Fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR

Abstract

The invention discloses a fusion positioning algorithm based on low earth orbit satellite Doppler measurement, DME and VOR, and relates to the technical field of satellite navigation, and the algorithm comprises the steps: obtaining Doppler frequency shift of a low earth orbit satellite, slant range information of the DME and azimuth angle data of the VOR, constructing a combined observation equation, and obtaining a corresponding Jacobian matrix; based on the geometric accuracy factor, channel and satellite selection is carried out through a genetic algorithm, DME, VOR and low-orbit satellites are optimized and selected, and an optimal navigation source combination is obtained; motion models in different flight modes are constructed, interactive multi-model Kalman filtering is utilized to dynamically estimate the state of the aircraft, and position information is updated in real time. Therefore, by the adoption of the method, real-time positioning of the aircraft under complex conditions is achieved, the anti-interference capability of the system is improved, and the overall positioning precision and stability of the system are improved.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation technology, and in particular to a fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR. Background Art

[0002] In civil aviation navigation systems, traditional land-based navigation technologies such as very high frequency omnidirectional range (VOR) and distance measurement equipment (DME) have been widely used. These systems provide accurate distance and azimuth information to aircraft through ground stations. Relying on their low cost, simple equipment and mature technology, land-based navigation systems have become one of the important navigation methods for aircraft. However, with the increase in aviation demand and the complexity of the flight environment, the shortcomings of traditional land-based navigation systems in terms of coverage and reliability have gradually emerged, especially in the mountainous and remote areas of western China. These areas have complex terrain, and the signal transmission of VOR and DME is limited by terrain obstruction, resulting in the emergence of navigation blind spots. Aircraft face great challenges in safe flight in these areas.

[0003] In addition, the Global Navigation Satellite System (GNSS) also occupies an important position in modern aviation navigation. With its global coverage, high positioning accuracy and convenience, GNSS has become one of the main navigation methods for aircraft. However, the GNSS system also faces security issues such as signal interference and spoofing attacks. Especially in high electromagnetic interference environments, GNSS signals are easily interfered with or even completely fail, causing aircraft to lose their main navigation basis, which poses a major threat to flight safety. Therefore, relying solely on GNSS for navigation is not enough to ensure the safe operation of aircraft in critical areas, especially in complex electromagnetic environments and severe weather conditions.

[0004] In order to meet these challenges, in recent years, low-orbit satellite (LEO) systems have gradually entered the field of aviation navigation as a new navigation supplement. Compared with traditional GNSS satellites, low-orbit satellites have lower orbital altitudes and stronger signal strengths, and can provide higher update frequencies and better signal anti-interference capabilities. The global coverage of LEO satellites and their unique Doppler frequency shift measurement technology provide aircraft with a new source of navigation information, especially in areas where traditional navigation signals are insufficiently covered. LEO satellites can effectively fill this gap.

[0005] In order to overcome the limitations of a single navigation method, multi-sensor fusion technology has become a hot topic of research in recent years. By fusing multiple navigation information sources, the accuracy and reliability of the positioning system can be improved. Although the fusion of multi-source information provides a solution to the problem of insufficient coverage of ground navigation systems, it still faces many challenges. On the one hand, the core of the fusion algorithm lies in how to effectively process data from different sensors to ensure the anti-interference ability and positioning accuracy of the navigation system. On the other hand, the geometric dilution of precision (DOP) is also an important parameter affecting positioning accuracy. DOP reflects the geometric relationship between the navigation device and the positioning base station or satellite. A smaller DOP value means better positioning accuracy. In order to minimize DOP, it is usually necessary to make a reasonable selection of ground navigation stations and satellites. Therefore, it is necessary to provide a positioning algorithm based on the fusion of low-orbit satellite Doppler measurement, DME distance information and VOR azimuth data to provide aircraft with a more robust and accurate navigation solution, especially when GNSS is unavailable or unreliable, to provide a strong guarantee for flight safety. Summary of the invention

[0006] The purpose of the present invention is to provide a fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, which can make up for the problem of insufficient coverage of traditional navigation methods in complex terrain or environment, provide solutions for high-precision and anti-interference navigation in complex flight environments, and ensure the flight safety of aircraft in various complex scenarios.

[0007] To achieve the above object, the present invention provides a fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, including:

[0008] S1, obtain the Doppler frequency shift of the low-orbit satellite, the slant range information of the DME and the azimuth data of the VOR, and construct the combined observation equation and obtain the corresponding Jacobi matrix;

[0009] S2. Based on the geometric precision factor, the genetic algorithm is used to select the station and satellite, and the DME, VOR and low-orbit satellites are optimized to obtain the optimal navigation source combination;

[0010] S3. Construct motion models under different flight modes, and use interactive multi-model Kalman filtering to dynamically estimate the state of the aircraft and update the position information in real time.

[0011] Preferably, the combined observation equation corresponds to the form of the Jacobian matrix H, as follows:

[0012]

[0013] Where, d i represents the distance between the i-th DME station and the aircraft, θ jrepresents the azimuth between the jth VOR station and the aircraft, represents the pseudorange change rate of the kth low-orbit satellite, (x, y, z) represents the position coordinates of the aircraft, and ν x , νy, ν z They represent the velocity components of the aircraft in the x, y, and z directions respectively. Indicates the receiver clock drift.

[0014] Preferably, the station and satellite selection by genetic algorithm includes iterating by crossover and mutation operations to find the optimal combination of DME, VOR and low-orbit satellite.

[0015] Preferably, the motion models in different flight modes include a uniform speed model and a turning model, each motion model independently performs state prediction and update, and the state estimation is weightedly fused according to the prediction probability of each motion model to obtain an overall state estimation.

[0016] Preferably, the state equation of the motion model is as follows:

[0017] X(t+1)=Φ i X(t)+G i (t);

[0018] In the formula, X(t+1) and X(t) are the state vectors of the system at time t+1 and t respectively, Φ i , G i (t) represent the state transfer matrix and process noise matrix of the i-th motion model respectively;

[0019] Z(t)=HX(t)+V(t);

[0020] Where Z(t) represents the observation vector and V(t) represents the measurement noise matrix;

[0021] The state estimate and covariance estimate obtained by a single filter are as follows:

[0022] X i (t|t)=X i (t|t-1)+K i (t)[Z(t)-HX i (t|t-1)];

[0023] P i (t|t)=[IK i (t)H]P i (t|t-1);

[0024] Where Z(t) represents the observation vector, X i (t|t),P i(t|t) represents the state estimate and covariance estimate of the i-th motion model at time t, I represents the identity matrix, X i (t|t-1)] represents the state prediction value of the i-th motion model at time t, P i (t|t-1) represents the updated covariance;

[0025] in,

[0026] K i (t) = P i (t|t-1)H T [HP i (t|t-1)H T +R] -1 ;

[0027] In the formula, K i (t) represents the Kalman gain, and R represents the covariance of the measurement noise.

[0028] Preferably, the prediction probability of the motion model is updated using the maximum likelihood method as follows:

[0029] At time t, the maximum likelihood function that best matches the j-th motion model and the i-th motion model is as follows:

[0030]

[0031] in,

[0032] S j (t) = HP j (t|t-1)H T +R;

[0033] d j (t) = Z(t) - HX j (t|t-1);

[0034] In the formula, Λ j (t) represents the maximum likelihood function of the jth motion model, d j (t), S j (t) respectively represent the measurement error matrix and measurement error covariance matrix of the j-th motion model;

[0035] At time t, the predicted probability of the jth motion model is updated as follows:

[0036]

[0037] in,

[0038]

[0039] In the formula, c represents the normalization constant, uj (t) represents the predicted probability of the jth motion model at time t, u i (t-1) represents the predicted probability of the i-th motion model at time t-1, p ij represents the transition probability from the i-th motion model to the j-th motion model, Represents the predicted probability after fusion.

[0040] Preferably, the overall state is estimated as follows:

[0041]

[0042] Where X(t|t) represents the estimation of the overall state, and n represents the type of motion model;

[0043] The overall covariance is:

[0044]

[0045] Where P(t|t) represents the covariance of the overall state.

[0046] Therefore, the present invention adopts the above-mentioned fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, which has the following technical effects:

[0047] (1) The DME, VOR, and low-orbit satellites are optimized and selected through genetic algorithms to ensure the optimal geometric structure to minimize the DOP value. This can not only make up for the problem of insufficient coverage of the ground navigation system, but also enhance the system's anti-interference ability in complex environments. At the same time, it can effectively search for the optimal navigation source combination and improve the overall positioning accuracy and stability of the system.

[0048] (2) The interactive multi-model (IMM) Kalman filter technology is used to fuse the multi-source data of low-orbit satellite Doppler frequency shift, DME slant range and VOR azimuth angle, and switch between different flight modes to obtain the aircraft's precise position and velocity information in real time.

[0049] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of the fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR. DETAILED DESCRIPTION

[0051] The present invention can be explained in more detail by the following examples. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following examples.

[0052] like Figure 1 As shown, the fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR provided by the present invention has the following specific steps:

[0053] S1. Use the receiver installed on the aircraft to obtain the signal of the low-orbit satellite, including the basic information such as the satellite's position, speed and acceleration, and the Doppler frequency shift caused by the satellite's relative motion.

[0054] The Doppler observation equation can be derived from the pseudorange observation equation as follows:

[0055]

[0056] in,

[0057]

[0058] In the formula, is the derivative of pseudorange, D is the Doppler frequency shift, in Hz; is the wavelength of the transmitted signal, in meters; c is the speed of light in a vacuum; v s 、v r Represent the speed of satellite and receiver respectively; are the clock drifts of the receiver and satellite respectively; are the delay change rates of the troposphere and ionosphere, respectively, in meters per second; is the pseudorange rate measurement noise including unmodeled errors; w e is the angular velocity of the Earth's rotation; p s =[x s ,y s ,z s ] T 、p r =[x,y,z] T are the position coordinates of the satellite and the receiver respectively; v r =[v x ,v y ,v z ] T are the speeds of the satellite to the receiver.

[0059] DME2100 is used to receive radio frequency signals from the ground DME navigation station. The DME navigation station measures the slant distance between the aircraft and the DME navigation station through the time delay of two-way pulses. The receiver calculates the round-trip time of the signal and, based on the speed of electromagnetic wave propagation, obtains the slant distance between the aircraft and the DME in real time.

[0060] The observation equation of the distance between the aircraft and the ground station is as follows:

[0061]

[0062] Among them, [x D ,y D ,z D ] is the position coordinate of DME, [x, y, z] is the position coordinate of aircraft, and d is the distance value measured by DME.

[0063] The VOR navigation station uses phase comparison technology to determine the aircraft's azimuth relative to the VOR through the phase difference between the reference signal and the variable signal. After the receiver receives the phase difference, it calculates the aircraft's precise direction relative to the VOR.

[0064] The observation equation of the azimuth between the aircraft and the VOR station is as follows:

[0065]

[0066] Among them, [x V ,y V ,z V ] is the location coordinate of the VOR station, and θ is the azimuth measured by the VOR.

[0067] Based on the observation equations of each sensor, a combined observation equation is constructed. In this process, the present embodiment uses the observation equations of the Doppler shift, DME slant range and VOR azimuth of the low-orbit satellite to derive the corresponding Jacobian matrix and linearize these nonlinear measurement models. The Jacobian matrix provides an accurate description of the observation equation of the IMM Kalman filter.

[0068] The state quantity is selected as To describe the aircraft's geocentric Earth-fixed rectangular coordinate system coordinates, velocity and receiver clock error drift. Since there are four unknown quantities in velocity and receiver clock error, at least four low-orbit satellites are required, and the total number of DME, VOR and low-orbit satellites should be no less than 7.

[0069] Since the state of the aircraft is unknown in actual application, it is necessary to 0 , and the true value of the state quantity at the initial moment is obtained through Newton iteration. Taking i DME stations, j VOR stations and k low-orbit satellites as an example of combined positioning, the expression of the combined observation equation is as follows:

[0070] L=H·ΔX r +ε;

[0071] Where L represents the combined observation matrix; H represents the Jacobian matrix, and each row represents the partial derivative of each sensor observation with respect to the state quantity; ΔX r represents the state correction of the receiver; ε represents the unmodeled error.

[0072] in,

[0073]

[0074]

[0075] Where Δx, Δy, and Δz represent the corrections to the x, y, and z coordinates of the aircraft, respectively, and Δv x , Δv y , Δv z They represent the corrections of the aircraft's velocity components in the x, y, and z directions, respectively. Indicates the correction amount of the receiver clock drift.

[0076] Based on the combined observation equation, the correction ΔX of the receiver position, velocity and clock drift can be obtained according to the least squares method: r , thereby updating the receiver's state vector to X 0 +ΔX r , and updated according to the Newton iteration method to obtain the initial state of the aircraft as the basis for subsequent prediction and filtering.

[0077] In this embodiment, the geometric dilution of precision (DOP) is used to describe the performance of the positioning algorithm, and its expression is as follows:

[0078]

[0079] S2. In order to ensure the reasonable geometric distribution of multi-source data, the genetic algorithm evaluates the advantages and disadvantages of each navigation source combination according to the geometric precision factor (DOP). The specific operation steps are as follows:

[0080] First, seven navigation sources are preliminarily selected, including at least four low-orbit satellites, and several groups of navigation source combination codes are generated.

[0081] The code of the navigation source combination is expressed in binary form, 1 means selection, and 0 means non-selection:

[0082] The first two digits represent the low-orbit satellites with the largest and smallest elevation angles, and are both initialized to 1; then, according to the number of remaining visible low-orbit satellites, an equal number of binary codes are set to indicate the selection status of the remaining visible low-orbit satellites; in the middle, the DME station number digit can be used to indicate the selection status of the DME station; finally, the VOR station number digit can be used to indicate the selection status of the VOR station.

[0083] The genetic algorithm continuously iterates by performing crossover and mutation operations to further reduce the geometric dilution of precision (DOP) to obtain the optimal combination of ground stations (DME stations or VOR stations) and low-orbit satellites.

[0084] Among them, the crossover operation: keep the total number of 1s unchanged, randomly select two groups of codes and select the starting point on their binary codes, exchange the number of 1s in the same interval to explore new combinations; mutation operation: randomly select a code bit as the mutation point and exchange it with the first different code bit after the point. This random mutation operation can introduce new combinations and avoid falling into the local optimal solution.

[0085] In each iteration, ensure that each combination of navigation sources meets the following conditions:

[0086] (1) A total of seven navigation sources are selected; (2) at least four are from low-orbit satellites; and (3) the remaining three can be DME or VOR navigation stations, at least one of which is a ground-based navigation station. This legality check ensures that each combination can meet the navigation requirements of the system and provide sufficient data support for subsequent fusion processing.

[0087] After multiple iterations of the genetic algorithm, the optimal combination of seven navigation sources was found to ensure their good geometric distribution. At the same time, the positioning accuracy of the system was improved by minimizing the geometric dilution of precision (DOP), laying the foundation for subsequent data fusion and filtering processing, ensuring that the acquired data has the optimal spatial distribution and accuracy.

[0088] In addition, in order to accelerate the optimization process, the system also sets the following genetic operation parameters: (1) The population size is large enough to ensure that a variety of combinations are explored; (2) The crossover probability is set to 0.9 to ensure that most individuals undergo crossover operations; (3) The mutation probability is set to 0.9 to maintain the diversity of the population and prevent early convergence; (4) The cutoff threshold D is set to 1 to ensure that the genetic operation is stopped when the optimal DOP value is approached; (5) The genetic generation number T is set to 100 iterations to ensure sufficient search depth. By setting these genetic parameters, the system can quickly find the navigation source combination with the smallest DOP.

[0089] Since land-based navigation systems (DME or VOR navigation stations) are stable and mature, while low-orbit satellites have global coverage and high update rates, the two complement each other. Therefore, combining the advantages of land-based navigation systems and low-orbit satellite navigation systems to form a combined navigation system can effectively solve the navigation blind spot problem in complex terrains such as western China, while improving the system's anti-interference ability, providing an effective solution for improving aircraft navigation accuracy and reliability.

[0090] S3. Based on the optimal combination of navigation sources, obtain the Doppler shift of the low-orbit satellite, the slant range information of the DME and the azimuth data of the VOR under the combination, and use the interactive multi-model (IMM) Kalman filter to dynamically estimate the state of the aircraft in different flight modes and update the position information in real time, as follows:

[0091] In order to meet the positioning requirements of aircraft under different flight conditions, motion models can be constructed according to actual conditions, such as uniform speed models and turning models. These models are designed according to different motion modes of aircraft and can adapt to straight flight and turning flight respectively. During the entire filtering process, the system dynamically selects the most suitable model based on real-time data to ensure that accurate position information can be provided under different flight conditions. Assume that the i-th motion model is a uniform linear motion model and the j-th motion model is a uniform turning model, then p ij is the probability of changing from the i-th motion model to the j-th motion model, and its model transition probability matrix P is:

[0092]

[0093] Before starting filtering, the system can set the position, velocity and covariance obtained by the combined positioning at the previous moment as the initial state of each motion model, and the initial probability of the model state is set to 0.5.

[0094] The system runs the uniform linear motion model (CV) and the uniform turning model (CT) simultaneously, and each model independently predicts and updates the state. For the observed data at each moment, the two models perform Kalman filtering and output their respective state estimates. Among them, the state equations of the CV and CT models can be expressed as:

[0095] X(t+1)=Φ i X(t)+G i (t);

[0096] In the formula, X(t+1) and X(t) are the state vectors of the system at time t+1 and t respectively, Φ i , G i (t) represent the state transfer matrix and process noise matrix of the i-th motion model respectively.

[0097] Among them, the state transfer matrix Φ of the uniform linear motion model CV and the process noise matrix G CV ,as follows:

[0098]

[0099] In the uniform turning motion model, the process noise matrix G CT With G CV Consistent, but the state transfer matrix Φ CT There are some differences, as follows:

[0100]

[0101] Where ω is the angular velocity and can be set to 0.001, G CTis the process noise of uniform turning motion, and Δt is the step size set to 1s.

[0102] The observation equation of the centralized arbitrary motion model is as follows:

[0103] Z(t)=HX(t)+V(t);

[0104] Where Z(t) represents the observation vector, V(t) represents the measurement noise matrix, and H represents the Jacobian matrix.

[0105] At time t, the system state estimate X output by a single filter is i (t|t) is:

[0106] X i (t|t)=X i (t|t-1)+K i (t)[Z(t)-HX i (t|t-1)];

[0107] K i (t) = P i (t|t-1)H T [HP i (t|t-1)H T +R] -1 ;

[0108] In the formula, K i (t) represents the Kalman gain, X i (t|t-1)] represents the state prediction value of the i-th motion model at time t, and R represents the covariance of the measurement noise.

[0109] The corresponding covariance estimate is:

[0110] P i (t|t)=[IK i (t)H]P i (t|t-1);

[0111] Where P i (t|t-1) represents the updated covariance and I represents the identity matrix.

[0112] In the IMM algorithm, the updating of the model directly affects the effectiveness of the algorithm. In this embodiment, the maximum likelihood function method is used to implement the updating of the model: the weight of the most suitable tracking model is given by calculating the similarity between the current motion model and the current motion target state, as follows:

[0113] Assume that time t is the jth motion model, and its maximum likelihood function that best matches the i-th motion model is:

[0114]

[0115] in,

[0116] S j (t) = HP j (t|t-1)H T +R;

[0117] d j (t) = Z(t) - HX j (t|t-1);

[0118] In the formula, Λ j (t) represents the maximum likelihood function of the jth motion model, d j (t), S j (t) represent the measurement error matrix and measurement error covariance matrix of the jth motion model respectively.

[0119] At this time, the predicted probability of the jth motion model is updated as follows:

[0120]

[0121] in,

[0122]

[0123] In the formula, c represents the normalization constant, u j (t) represents the predicted probability of the jth motion model at time t, u i (t-1) represents the predicted probability of the i-th motion model at time t-1, p ij represents the transition probability from the i-th motion model to the j-th motion model, Represents the predicted probability after fusion.

[0124] Finally, based on the results (state estimation) calculated by each motion model individually and the weight of model matching (prediction probability), the state estimation is fused to obtain the overall state estimation, as follows:

[0125]

[0126] In the formula, X(t|t) represents the estimation of the overall state, n represents the type of motion model, and u i (t) represents the i-th motion model.

[0127] The overall covariance is:

[0128]

[0129] Where P(t|t) represents the covariance of the overall state.

[0130] Through the interactive multi-model (IMM) Kalman filter, the aircraft can dynamically switch between different motion models, which is particularly suitable for handling the aircraft's changeable flight state, thereby achieving more accurate navigation solutions.

[0131] Therefore, the present invention adopts the above-mentioned fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR to achieve high-precision, interference-resistant navigation positioning in complex flight environments, and ensure the flight safety of aircraft in various complex scenarios.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, characterized by: The following steps are involved: S1, obtain the Doppler frequency shift of the low-orbit satellite, the slant range information of the DME and the azimuth data of the VOR, and construct the combined observation equation and obtain the corresponding Jacobi matrix; S2. Based on the geometric precision factor, the genetic algorithm is used to select the station and satellite, and the DME, VOR and low-orbit satellites are optimized to obtain the optimal navigation source combination; S3. Construct motion models under different flight modes, and use interactive multi-model Kalman filtering to dynamically estimate the state of the aircraft and update the position information in real time.

2. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 1 is characterized in that: The form of the Jacobian matrix H corresponding to the combined observation equation is as follows: Where, d i represents the distance between the i-th DME station and the aircraft, θ j represents the azimuth between the jth VOR station and the aircraft, represents the pseudorange change rate of the kth low-orbit satellite, (x, y, z) represents the position coordinates of the aircraft, and ν x , νy, ν z They represent the velocity components of the aircraft in the x, y, and z directions respectively. Indicates the receiver clock drift.

3. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 1 is characterized in that: The genetic algorithm is used to select stations and satellites, including the use of crossover and mutation operations to iterate and find the optimal combination of DME, VOR and low-orbit satellites.

4. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 1 is characterized in that: The motion models under different flight modes include a uniform speed model and a turning model. Each motion model independently predicts and updates its state, and based on the prediction probability of each motion model, the state estimation is weightedly fused to obtain the overall state estimation.

5. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 4 is characterized in that: The state equation of the motion model is as follows: X(t+1)=Φ i X(t)+G i (t); In the formula, X(t+1) and X(t) are the state vectors of the system at time t+1 and t respectively, Φ i , G i (t) represent the state transfer matrix and process noise matrix of the i-th motion model respectively; Z(t)=HX(t)+V(t); Where Z(t) represents the observation vector and V(t) represents the measurement noise matrix; The state estimate and covariance estimate obtained by a single filter are as follows: X i (t∣t)=X i (t∣t-1)+K i (t)[Z(t)-HX i (t∣t-1)]; P i (t|t)=[I-K i (t)H]P i (t|t-1); In the formula, X i (t|t),P i (t|t) represents the state estimate and covariance estimate of the i-th motion model at time t, I represents the identity matrix, X i (t|t-1)] represents the state prediction value of the i-th motion model at time t, P i (t|t-1) represents the updated covariance; in, K i (t)=P i (t|t-1)H T [HP i (t|t-1)H T +R] -1 ; In the formula, K i (t) represents the Kalman gain, and R represents the covariance of the measurement noise.

6. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 4 is characterized in that: The maximum likelihood method is used to update the predicted probability of the motion model as follows: At time t, the maximum likelihood function that best matches the j motion model and the i motion model is as follows: in, S j (t)=HP j (t∣t-1)H T +R; d j (t)=Z(t)-HX j (t|t-1); In the formula, Λ j (t) represents the maximum likelihood function of the jth motion model, d j (t), S j (t) respectively represent the measurement error matrix and measurement error covariance matrix of the j-th motion model; At time t, the predicted probability of the jth motion model is updated as follows: in, In the formula, c represents the normalization constant, u j (t) represents the predicted probability of the jth motion model at time t, u i (t-1) represents the predicted probability of the i-th motion model at time t-1, p ij represents the transition probability from the i-th motion model to the j-th motion model, Represents the predicted probability after fusion.

7. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 4 is characterized in that: The overall status is estimated as follows: Where X(t|t) represents the estimation of the overall state, and n represents the type of motion model; The overall covariance is: Where P(t|t) represents the covariance of the overall state.

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