Relative state estimation method under complex motion of space target

Abstract

The invention discloses a relative state estimation method under complex motion of a space target, which comprises the following steps: aiming at the defect that the existing algorithm cannot effectively track the motion state of the complex actual space target, utilizing an interactive multi-model filtering algorithm based on an improved extended acceleration observer to estimate the relative state of the space target. Target state estimation which is high in estimation precision, low in system complexity and close to engineering practical application is achieved. The method comprises the following steps: constructing different dynamic models according to a complex motion scene of a space target, and establishing a state equation and an observation equation; establishing a single strong tracking filtering model under a non-maneuvering condition and a maneuvering condition; performing model probability updating in a multi-model interaction algorithm; and giving a final output result of the interaction data according to a result of independent calculation of each model and a probability update weight of model matching.

Description

Technical Field

[0001] The present invention belongs to the technical field of space on-orbit service and maintenance and space safety, and in particular relates to a relative state estimation method for a space target under complex motion. Background Art

[0002] With the rapid development of aerospace technology, the size of my country's space assets has grown rapidly. The increase in the number of space assets has led to increasingly prominent issues regarding their on-orbit lifespan and safe operation. As an important means of maintaining the long-term, stable, and safe operation of spacecraft, on-orbit services reflect important strategic significance. On-orbit services are achieved by approaching and capturing target spacecraft, and on this basis, refueling, maintenance, attitude orbit takeover control, and other operations are carried out. In order to achieve a safe close approach to non-cooperative targets (space debris, etc.), it is first necessary to obtain status information of non-cooperative targets. Therefore, the demand for state estimation of non-cooperative targets in space is becoming more urgent.

[0003] At present, there are three main types of classic algorithms for the study of space target maneuvering state estimation methods:

[0004] Algorithm 1 is a filtering algorithm based on maneuver detection and covariance adaptation, mainly based on strong tracking filtering or improved strong tracking filtering. The main principle is that when the target maneuver is detected, the observation covariance is continuously increased to increase the influence of the observation on the state quantity, thereby improving the correction ability of the observation on the state quantity, thereby ensuring the rapid convergence of the filter. For example, in the patent "A Maneuvering Target Tracking Method Based on Improved SRCKF Strong Tracking Filter (CN110706265B)" published by Sheng Weidong et al., on the basis of the classic strong tracking filtering algorithm, a fading factor with a time factor is used for threshold judgment, so as to realize the estimation of the state of the missile target in the free flight under the influence of gravity only by the angle measurement information. In the patent "A Maneuvering Target Tracking Method Based on Improved Kalman Filter (CN115964603A)" published by Lin Xu et al., on the basis of the classic Kalman filtering algorithm, an adaptive fading factor is used to realize the estimation of the maneuvering target state under the premise of inaccurate statistical characteristics of the prior noise.

[0005] However, this type of method does not have acceleration information in state estimation. Therefore, for scenes with complex acceleration changes, the accuracy of stable tracking and state estimation is not high.

[0006] Algorithm 2 is a filter tracking algorithm of the extended acceleration observer, which is based on the Singer model filtering algorithm. The main principle is to add maneuvering acceleration as a state quantity, and assume that the maneuvering acceleration of the target is a zero-mean, stable one-stage Markov process, thereby ensuring the rapid convergence of the filter. In the patent "RA-Singer-EKF Maneuvering Target Tracking Algorithm Based on Radial Acceleration (CN103048658A)" published by Wang Guohong et al., a Singer model based on radial acceleration is built to achieve state estimation of multiple maneuvering targets.

[0007] However, this type of method sets the maneuvering acceleration as a zero-mean, stable one-stage Markov process, which is highly restrictive to the application scenarios.

[0008] Algorithm 3 is the interactive multiple model (IMM) filtering algorithm, which consists of multiple sub-filters, representing multiple models of target motion or different filter parameters. The main principle is to perform real-time maneuver model detection by setting model filters corresponding to the number of possible target models, setting weight coefficients and model update probability for each filter, and finally weighted calculation to obtain the current optimal estimated state. For example, Guo Jianhui et al. published "A method for maneuvering target state estimation based on interactive multi-model colorless filtering (CN113628274A)" which uses a colorless filtering algorithm when tracking maneuvering targets (uniformly accelerated motion, constant acceleration). Yin Juqi et al. published "Improved Adaptive IMM Algorithm for Space Maneuvering Target Tracking" in the journal "System Engineering and Electronic Technology". In the non-maneuvering model and simple maneuvering model (two-pulse maneuvering) scenario, an IMM algorithm with an improved model likelihood function was proposed to overcome the singularity problem when correcting the model transfer probability and estimate the tracking state.

[0009] However, this type of method generally requires the establishment of a more accurate target motion model, which is different from the motion scene of the actual space target. When the motion state changes a lot, the classic approach is to fit multiple motion segments by adding sub-filters. However, as the number of sub-filters increases, the amount of calculation increases.

[0010] A comparative analysis of the three existing classic algorithms is conducted. Each algorithm has its advantages and applicable application scenarios. However, with the complexity of space missions, there is currently no public literature on relative state estimation methods for complex target motion scenarios (target motion segmentation, time-varying maneuvering acceleration, etc.). Summary of the invention

[0011] The technical problem to be solved by the present invention is: in view of the shortcoming that the existing algorithms cannot effectively track scenes with complex acceleration changes, an interactive multi-model filtering algorithm based on an improved extended acceleration observer is proposed to realize relative state estimation of space targets under complex maneuvers.

[0012] In order to solve the above technical problems, the technical solution adopted by the present invention is: a relative state estimation method under complex motion of a space target, comprising the following steps:

[0013] Step S1: input model interaction;

[0014] S1.1: Construct different dynamic models according to the complex motion scenarios of space targets;

[0015] The present invention comprehensively considers the actual motion state of space targets, a low-complexity system that is conducive to engineering implementation, and a high state estimation accuracy. Two dynamic models are constructed, namely, a dynamic model based on high-precision orbit recursion corresponding to the non-maneuvering motion state, and a dynamic model based on orbit recursion combined with acceleration time-varying corresponding to the maneuvering motion state;

[0016] The absolute dynamic equations of the target star and the tracking star are:

[0017]

[0018]

[0019] Where, μ = 398600.44 km 3 / s 2 is the gravitational constant, r t , r c The position vectors of the target star and the tracking star relative to the center of the earth in the inertial coordinate system, a tc , a cc are the control accelerations of the target star and the tracking star in the inertial coordinate system, J t , J c are the perturbation accelerations of the target star and the tracking star in the inertial coordinate system respectively;

[0020] Let r = r t -r c Subtracting them gives:

[0021]

[0022] Where r is the relative position vector between the target star and the tracking star. If the relative distance between the two stars in space is not very large, ΔJ can be simplified to 0.

[0023] According to the differential equation of relative motion:

[0024] r = a c +ω I ×(ω I ×r)+ω I ×r+2ω I ×v c

[0025] Among them, a c , v c are the relative acceleration and relative velocity of the target star relative to the tracking star in the tracking star orbit coordinate system, and v c = r, ω I To track the rotational angular velocity of the star orbit coordinate system relative to the inertial coordinate system, that is, to track the absolute angular velocity of the star orbit coordinate system, we can obtain the following equations by combining (3) and (4):

[0026]

[0027] When the relative distance between the two stars is very small compared to the orbital radius, considering the factors to reduce the complexity of the system, ignoring the nonlinear terms, retaining the linear terms, and ignoring the control acceleration of the tracking star, the linearized form of the dynamic equation is obtained as follows:

[0028]

[0029] Where x, y, and z are the projections of the relative positions of the two stars on the three axes in the tracking star orbit coordinates;

[0030] S1.1.1 Dynamic model formula for target satellite in non-maneuvering condition;

[0031] When the target satellite is not maneuvering, the situation is relatively simple. In formula (6), a tc =0, the kinetic model formula is as follows:

[0032]

[0033] S1.1.2 Dynamic model formula for target satellite maneuvering;

[0034] When the target star maneuvers, the traditional method is to perform N consecutive constant thrust maneuvers with a constant acceleration. However, the complex motion of the target is a continuous variable thrust maneuver with a time-varying acceleration, which cannot be accurately modeled.

[0035] Therefore, the present invention starts from the application scenario of actual maneuvering changes. The target moves at a certain maneuvering acceleration at the current moment, and the value range of the target maneuvering acceleration at the next moment is limited. In a certain neighborhood of the acceleration at the current moment, a fuzzy model of acceleration is established accordingly.

[0036] The maneuvering acceleration of the target is a tc (t) is a non-zero mean Markov process described by the modified Rayleigh distribution. Based on the Singer model (zero mean Markov process), the Rayleigh distribution is added to describe the acceleration variance at the current moment with the acceleration mean.

[0037] a tcThe autocorrelation function of (t) is:

[0038]

[0039] in, f is the maneuvering frequency, defined as the inverse of the maneuvering time constant, usually an empirical value, is the acceleration variance:

[0040]

[0041] in, is the mean value of maneuvering acceleration, and the acceleration update value at the previous moment is used as the mean value of acceleration.

[0042] Maneuvering acceleration a tc (t) can be expressed by the first-order time correlation model of white noise, and we can get:

[0043] a tc (t) = -fa tc (t)+n(t);

[0044] Among them, n(t) represents the mean The variance is Gaussian white noise.

[0045] Therefore, in the kinetic model formula (6), the subsequent calculations will use formulas (8), (9), and (10);

[0046] S1.2 Motion state equations established according to different dynamic models

[0047] In step S1.1, the dynamic equations for non-maneuvering and maneuvering conditions were established respectively. Now, the motion state equations for discrete conditions are established for non-maneuvering and maneuvering conditions respectively.

[0048] S1.2.1 Equation of motion for non-maneuvering conditions:

[0049] X k =F k-1 X k-1 +N k-1 ;

[0050] Among them, X k and X k-1 represent the state vectors of the target at time k and k-1 respectively, X k =[x k x k 0], x k represents the relative position of the target k and the tracking star at time k, x k represents the target speed at time k, 0 represents the target maneuvering acceleration is 0, F k-1is the state transfer matrix, N k-1 is the noise at time k-1. Discretize the model with sampling time T and get:

[0051]

[0052] S1.2.2 Equations of motion in maneuvering situations

[0053] Combining equation (6) and equation (10), the motion state model of the continuous system in the maneuvering situation is:

[0054]

[0055] The above model is a nonlinear model. In order to meet the requirements of the filtering algorithm, it needs to be discretized and linearized first. Discretize the model with sampling time T and get:

[0056]

[0057] Among them, X k and X k-1 represent the state vectors of the target at time k and k-1 respectively, X k =[x k x k x k ], x k represents the relative position of the target k and the tracking star at time k, x k represents the target speed at time k, x k Represents the target maneuvering acceleration. V k-1 is the noise at time k-1. k-1 represents the control matrix of the maneuvering target at time k-1, is the mean acceleration of the maneuvering target.

[0058] definition:

[0059]

[0060] The equation (15) is rounded to the nominal value of the state Linearization gives:

[0061]

[0062] In season F=I+A(X) T ,Right now

[0063]

[0064] From this we get:

[0065]

[0066] Among them, F k-1 is the state transfer matrix.

[0067] S1.3 System observation equations;

[0068] There are many ways to implement relative navigation for non-cooperative targets in space, including: dual line-of-sight angle measurement method, single line-of-sight angle combined with orbital maneuvering method, and line-of-sight angle combined with ranging method. The dual line-of-sight angle measurement method uses two observation satellites to observe the target satellite at the same time, and realizes relative navigation through a known baseline and two line-of-sight angle measurement vector solutions; the single line-of-sight angle combined with orbital maneuvering method requires the tracking satellite to perform certain maneuvers and changes in orbit when approaching the target; the line-of-sight angle combined with ranging method is generally used for medium and long-range observations, and the relative distance and line-of-sight angle are measured by sensors to obtain the three-dimensional relative position. The present invention uses the line-of-sight angle combined with ranging method to construct the system observation equation, and the construction of the observation equation is consistent whether it is maneuvered or non-maneuvered:

[0069] The observed quantities are the elevation angle α, azimuth angle β and line of sight distance ρ of the target star in the tracking star orbit coordinate system, and are specifically defined as:

[0070] ρ: the line-of-sight distance of the target star relative to the tracking star;

[0071] α: The elevation angle of the target star’s line of sight in the tracking star’s orbital coordinate system, defined as the angle between the target star’s line of sight relative to the tracking star and its projection in the tracking star’s orbital plane (XZ plane), with the positive direction towards the positive Y axis being positive;

[0072] β: The azimuth of the target star's line of sight in the tracking star's orbital coordinate system, defined as the angle between the projection of the target star's line of sight relative to the tracking star's line of sight on the tracking star's orbital plane (XZ plane) and the positive direction of the X-axis. From the positive direction of the X-axis to the projection, it follows a right-hand spiral, and the positive direction is positive when it points to the positive direction of the Y-axis.

[0073] The range of elevation angle α and azimuth angle β is:

[0074]

[0075] Observations obtained by tracking and aiming equipment:

[0076]

[0077] Among them, x, y, and z are the projections of the relative positions between the two stars in the tracking star orbit coordinates on the three axes.

[0078] The observation equation using the above observations is:

[0079]

[0080] in,

[0081]

[0082] Among them, Z(t) is the measured value, h(X) is the calculated value, and n is the measurement error;

[0083] Discretize and linearize the observation equation to obtain the observation equation:

[0084]

[0085] in,

[0086]

[0087] Step S2: Setting single model strong tracking Kalman filter parameters;

[0088] Since the strong tracking filter algorithm has excellent tracking effect, it is used to filter and predict the target in multi-model interactive tracking. The input of the j model at time k-1 (j represents the non-maneuvering model and the maneuvering model in this invention) is the optimal estimate X 0j (k-1k-1) and update the covariance p 0j (k-1k-1), the tracking process is similar to the single-model strong tracking Kalman filter algorithm, and the multi-model strong tracking Kalman filter process is as follows:

[0089] Its Kalman filter first-order prediction equation and prediction covariance matrix are:

[0090] X j (k|k-1)=F j X 0j (k-1|k-1);

[0091]

[0092] Among them, F is the state transfer matrix, Q is the system noise matrix, λ k-1 is the adaptive fading factor in the strong tracking filter, and its value is as follows:

[0093]

[0094] The Kalman filter gain is:

[0095] K j (k) = p j (k|k-1)H T [Hp j (k|k-1)H T +R j ] -1 ;

[0096] Among them, H is the observation matrix, R is the observation noise matrix,

[0097] The system state estimate and covariance estimate corresponding to a single filter output at time K are:

[0098] X j (k|k)=X j (k|k-1)+K j (k)[Z(k)-HX j (k|k-1)];

[0099] p j (k|k)=[IK j (k)H]p j (k|k);

[0100] Step S3: Model probability update

[0101] In the multi-model interaction algorithm, model update directly affects the effectiveness of the algorithm. This algorithm uses the maximum likelihood function method to update the model; by calculating the similarity between the current model and the current state of the moving target, the weight of the most suitable tracking model is given.

[0102] The maximum likelihood function that best matches the j model at time k is:

[0103]

[0104] Where S j (k) = Hp j (k|k-1)H T +R,d j (k) = Z j (k)-H j X j (k|k-1);

[0105] Then the update probability of model j can be obtained as:

[0106]

[0107] Where c is the normalization constant;

[0108] Step S4: Data fusion

[0109] The final output of the interaction data at time k is given according to the results calculated by each model individually and the weight of model matching, namely:

[0110] Overall estimates:

[0111]

[0112] Population covariance:

[0113]

[0114] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0115] 1. The present invention discloses a relative state estimation method for space targets under complex motion. This method aims to address the shortcoming that existing algorithms cannot effectively track the complex motion states of actual space targets. By utilizing an interactive multi-model filtering algorithm based on an improved extended acceleration observer, this method realizes a target state estimation method with high estimation accuracy, low system complexity, and close to actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] In order to facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0117] Figure 1 for Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0118] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0119] Example 1

[0120] See also Figure 1 As shown, the present invention provides a relative state estimation method for a space target under complex motion, comprising the following steps:

[0121] Step 1: Establish a dynamic model;

[0122] (1) Non-maneuvering situations,

[0123]

[0124] Where x, y, and z are the projections of the relative positions of the two stars on the three axes under the tracking star orbit coordinates, ω I In order to track the angular velocity of the star orbit coordinate system relative to the inertial coordinate system,

[0125] (2) Maneuverability

[0126]

[0127] where a tcx 、a tcy 、a tczare the projections of the relative acceleration of the target star relative to the tracking star in the tracking star orbit coordinate system on the three axes,

[0128] The maneuvering situation in the present invention is based on the application scenario of actual maneuvering changes. The target moves at a certain maneuvering acceleration at the current moment. The value range of the target maneuvering acceleration at the next moment is limited, and within a certain neighborhood of the acceleration at the current moment, a fuzzy model of acceleration is established accordingly.

[0129] The maneuvering acceleration of the target is a tc (t) is a non-zero mean Markov process described by a modified Rayleigh distribution. Based on the Singer model (zero mean Markov process), the Rayleigh distribution is added to describe the acceleration variance at the current moment using the acceleration mean.

[0130] a tc The autocorrelation function of (t) is:

[0131]

[0132] in, f is the maneuvering frequency, defined as the inverse of the maneuvering time constant, usually an empirical value, is the acceleration variance,

[0133]

[0134] in, is the mean value of maneuvering acceleration, and the acceleration update value at the previous moment is used as the mean value of acceleration.

[0135] Maneuvering acceleration a tc (t) can be expressed by the first-order time correlation model of white noise, and we can get:

[0136]

[0137] Among them, n(t) represents the mean The variance is Gaussian white noise;

[0138] Step 2: Establish observation model,

[0139] Observations obtained by tracking and aiming equipment:

[0140]

[0141] Where x, y, and z are the projections of the relative positions of the two stars on the three axes in the tracking star orbit coordinates. The observed quantities are the elevation angle α, azimuth angle β, and line of sight distance ρ of the target star in the tracking star orbit coordinate system.

[0142] The observation equation using the above observations is:

[0143]

[0144] Where h(X) is the measured value, n is the measurement noise,

[0145] Step 3: Set up the interactive multi-model filtering algorithm,

[0146] The main design idea is to automatically identify and switch between models based on Bayesian theory: at any tracking moment, real-time maneuver model detection is performed by setting model filters corresponding to the number of possible target models, setting weight coefficients and model update probabilities for each filter, and finally weighted calculation to obtain the current optimal estimation state, thereby achieving the purpose of model tracking.

[0147] It mainly includes three modules: sub-filter design, probability update and data fusion.

[0148] (1) Sub-filter design

[0149] Since the strong tracking filter algorithm has excellent tracking effect, it is used to filter and predict the target in multi-model interactive tracking. The input of the j model at time k-1 (j represents the non-maneuvering model and the maneuvering model in this invention) is the optimal estimate X 0j (k-1|k-1) and update the covariance p 0j (k-1|k-1), the tracking process is similar to the single-model strong tracking Kalman filter algorithm, and the multi-model strong tracking Kalman filter process is as follows:

[0150] Its Kalman filter first-order prediction equation and prediction covariance matrix are:

[0151] X j (k|k-1)=F j X 0j (k-1|k-1);

[0152]

[0153] Among them, F is the state transfer matrix, Q is the system noise matrix, λ k-1 is the adaptive fading factor in the strong tracking filter, and its value is as follows:

[0154]

[0155] The Kalman filter gain is:

[0156] K j (k) = p j (k|k-1)H T [Hp j (k|k-1)H T+R j ] -1 ;

[0157] Among them, H is the observation matrix and R is the observation noise matrix

[0158] The system state estimate and covariance estimate corresponding to the output of a single filter at time K are

[0159] X j (k|k)=X j (k|k-1)+K j (k)[Z(k)-HX j (k|k-1)];

[0160] p j (k|k)=[IK j (k)H]p j (k|k);

[0161] (2) Probability Update

[0162] In the multi-model interaction algorithm, model update directly affects the effectiveness of the algorithm. This algorithm uses the maximum likelihood function method to update the model; by calculating the similarity between the current model and the current state of the moving target, the weight of the most suitable tracking model is given.

[0163] The maximum likelihood function that best matches the j model at time k is:

[0164]

[0165] Where S j (k) = Hp j (k|k-1)H T +R,d j (k) = Z j (k)-H j X j (k|k-1);

[0166] Then the update probability of model j can be obtained as:

[0167]

[0168] Where c is the normalization constant;

[0169] (2) Data Fusion

[0170] The final output of the interaction data at time k is given according to the results calculated by each model individually and the weight of model matching, namely:

[0171] Overall estimates:

[0172]

[0173] Population covariance:

[0174]

[0175] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to only specific implementation methods. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A relative state estimation method for a space target under complex motion, characterized in that: The following steps are involved: Step S1: input model interaction; S1.1: Construct different dynamic models according to the complex motion scenarios of space targets; S1.1.1: Dynamic model formula for target satellite in non-maneuvering condition, When the target star is non-maneuvering, the dynamic model formula is as follows: Where x, y, and z are the projections of the relative positions of the two stars on the three axes under the tracking star orbit coordinates, ω I To track the angular velocity of the star orbit coordinate system relative to the inertial coordinate system; S1.1.2: Dynamic model formula for target satellite maneuvering. When the target star maneuvers, the dynamic model formula is as follows: where a tcx 、a tcy 、a tcz are the projections of the relative acceleration of the target star relative to the tracking star in the tracking star orbit coordinate system on the three axes; S1.2: The motion state equations established according to different dynamic models, S1.2.1: Equations of motion for the non-maneuvering case: X k =F k-1 X k-1 +N k-1 ; Among them, X k and X k-1 represent the state vectors of the target at time k and k-1 respectively, X k =[x k x k 0], x k represents the relative position of the target k and the tracking star at time k, x k represents the target speed at time k, 0 represents the target maneuvering acceleration is 0, F k-1 is the state transfer matrix, N k-1 is the noise at k-1 moment; S1.2.2: Equations of motion for maneuvering situations: Among them, X k and X k-1 represent the state vectors of the target at time k and k-1 respectively, X k =[x k x k x k ], x k represents the relative position of the target k and the tracking star at time k, x k represents the target speed at time k, x k Indicates the target maneuvering acceleration. F k-1 is the state transfer matrix, n k-1 is the noise at time k-1. k-1 represents the control matrix of the maneuvering target at time k-1, is the mean acceleration of the maneuvering target; S1.3: Establishing the system observation equation Observations obtained by tracking and aiming equipment: Where x, y, and z are the projections of the relative positions of the two stars on the three axes in the tracking star orbit coordinates, and the observed quantities are the elevation angle α, azimuth angle β, and line of sight distance ρ of the target star in the tracking star orbit coordinate system; The observation equation using the above observations is: Where h(X) is the measured calculated value and n is the measurement noise; Step S2: Setting single model strong tracking Kalman filter parameters; Since the strong tracking filter algorithm has excellent tracking effect, it is used to filter and predict the target in multi-model interactive tracking. The input of the j model at time k-1 (j represents the non-maneuvering model and the maneuvering model in this invention) is the optimal estimate X 0j (k-1|k-1) and update the covariance p 0j (k-1|k-1), the tracking process is similar to the single-model strong tracking Kalman filter algorithm, and the multi-model strong tracking Kalman filter process is as follows: Its Kalman filter first-order prediction equation and prediction covariance matrix are: X j (kk-1)=F j X 0j (k-1|k-1); p j (kk-1)=λ k-1 F j p 0j (k-1|k-1)F j T +Q j ; Among them, F is the state transfer matrix, Q is the system noise matrix, λ k-1 is the adaptive fading factor in the strong tracking filter, and its value is as follows: The Kalman filter gain is: K j (k)=p j (k|k-1)H T [Hp j (k|k-1)H T +R j ] -1 ; Among them, H is the observation matrix, R is the observation noise matrix, and the system state estimation and covariance estimation corresponding to the output of a single filter at time K are: X j (k|k)=X j (k|k-1)+K j (k)[Z(k)-HX j (k|k-1)]; p j (k|k)=[I-K j (k)H]p j (k|k); Step S3: model probability update; In the multi-model interaction algorithm, model update directly affects the effectiveness of the algorithm. The algorithm uses the maximum likelihood function method to update the model. The weight of the most suitable tracking model is given by calculating the similarity between the current model and the current moving target state. The maximum likelihood function that best matches the j model at time k is: Where S j (k)=Hp j (k|k-1)H T +R,d j (k) = Z j (k)-H j X j (k|k-1); then the update probability of model j can be obtained as: Where c is the normalization constant; Step S4: data fusion; The final output of the interaction data at time k is given according to the results calculated by each model individually and the weight of model matching, namely: Overall estimates: Population covariance:

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