability and are therefore widely used in maneuvering target tracking. The CS model assumes a nonzero mean acceleration, which better reflects the actual motion characteristics of maneuvering targets. Furthermore, the model can adaptively improve system errors, making it a preferred choice when selecting a maneuvering model.

[0053] In the IMM-UKF method of this embodiment of the present invention, the model set selected should consider all possible variations in the target's motion state. However, due to computational complexity and the performance of the method itself, the selection should include at least one non-maneuvering model and one maneuvering model. To best match the maneuvering target's motion state and avoid significant competition between models, this embodiment sets the system's prior model count to three: a kinematic model (constant velocity model), a uniform acceleration model, and a statistical model. These three models are described below.

[0054] The CV model is established as follows:

[0055] The target moves in a straight line at a uniform speed. If there is no external interference, the acceleration of the target Since external environmental interference is inevitable, the generated acceleration is regarded as the first zero-mean Gaussian white noise w(t), that is:

[0056]

[0057] The discretized state equation is:

[0058]

[0059] The process noise variance Q is:

[0060]

[0061] Among them, the state x(k), They represent the position and velocity of the target at the kth moment respectively, and T is the sampling period.

[0062] The CA model is established as follows:

[0063] The target moves in a straight line with uniform acceleration, and the rate of change of acceleration Due to external interference, the acceleration change rate satisfies the first zero-mean Gaussian white noise w(t), that is:

[0064]

[0065] The discretized state equation is:

[0066]

[0067] The process noise variance Q is:

[0068]

[0069] Among them, the state x(k), They represent the position, velocity and acceleration of the target at the kth moment respectively.

[0070] The CS model is established as follows:

[0071] The CS model's acceleration mean is the predicted value of the current acceleration, and its statistical characteristics conform to a modified Rayleigh distribution, with its variance determined by the mean. Therefore, using the CS model to estimate the target state allows for the real-time acquisition of the target acceleration mean, thereby modifying the acceleration distribution. Ultimately, the variance is fed back into the filter gain at the next moment to adaptively improve the system error.

[0072] When the target maneuvers, the acceleration model is:

[0073]

[0074]

[0075] in, is the target acceleration, is the mean maneuvering acceleration, a(t) is the colored noise of target acceleration, α is the maneuvering frequency, is the second zero-mean Gaussian white noise, is the acceleration variance.

[0076] and The relationship is as follows:

[0077]

[0078] Among them, a M is the maximum acceleration of the maneuvering target, which is a priori parameter.

[0079] The discretized state equation is:

[0080]

[0081] The process noise variance Q is:

[0082]

[0083]

[0084] Among them, the state x(k), and They represent the position, velocity and acceleration of the target at the kth moment respectively.

[0085] In the embodiment of the present invention, Figure 1 As shown in Figure 2, the overall process of the target tracking method is as follows:

[0086] Obtain the state estimation value and covariance estimation value of each model for the target at time (k-1), and calculate the state estimation input value and covariance estimation input value of each model at time k in combination with the Markov probability transfer matrix; in each model, based on the state estimation input value and covariance estimation input value at time k, combined with the measurement noise information Determine the state estimate and covariance estimate of the target at time k in each model; and calculate the mixed state estimate and mixed covariance of the target based on the state estimate and covariance estimate of the target at time k.

[0087] Specifically, each model first performs input interaction and calculates the initial state of the current cyclic mixing estimate. Assuming there are r motion models (r = 3 in this embodiment), the transition between each model is determined by the Markov probability transfer matrix P. First, the input interaction probability μ from model i to model j at time k-1 is calculated. ij (k-1|k-1), the specific calculation is as follows:

[0088]

[0089]

[0090]

[0091] Among them, p ij represents the probability of transferring from model i to model j, μ i (k-1) is the model probability of model i at time k-1, is a normalization constant used to calculate the probability of interaction between model i and model j. In this embodiment, the subscript j=1,...,r represents the jth model among r models.

[0092] Then, the state estimation input value and covariance estimation input value of each model at time k are calculated by combining the Markov probability transfer matrix. Specifically, the input interaction probability μ at time k-1 is ij (k-1|k-1) and the state estimate of model i at time k-1 are interactively calculated to obtain the mixed state estimate of model j and covariance estimation The calculation is as follows:

[0093]

[0094]

[0095] in, is the state estimation input value of the j-th model at time k, is the state estimate of the i-th model at time (k-1), μ ij (k-1|k-1) is the input interaction probability from the i-th model to the j-th model at time (k-1), r is the total number of models, is the covariance estimation input value of the j-th model at time k, is the covariance estimate of the i-th model at time (k-1).

[0096] The mixed state and covariance estimates calculated by equations (16) and (17) are used as input, and the fuzzy adaptive UKF filtering (FAUKF) is performed on each model in combination with the measurement data, and the measurement noise is adjusted in real time to obtain the state estimates of each model. Covariance P j (k|k) and the measurement noise covariance

[0097] First, perform UT transformation to calculate 2n+1 sampling points and their corresponding weights, where n is the dimension of the state. The calculation formula is as follows:

[0098]

[0099]

[0100] Among them, the subscripts m and c of the weight ω represent the mean and covariance respectively, and the superscript represents the i-th sampling point of the model; the parameter in, Controls the distribution of sampling points, with a value range of 10 -4 ~1 to avoid non-local effects; κ is a candidate parameter, which is usually 3-n when the state dimension is less than 3 and 0 when the vector dimension is large; β is a non-negative coefficient, which is usually 2 for Gaussian systems.

[0101] Secondly, the above 2n+1 sampling points are brought into the nonlinear state equation and the state one-step prediction is calculated and the corresponding covariance P j (k|k-1).

[0102]

[0103]

[0104]

[0105] Use the UT transformation again and substitute the new Sigma point set into the nonlinear measurement equation to calculate the predicted mean of the measurement Covariance estimate P ZZ,j (k) and the cross-covariance matrix P of the state and measurement XZ,j (k).

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] Finally, the filter gain matrix is ​​calculated and the state estimation of each model is obtained and the corresponding covariance P j (k|k), that is, determining the state estimate and covariance estimate of the target at time k in each model, including:

[0112] K j (k) = P XZ,j (k)(P ZZ,j (k)) -1 (28)

[0113]

[0114]

[0115] in, is the state estimate of the target at time k of the j-th model, K is the one-step prediction value of the target state at the jth model k moment, j (k) is the Kalman filter gain of the jth model at time k during filtering, Z(k) is the observed value of the target at time k, is the mean of the observation prediction of the jth model at time k, P j (k|k) is the covariance estimate of the target at time k for the jth model.

[0116] The difference between FAUKF and UKF is that the measurement noise variance matrix in FAUKF is: The noise estimator constructed based on FIS is used to estimate the noise, so that the measurement noise can be adaptively adjusted. Due to the differences between the internal elements of the measurement noise covariance matrix, the present invention uses multiple adjustment factors to adjust the noise of the measurement noise. Adjust each portion.

[0117]

[0118]

[0119]

[0120] Among them, η j (k) is the output parameter matrix of FIS, and the value range of each element inside is (0,1); j (k) is the adaptive adjustment factor matrix, represented by η j (k) Construct a logarithmic function to realize the measurement noise covariance Adaptive adjustment of q j (k) is the input parameter matrix of FIS, which is usually composed of the actual covariance of the new information C j (k) and the theoretical covariance P ZZ,j However, FIS requires the input value to be within a certain range. It is difficult to ensure that the input fluctuates within a small range by using the ratio method or the difference method. Therefore, the FIS of this embodiment normalizes the input so that it can more comprehensively express C j (k) and P ZZ,j (k) various deviations, and It can quickly converge to the actual measurement noise covariance.

[0121] Since FIS requires the input value to be within a certain range, in the actual filtering process, C j (k) and P ZZ,j The ratio or difference of (k) cannot be predicted. When using the ratio method or the difference method, the input parameters of the calculation may not belong to the input fuzzy set range preset by the fuzzy inference system, which may cause the system to crash. Although it is possible to consider increasing the input fuzzy set range, when the measurement noise level changes greatly, C j (k) and P ZZ,j (k) values ​​vary greatly, and it is still impossible to guarantee that the input can fall within the determined range. Secondly, even if the system reliability can be guaranteed by increasing the range of fuzzy sets, if the differences between different fuzzy sets are too large, it will lead to the difficulty in establishing fuzzy inference rules, the fuzzy parameters will be difficult to adjust and cannot be well utilized, and ultimately the measurement noise covariance adjustment process will be slowed down, which will lead to the problem of low filtering estimation accuracy.

[0122] In order to solve the above problems, the present invention considers normalizing the range of each input and output parameter, that is, the value range is (0,1). On the one hand, when the measurement noise level changes greatly, C j (k) increases rapidly, the input parameters will still fall within the set range, ensuring the reliability of the system; and because the input at this time can fully express C j(k) and P ZZ,j (k) Various deviations from It can quickly converge to the actual measurement noise covariance. On the other hand, the use of fuzzy sets with symmetrical distribution solves the problem caused by large differences between fuzzy sets.

[0123] The output parameter range used in this invention is (0,1). If the parameter is used directly to correct Can only guarantee unchanged or reduced, it cannot meet the adaptive requirements of the system; secondly, when C j (k) and P ZZ,j When the (k) values ​​are equal, the output parameter takes the value of 0.5. Therefore, a logarithmic function with a base of 0.5 is constructed to establish an adaptive adjustment factor matrix. At this time, the output parameter value can be taken to make Increase, decrease or remain unchanged in real time to meet the adaptive needs of the system. Moreover, since the output value obtained by fuzzy reasoning will not reach 0 or 1, the adaptive adjustment factor obtained by formula (32) is avoided. Infinite or 0 values ​​appear.

[0124] Specifically, the fuzzy reasoning method is used to determine the adaptive adjustment factor of the measurement noise information at time k, including: Generate the input parameter matrix q of the fuzzy inference method j (k); wherein, Indicates C j The i-th element on the main diagonal of (k), Indicates P ZZ,j (k) is the i-th element on the main diagonal of the matrix, Z(k) is the measurement value at time k, M is the smoothing window, the superscript i represents the i-th element of the vector, and ii represents the i-th element on the main diagonal of the matrix.

[0125] In addition, if Figure 2 As shown in the figure, the noise estimator structure of the FIS consists of four parts: fuzzification, a fuzzy rule base, fuzzy reasoning, and output parameter defuzzification. Fuzzification transforms precise numerical values ​​into fuzzy sets within their domain; the fuzzy rule base consists of fuzzy if-then rules; fuzzy reasoning makes inferences based on fuzzy logical relationships and fuzzy rules; and output parameter defuzzification is the inverse operation of fuzzification, converting the output fuzzy set into precise numerical values.

[0126] First, fuzzification is performed to determine the fuzzy sets and membership functions of the input and output. The fuzzy set is determined by the range of fuzzy parameter values. In this embodiment, the input and output are normalized parameters, so the fuzzy sets are all S (small), M (medium), and L (large). The membership function is a quantitative description of the fuzzy characteristics of the fuzzy set, including trigonometric functions, trapezoidal functions, and Sigmoid functions. In this embodiment, the membership functions of the input and output are all trigonometric functions, as shown in the following example. Figure 3 shown.

[0127] Secondly, determine the fuzzy rules and perform fuzzy reasoning. In this embodiment, the adjustment rules are based on C j (k) and P ZZ,j (k) is designed based on the consistency of It can be seen that when q j (k) Elements When the value is 0.5, it means C j (k) and P ZZ,j (k) is consistent, the noise measurement is more accurate, then η j The value of (k) should be kept at 0.5; when subjected to external interference, if q j (k) Each element is less than 0.5, indicating that P ZZ,j (k) greater than C j (k), the measurement noise covariance is If it is too large, then η j The value of (k) should be greater than 0.5 so that Decrease; if q j (k) Each element is greater than 0.5, indicating that P ZZ,j (k) is less than C j (k), the measurement noise covariance is If it is too small, then η j The value of (k) should be less than 0.5 so that Increase. The basic adjustment process is expressed by the following formula:

[0128]

[0129] More specifically, the adjustment rules in the fuzzy reasoning method can be:

[0130]

[0131] in, η j (k) is the output parameter matrix of the fuzzy inference method, is η j The nth element on the main diagonal of (k), ξ j(k) is the adaptive adjustment factor of the measurement noise information at time k, for ξ j (k) The nth element on the main diagonal of

[0132] The fuzzy control rules are shown in Table 1 below.

[0133] Table 1 Fuzzy control rules table

[0134]

[0135] Commonly used fuzzy reasoning methods include Tsukamoto and Mamdani, among which Mamdani can handle targets with changing maneuvering states. Therefore, the present invention adopts the Mamdani method for fuzzy reasoning.

[0136] Finally, the output parameters are defuzzified. The present invention adopts the centroid method, that is, the output is the centroid of the area enclosed by the membership function curve, which is calculated as follows:

[0137]

[0138] Among them, μ represents the exact value of the output, μ(u i ) is the membership function, u i Represents an element of a fuzzy set.

[0139] After the above process, the new information vector is used to construct the maximum likelihood function to update the probability μ of model j at time k. j (k). The updating method of model probability is:

[0140]

[0141]

[0142]

[0143]

[0144] Among them, v j (k) is the measurement innovation, Λ j (k) is the maximum likelihood function of the j-th model at time k, is the normalization constant when calculating the probability of input interaction from model i to model j, and c is the normalization constant when calculating the probability of model j.

[0145] Finally, the obtained model probability is used as the weight to weight the state and covariance of each model after filtering, complete the output interaction, and obtain the mixed state estimate and covariance. That is, the mixed state estimate of the target is calculated based on the state estimate and covariance estimate of the target at time k, including:

[0146]

[0147]

[0148] in, is the mixed state estimate of the target at time k, is the state estimate of the jth model at time k, μ j (k) is the model probability of the jth model at time k.

[0149] In addition, the measurement equation of the target tracking method used in the embodiment of the present invention is:

[0150]

[0151] Among them, (x, y, z) is the target coordinate, (x0, y0, z0) is the sensor coordinate, V 3×1 are the measurement errors, observing the range, azimuth and elevation of the target respectively.

[0152] This completes the interactive multi-model maneuvering target tracking method based on fuzzy inference adaptive UKF. In summary, the IMM-FAUKF method, based on the principle of innovation covariance consistency, introduces a FIS with normalized fuzzy parameters to perform real-time correction of the measurement noise covariance. This solves the problem of poor state estimation performance caused by statistical variations in measurement noise during maneuvering target tracking, further improving the state estimation accuracy of maneuvering targets.

[0153] In order to verify the effectiveness of the method of the present invention, the following verification examples were also carried out. The present invention sets the following scenario to construct the initial dynamic parameters of the target: a Cartesian coordinate system is established with kilometers as the unit, and the x, y, and z axes are respectively the east, north, and altitude directions. Assume that the enemy aircraft is performing a maneuver at an initial speed of 500m / s at the initial position (200, 800, 30), and the flight trajectory is as follows Figure 4 As shown. Our detection radar coordinates are taken as the origin, and the distance, azimuth and elevation angle of the enemy aircraft (called maneuvering target) are measured respectively, and the noise covariance R=diag([8 2 0.02 2 0.02 2 ]).

[0154] The method of the present invention is implemented according to the above steps, and IMM-UKF is used as a comparison method. The model set consists of CV, CA and CS models. The state vectors are the position, velocity and acceleration in the x, y and z axis directions respectively. The maximum acceleration a of the CS model is M =0.025km·s -2 , maneuver frequency α=1; Markov probability transfer matrix P and model probability u are:

[0155]

[0156] u=[0.35 0.35 0.3] (45)

[0157] The smoothing window of the actual innovation covariance is M=20, and the initial state of the filter and the corresponding covariance are:

[0158]

[0159]

[0160] The total simulation time is 900 seconds, the sampling interval is 1 second, and the measurement noise covariance during the simulation is set to:

[0161]

[0162] The whole process of maneuvering target tracking was simulated 100 times using Montel-Carlo simulations. The root mean square error (RMSE) was used as the evaluation criterion, which is defined as:

[0163]

[0164]

[0165] Where M is the number of Monte Carlo simulations, k = 1, 2, ..., N, N is the number of sampling times, X i (k) represents the true value of the i-th Monte Carlo simulation, It represents the estimated value of the i-th Monte Carlo simulation, and ARMSE is the root mean square error.

[0166] like Figure 5 and Figure 6 As shown in the figure, the position and velocity root mean square error comparison results of the IMM-UKF and IMM-FAUKF methods are shown in the figure. The average RMSE of the whole process is shown in Figure 7 As shown. Figure 5-6 It can be seen that when the measurement noise is accurate, IMM-UKF is the optimal algorithm, and the state estimation value obtained during filtering estimation is more accurate. However, the IMM-FAUKF method adjusts the measurement noise covariance throughout the simulation process and is a suboptimal algorithm. Therefore, the tracking accuracy of IMM-FAUKF is slightly lower than that of IMM-UKF in [0, 150] s and [750, 900] s.

[0167] When the measurement noise changes, that is, the measurement noise variance changes suddenly within [150,750]s, the estimation error of the IMM-UKF method increases significantly, while the estimation error of the IMM-FAUKF method increases only slightly compared to when the measurement noise is accurate. At this time, the tracking accuracy is better than that of the IMM-UKF method.

[0168] At the same time, according to Figure 7 It can be intuitively seen that the IMM-FAUKF method improves the position accuracy in the x, y, and z axes by 30.23%, 31.15%, and 32.83%, respectively, and the velocity accuracy by 57.29%, 61.99%, and 61.27%, respectively. The main reason is that when the external environment generates interference, the system's measurement noise covariance changes. The IMM-UKF method cannot adjust the measurement noise covariance during the filtering process, which increases the estimation error. In contrast, the IMM-FAUKF method proposed in this invention uses the principle of whether the theoretical value of the innovation covariance is consistent with the actual value, and uses the FIS with normalized input and output to adaptively adjust the measurement noise covariance. This solves the problem that the FIS input range is difficult to fully describe and enables the measurement noise covariance to converge quickly to its true value. This algorithm ensures the accuracy of the model, thereby improving the tracking performance of maneuvering targets.

[0169] In the present invention, taking maneuvering target tracking as the object, a new measurement noise estimator is constructed through FIS on the basis of the IMM-UKF method to solve the problem that the statistical characteristics of the measurement noise caused by interference from the external environment change, resulting in inaccurate or even divergent estimation. The present invention designs a fuzzy reasoning noise estimator in the interactive multi-model filtering algorithm module to ensure the consistency of the actual innovation covariance and the theoretical innovation covariance. The use of normalized fuzzy parameters can improve the convergence speed and accuracy of the measurement noise covariance and reduce the impact of the change of noise statistical characteristics on the state estimation value; the present invention can effectively improve the accuracy and stability of maneuvering target tracking.

[0170] The present invention also discloses an interactive multi-model maneuvering target tracking device based on fuzzy adaptive UKF, which includes a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the above-mentioned interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF is implemented.

[0171] The aforementioned device may be a computing device such as a desktop computer, laptop, PDA, or cloud server. The device may include, but is not limited to, a processor and memory. Those skilled in the art will appreciate that the device may include more or fewer components, or a combination of certain components, or different components, and may also include, for example, input / output devices, network access devices, and the like.

[0172] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0173] In some embodiments, the memory may be an internal storage unit of the device, such as a hard disk or memory of the device. In other embodiments, the memory may also be an external storage device of the device, such as a plug-in hard disk equipped on the device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card, etc. Furthermore, the memory may include both an internal storage unit of the device and an external storage device. The memory is used to store an operating system, an application program, a boot loader (BootLoader), data, and other programs, such as the program code of the computer program. The memory may also be used to temporarily store data that has been output or is about to be output.

[0174] It should be noted that the specific content of the above-mentioned device is based on the same concept as the embodiment of the method of the present invention. Its specific functions and technical effects can be found in the method embodiment part and will not be repeated here.

Claims

1. An interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF, characterized by: The following steps are involved when using the IMM-UKF method for target tracking: Get UKF Measurement noise information of the target at each moment , and according to the calculate Theoretical innovation covariance of the moment target ; according to The target measurement information at the moment calculates the actual innovation covariance of the target ; As mentioned and As input information, fuzzy reasoning method is used to determine Adaptive adjustment factor for moment-to-moment measurement noise information; Based on the adaptive adjustment factor and the Calculate the measurement noise information of the target at time k ; Based on the calculate Status information of the target at all times; Using fuzzy reasoning method to determine The adaptive adjustment factors of the momentary measurement noise information include: according to Generate input parameter matrix for fuzzy inference method ; in, , express The i-th element on the main diagonal of express The i-th element on the main diagonal of ; The adjustment rules in the fuzzy reasoning method are: ， in, , is the output parameter matrix of the fuzzy inference method, for The nth element on the main diagonal of , , , for Adaptive adjustment factor for measuring noise information at all times, for The nth element on the main diagonal of .

2. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 1, characterized in that: Also includes: Get The state estimation value and covariance estimation value of each model for the target at time k are calculated, and the state estimation input value and covariance estimation input value of each model at time k are calculated in combination with the Markov probability transfer matrix; In each model, based on the state estimation input value and covariance estimation input value at time k, combined with the measurement noise information , determine the state estimate and covariance estimate of the target at time k in each model; The target's mixed state estimate and mixed covariance are calculated based on the target's state estimate and covariance estimate at time k.

3. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 2, characterized in that: The mixed state estimate of the target is calculated based on the state estimate and covariance estimate of the target at time k, including: ， in, is the mixed state estimate of the target at time k, is the estimated state value of the j-th model at time k, is the model probability of the j-th model at time k.

4. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 3, characterized in that: The updating method of the model probability is: ， in, is the jth model in The maximum likelihood function at that moment, For computational models To Model Normalization constant when inputting interaction probabilities, For computational models Normalization constant when calculating the probability.

5. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 3 or 4, characterized in that: The state estimation input value and covariance estimation input value of each model at time k are calculated by combining the Markov probability transfer matrix, including: ， ， in, For the jth model The estimated state input value at time t, for The estimated state value of the i-th model at time, for The probability of input interaction from the i-th model to the j-th model at time, r is the total number of models, is the covariance estimation input value of the j-th model at time k, for The covariance estimate of the i-th model at time t.

6. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 5, characterized in that: Determining the state estimate and covariance estimate of the target at time k in each model includes: ， ， in, is the state estimate of the target at time k of the j-th model, is the one-step prediction value of the target state at time k of the j-th model, is the Kalman filter gain of the jth model at time k during filtering, is the observed value of the target at time k, is the observed prediction mean of the j-th model at time k, is the covariance estimate of the target at time k for the jth model, One-step prediction value for the state The corresponding covariance.

7. The interactive multi-model maneuvering target tracking method based on fuzzy adaptive UKF according to claim 6, characterized in that: The kinematic model in the IMM-UKF method includes a uniform motion model, a uniform acceleration motion model and a current statistical model.

8. An interactive multi-model maneuvering target tracking device based on fuzzy adaptive UKF, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for tracking a maneuvering target based on an interactive multi-model fuzzy adaptive UKF as described in any one of claims 1 to 7 is implemented.

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