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

Abstract

The application discloses a fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, relates to the technical field of satellite navigation, and comprises the following steps: acquiring the Doppler frequency shift of a low-orbit satellite, the slant range information of a DME and the azimuth angle data of a VOR, constructing a combined observation equation, and obtaining a corresponding Jacobian matrix; based on a geometric dilution of precision, selecting stations and stars through a genetic algorithm, optimizing the selection of the DME, the VOR and the low-orbit satellite, and obtaining an optimal navigation source combination; constructing a motion model under different flight modes, and dynamically estimating the state of an aircraft by using an interactive multiple model Kalman filter, and updating the position information in real time. Therefore, the real-time positioning of the aircraft under complex conditions is realized, 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 application relates to the field of satellite navigation technology, in particular to a fusion positioning algorithm based on low earth orbit satellite Doppler measurement, DME and VOR. BACKGROUND

[0002] In civil aviation navigation systems, traditional ground-based navigation technologies such as Very High Frequency Omnidirectional Range (VOR) and Distance Measuring Equipment (DME) have been widely used. These systems provide accurate distance and direction information to aircraft through ground stations, relying on their low cost, simple equipment and mature technology, ground-based navigation systems have become one of the important navigation means for aircraft. However, with the increase of aviation demand and the complexity of flight environment, the shortcomings of traditional ground-based navigation systems in coverage and reliability gradually appear, especially in the mountainous and remote areas of China, the terrain in these areas is complex, the signal transmission of VOR and DME is limited by terrain obstruction, leading to the emergence of navigation blind area. The safe flight of aircraft in these areas faces great challenges.

[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, GNSS systems also face security problems such as signal interference and spoofing attacks. Especially in high electromagnetic interference environment, GNSS signals are easily disturbed or even completely disabled, leading to the loss of main navigation basis for aircraft, 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 key areas, especially in complex electromagnetic environment and adverse weather conditions.

[0004] In order to cope with these challenges, in recent years, low earth orbit (LEO) system as a new navigation supplement means gradually enters the field of view of aviation navigation. Low earth orbit satellites have lower orbital height and stronger signal strength compared with traditional GNSS satellites, which can provide higher update frequency and better signal anti-interference ability. The global coverage of LEO satellites and its unique Doppler frequency shift measurement technology provide new navigation information sources for aircraft, especially in areas where traditional navigation signal coverage is insufficient, LEO satellites can effectively make up for this gap.

[0005] To overcome the limitations of single navigation methods, multi-sensor fusion technology has become a research hotspot in recent years. By fusing multiple navigation information sources, the accuracy and reliability of positioning systems can be improved. While multi-source information fusion offers a solution to the inadequate coverage of ground-based navigation systems, it still faces numerous challenges. The core of the fusion algorithm lies in effectively processing data from different sensors to ensure the navigation system's anti-interference capability and positioning accuracy. Furthermore, the geometric dilution of precision (DOP) is a key parameter affecting positioning accuracy. DOP reflects the geometric relationship between the navigation device and the positioning base station or satellite. A smaller DOP value indicates better positioning accuracy. Minimizing DOP typically requires the careful selection of ground navigation stations and satellites. Therefore, it is necessary to develop a positioning algorithm that fuses Doppler measurements from low-orbit satellites, distance information from distance measurement (DME), and azimuth angle data from frequency coordinates (VORs). This algorithm can provide aircraft with a more robust and accurate navigation solution, particularly when GNSS is unavailable or unreliable, effectively ensuring flight safety. Summary of the Invention

[0006] The purpose of this 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 environments, provide a solution for high-precision and anti-interference navigation in complex flight environments, and ensure the flight safety of aircraft in a variety of complex scenarios.

[0007] To achieve the above objectives, 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 Jacobian matrix;

[0009] S2. Based on the geometric dilution of precision, a genetic algorithm is used to select stations and satellites, optimizing the selection of DME, VOR, and low-orbit satellites 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 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 iteratively utilizing crossover and mutation operations to find the optimal combination of DME, VOR and low-orbit satellites.

[0015] Preferably, the motion models under 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] Where X(t+1) and X(t) are the state vectors of the system at time t+1 and time t, respectively. i , G i (t) represents the state transition 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] Where K i (t) represents the Kalman gain, and R represents the covariance of the measurement noise.

[0028] Preferably, the maximum likelihood method is used to update the predicted probability of the motion model 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] Where, Λ j (t) represents the maximum likelihood function of the j-th motion model, d j (t), S j (t) denotes the measurement error matrix and measurement error covariance matrix of the j-th motion model respectively;

[0035] At time t, the predicted probability of the j-th 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 estimated value of the overall state, and n represents the type of motion model;

[0043] The covariance of the population 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 genetic algorithm is used to optimize the selection of DME, VOR and low-orbit satellites 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 shift, DME slant range and VOR azimuth, and switch between different flight modes to obtain the precise position and velocity information of the aircraft 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 present invention provides a fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR, and the specific steps are as follows:

[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, velocity 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] Where, is the derivative of pseudorange, D is the Doppler 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 rates of change of tropospheric and ionospheric delays, 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 receiver respectively; v r =[v x ,v y ,v z ] T are the speeds of the satellite to the receiver respectively.

[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, calculates the slant distance between the aircraft and the DME in real time.

[0060] The observation equation for 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] VOR navigation stations use phase comparison technology to determine the aircraft's bearing relative to the VOR by comparing the phase difference between a reference signal and a variable signal. The receiver then calculates the aircraft's precise direction relative to the VOR after detecting the phase difference.

[0064] The observation equation for the azimuth angle 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, this embodiment uses the observation equations for the Doppler shift, DME slant range, and VOR azimuth of low-orbit satellites to derive the corresponding Jacobian matrix, linearizing these nonlinear measurement models. The Jacobian matrix provides a precise description of the observation equations for the IMM Kalman filter.

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

[0069] Since the state of the aircraft is unknown in actual applications, it is necessary to obtain the true value of the state at the initial moment through Newton iteration based on the given initial X0. 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 Respectively represent the correction amount of the aircraft's velocity components in the x, y, and z directions, Indicates the correction amount of the receiver clock drift.

[0076] Based on the combined observation equation and the least squares method, the correction ΔX of the receiver position, velocity and clock drift can be obtained: r , thereby updating the receiver's state vector to X0+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 performance of the positioning algorithm is described using the geometric dilution of precision (DOP), which is expressed as follows:

[0078]

[0079] S2. To ensure the geometric distribution of multi-source data is reasonable, the genetic algorithm evaluates the quality of each navigation source combination based on the geometric dilution of precision (DOP). The specific steps are as follows:

[0080] First, a preliminary selection of seven navigation sources is made, including at least four low-orbit satellites, and several sets 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 deselection:

[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; the middle digit is the number of available DME stations to indicate the selection status of the DME station; and finally, the number of available VOR stations is the number of available VOR stations 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] The crossover operation maintains the total number of 1s, randomly selects two sets of codes, picks a starting point on their binary codes, and swaps the number of 1s within the same interval to explore new combinations. The mutation operation randomly selects a code bit as the mutation point and swaps it with the first different code bit after that point. This random mutation operation can introduce new combinations and avoid falling into local optimal solutions.

[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 of them 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, ensuring 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, and ensuring that the acquired data has optimal spatial distribution and accuracy.

[0088] In addition, 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 population diversity and prevent premature 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 minimum DOP.

[0089] Since land-based navigation systems (DME or VOR navigation stations) are characterized by high stability and maturity, while low-orbit satellites have the characteristics of global coverage and high update rate, 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. At the same time, it can improve the system's anti-interference capability, providing an effective solution for improving aircraft navigation accuracy and reliability.

[0090] S3. Based on the optimal navigation source combination, obtain the Doppler shift of low-orbit satellites, slant range information of DME, and azimuth data of VOR under this combination. Utilize the Interactive Multi-Model (IMM) Kalman filter to dynamically estimate the aircraft state in different flight modes and update the position information in real time. The details are as follows:

[0091] In order to adapt to the positioning requirements of the aircraft in different flight states, motion models such as uniform speed models and turning models can be constructed according to actual conditions. These models are designed according to the different motion modes of the aircraft and can adapt to situations such as straight flight and turning flight. During the entire filtering process, the system dynamically selects the most appropriate model based on real-time data to ensure that accurate position information can be provided in different flight states. 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 transitioning 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 simultaneously runs a uniform linear motion model (CV) and a uniform turning model (CT), each independently performing state prediction and updating. For each moment of observation, both models perform Kalman filtering and output their respective state estimates. The state equations for the CV and CT models can be expressed as:

[0095] X(t+1)=Φ i X(t)+G i (t);

[0096] Where X(t+1) and X(t) are the state vectors of the system at time t+1 and time t, respectively. i , G i (t) represent the state transition 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] Where 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 update of the model directly affects the effectiveness of the algorithm. In this embodiment, the maximum likelihood function method is used to update the model: the weight of the most suitable tracking model is given by calculating the similarity between the current motion model and the current moving target state, as follows:

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

[0114]

[0115] wherein,

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

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

[0118] wherein, 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 the measurement error covariance matrix of the jth motion model, respectively.

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

[0120]

[0121] wherein,

[0122]

[0123] wherein, c represents a normalization constant, u j (t) represents the prediction probability of the jth motion model at time t, u i (t-1) represents the prediction probability of the ith motion model at time t-1, p ij represents the transition probability from the ith motion model to the jth motion model, represents the fused prediction probability.

[0124] Finally, according to the results (state estimation) calculated separately by each motion model and the weights (prediction probability) matched by the models, state estimation fusion is performed to obtain the overall state estimation as follows:

[0125]

[0126] wherein, X(t|t) represents the estimate of the overall state, n represents the number of motion models, u i (t) represents the ith motion model.

[0127] The overall covariance is:

[0128]

[0129] wherein, 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, ensuring 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 solutions of the present invention rather than to limit the same. 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 solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions 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. The combined observation equation corresponds to the Jacobian matrix The form is as follows: ； Where, Indicates the The distance between the DME station and the aircraft, Indicates the The bearing angle between the VOR station and the aircraft, Indicates the The pseudorange change rate of low-orbit satellites, represents the position coordinates of the aircraft, 、 、 Represent the velocity components of the aircraft in the x, y, and z directions, respectively. Indicates the receiver clock drift; S2. Based on the geometric dilution of precision, a genetic algorithm is used to select stations and satellites, optimizing the selection of DME, VOR, and low-orbit satellites 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 genetic algorithm for station and satellite selection involves iteratively using crossover and mutation operations to find the optimal combination of DME, VOR, and low-orbit satellites.

3. 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 performs state prediction and update, and the state estimation is weightedly fused according to the prediction probability of each motion model to obtain the overall state estimation.

4. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 3 is characterized in that: The state equation of the motion model is as follows: ； Where, 、 They are 、 The state vector of the system at time t, 、 Respectively represent The state transfer matrix and process noise matrix of a motion model; ； Where, represents the observation vector, represents the measurement noise matrix; The state estimate and covariance estimate obtained by a single filter are as follows: ； ； Where, 、 Respectively Moment state estimation and covariance estimation of a motion model, represents the identity matrix, express Moment The state prediction value of the motion model, represents the updated covariance; in, ； Where, represents the Kalman gain, represents the covariance of the measurement noise.

5. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 3 is characterized in that: The maximum likelihood method is used to update the predicted probability of the motion model as follows: time, Motion Model and The maximum likelihood function that best matches the motion model is as follows: ； in, ； ； Where, Indicates the The maximum likelihood function of the motion model, 、 Respectively represent The measurement error matrix and measurement error covariance matrix of the motion model; Moment, The predicted probability of the motion model is updated as follows: ； in, ； ； Where, represents the normalization constant, express Moment The predicted probability of the motion model, express Moment The predicted probability of the motion model, Indicates that from motion model to The transition probability of a motion model, Represents the predicted probability after fusion.

6. The fusion positioning algorithm based on low-orbit satellite Doppler measurement, DME and VOR according to claim 3 is characterized in that: The overall status estimate is as follows: ； Where, represents the estimated value of the overall state, Indicates the type of motion model, express Moment The state estimation of the motion model, express Moment The predicted probability of each motion model; The covariance of the population is: ； Where, represents the covariance of the overall state, express Moment Covariance estimation of a motion model.

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