Signal prediction method under carrier spin state based on stochastic differential equations

Abstract

The present invention belongs to the field of signal processing technology, and specifically relates to a method for predicting signals under a carrier spinning state based on a stochastic differential equation, aiming to solve the problem that the existing technology cannot accurately measure the speed, attitude, and position of the carrier, and may even fail in positioning, speed determination, and attitude measurement, thereby causing related decision-making failure or unusability. The present invention includes: constructing an initial mathematical model of the signal in continuous time based on the real signal and observation noise; sampling the signal at equal time intervals to obtain N groups of observation vectors; calculating the signal parameters to be solved based on the stochastic differential equation of the signal, and obtaining a prediction mathematical model of the signal; and predicting, interpolating, smoothing, or filtering the signal at any time based on the prediction mathematical model. The present invention improves the measurement accuracy of the carrier's position, speed, attitude, etc., and improves the availability and reliability of the carrier's positioning, speed determination, and attitude measurement.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a signal prediction method under a carrier spin state based on a stochastic differential equation. Background Art

[0002] When using the Global Navigation Satellite System (GNSS) to locate and measure the speed of a moving vehicle in real time, the Doppler shift calculated by the signal tracking loop is a key factor in determining velocity accuracy. In certain scenarios, the vehicle undergoes acceleration and variable acceleration accompanied by high-speed spin. The Doppler shift is the superposition of the relative motion between the vehicle and the satellite and the periodic variable acceleration caused by the spin. Since the spin speed is often as high as 10-30 revolutions per second or more, the spin effect causes the relative velocity and acceleration between the vehicle and the satellite to be large and to change periodically over a short period of time. This effect prevents the receiver from accurately determining the speed in real time. Therefore, it is necessary to identify and eliminate the spin effect in the Doppler shift of the receiver's vehicle relative to each satellite to ensure the reliability and high accuracy of the velocity determination results.

[0003] The Doppler shift with a spin effect is the superposition of the carrier's own motion and the periodic acceleration caused by the spin. In extremely short time periods, such as 100-500 milliseconds, the former can be viewed as a deterministic trend, such as a first- or second-order polynomial, while the latter can be viewed as a sine wave with unknown parameters such as frequency. Therefore, this problem is actually an optimization problem aimed at parameter estimation. Because the frequency parameters are highly nonlinear with respect to the objective function, the key is to quickly and accurately determine the frequency parameters. Currently available frequency parameter estimation methods include the periodic method, phase change method, filtering method, maximum likelihood method, and Fourier interpolation method. Among them, the first three methods have low estimation accuracy and are only suitable for high signal-to-noise ratio environments. The latter two methods are suitable for various signal-to-noise ratio environments, but they still have some shortcomings, such as dependence on the selection of iterative initial values ​​or hyperparameters, limited calculation accuracy, and unsuitability for non-stationary signals. They cannot meet the requirements of real-time, fast, high-precision, and adaptive performance.

[0004] At present, the existing signal measurement methods have low calculation accuracy for frequency parameters, which leads to poor measurement accuracy of parameters such as amplitude and phase. Taking the Doppler frequency shift measurement when the carrier is in a spinning state as an example, the inability to accurately measure parameters such as frequency will lead to a large error between the Doppler frequency shift value of the carrier obtained by capture and tracking and its true value, which in turn leads to the inability to accurately measure the speed, attitude, and position of the carrier, and may even cause positioning, speed control, and attitude measurement to fail, which in turn leads to related decision-making failure or unusability.

[0005] Based on this, the present invention proposes a signal prediction method under the carrier spin state based on stochastic differential equations. Summary of the Invention

[0006] In order to solve the above-mentioned problems in the prior art, namely, the prior art relies on the selection of iterative initial values ​​or hyperparameters, has limited calculation accuracy, is not suitable for non-stationary signals, and cannot meet the requirements of real-time, fast, high-precision, and self-adaptation, thereby resulting in the inability to accurately measure the speed, attitude, and position of the carrier, and may even fail in positioning, speed control, and attitude measurement, thereby causing related decision-making failure or unusability. The present invention provides a signal prediction method under the carrier spinning state based on a stochastic differential equation, which comprises the following steps:

[0007] Step S1, constructing an initial mathematical model of the signal in continuous time based on the real signal and the observation noise, wherein the initial mathematical model includes a plurality of pre-constructed signal parameters to be solved;

[0008] Step S2, based on the initial mathematical model, sampling the signal at equal time intervals to obtain N groups of observation vectors;

[0009] Step S3, calculating the signal parameter to be solved based on the observation vector and the stochastic differential equation of the signal;

[0010] Step S4, combining the solved signal parameters and the initial mathematical model to obtain a signal prediction mathematical model;

[0011] Step S5, processing the signal at any time based on the prediction mathematical model to obtain the position, speed or posture of the carrier; the processing method includes prediction, interpolation, smoothing or filtering.

[0012] In some preferred embodiments, the initial mathematical model y(t) is constructed as follows:

[0013] y(t)=x(t)+ε(t), t∈R;

[0014] Where x(t) is the true signal and ε(t) is the observation noise.

[0015] In some preferred embodiments, the real signal x(t) and the observation noise ε(t) are calculated by:

[0016]

[0017] in, are the signal parameters to be solved, t is the time when the signal is observed; the non-periodic part of the signal is represented by a second-order polynomial in a short time, and its constant term, first-order and second-order coefficients are (b, c, d) respectively. The amplitude, frequency and phase parameters of the periodic part of the signal are

[0018] ε(t)~N(0,σ2 );

[0019] Among them, σ 2 is the variance of the signal noise. A larger value indicates a larger signal noise.

[0020] In some preferred embodiments, the observation vector (i, y i ), which is calculated as follows:

[0021] y i =y(iΔt)=x i +ε i ;

[0022] Where, i∈{1,2,Λ,N}, Δt is the equal time interval.

[0023] In some preferred embodiments, the signal parameter to be solved is calculated as follows:

[0024] Step S31: Calculate the matrix Z and the matrix H according to the stochastic differential equation of the signal:

[0025]

[0026]

[0027] Step S32: Calculate the signal parameter β based on the matrix Z and the matrix H, and iterate β to obtain according to Calculate the signal parameters to be solved

[0028] Z=Hβ+e,e~N(0,σ 2 Σ); where β represents the reparameterization of (f,b,c,d), The estimated value obtained by solving for β;

[0029] Step S33, based on the solved signal parameters Calculate the signal parameters to be solved

[0030] In some preferred embodiments, stochastic differential equations are used for modeling, and the signal parameters (f, b, c, d) to be solved are reparameterized and linearized before solving, wherein (f, b, c, d) are reparameterized and linearized as follows:

[0031]

[0032] Among them, β1, β2, β3, and β4 are the parameters corresponding to the weighted parameters of f, b, c, and d respectively and the parameters after linearization.

[0033] In some preferred embodiments, e~N(0,σ 2 Σ) where Σ is the exact covariance matrix of the noise e about Z = Hβ + e, Σ∈Σ ij ,Σ ij is the element corresponding to the i-th row and j-th column of the Σ matrix;

[0034]

[0035] In some preferred embodiments, the signal parameters to be solved are The calculation method is:

[0036] Step S321 , constructing a matrix Σ by using a priori values ​​or empirical values ​​as initial values, wherein the signal parameter f to be solved is initialized;

[0037] Step S322, calculate Then get

[0038] Step S323, the signal parameter f is based on the initialization signal parameter f to be solved or the signal parameter f in step S322. Update and loop step S321-step S322 until two consecutive The loop stops when the change is less than the preset threshold.

[0039] In some preferred embodiments, the signal parameters to be solved are The calculation method is:

[0040] Step S331, calculate

[0041] in, and Respectively represent the estimated values ​​of the signal amplitudes of the cosine function corresponding to the first column and the sine function corresponding to the second column in the matrix X, for and A 2D column vector composed of X is an N×2 dimensional matrix, Among them, X ij is the element corresponding to the i-th row and j-th column of matrix X;

[0042] Step S332, based on and Calculated

[0043]

[0044] Among them, ||·||2 is the L2 norm.

[0045] In some preferred embodiments, the prediction mathematical model of the signal is:

[0046]

[0047] is the predicted value of the future moment or the interpolated value of the past unobserved moment or the smoothed value or filtered value of the observed moment. When t is greater than NΔt, The value is the predicted value of the signal at time t in the future. When t is less than or equal to NΔt, The value is an interpolation of past unobserved moments or a smoothed or filtered value of observed moments.

[0048] Beneficial effects of the present invention:

[0049] (1) Linearizing the frequency parameters improves the calculation accuracy and solution speed. In the existing frequency estimation methods for periodic signals, the frequency parameters are nonlinear with respect to the objective function, resulting in slow solution and calculation convergence speed and low accuracy. The innovation of this method lies in that by introducing stochastic differential equations, the frequency parameters are linearized, thereby greatly reducing the computational complexity, achieving fast solution, and significantly improving the calculation accuracy. It is particularly suitable for application scenarios with high real-time and precision requirements.

[0050] (2) In the least squares solution, the iterative weighted estimation method is used to significantly improve the estimation accuracy of parameters such as frequency. This method accurately models the temporal correlation of the errors and calculates the corresponding covariance matrix, which greatly improves the accuracy of the estimated values ​​of the frequency parameters.

[0051] (3) It is suitable for a variety of application scenarios, not just the single scenario of the carrier spin state. Existing frequency and other parameter estimation methods for periodic signals often require signal stationarity and generally cannot be superimposed on other trend or non-trend functional signals. This method further expands the applicable scenarios and does not require the assumption of signal stationarity. It is applicable to any periodic signal superimposed with a constant mean or a known parameter-containing functional signal.

[0052] (4) This method can predict, interpolate, smooth, or filter signals at any time in the past or in the future. By modeling and estimating parameters of continuous time, this method can not only predict signals in the future, but also calculate interpolated values ​​of past unobserved moments or smoothed or filtered values ​​of observed moments, that is, the true signal obtained after removing noise.

[0053] (5) Compared with existing methods, more accurate frequency, amplitude, phase and other parameter estimation can be obtained for the carrier signal in the spinning state, and the real-time Doppler frequency shift of the carrier can be captured, tracked, measured and calculated with higher precision, thereby improving the measurement accuracy of the carrier's position, speed, attitude, etc., and improving the availability and reliability of the carrier's positioning, speed and attitude measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Other features, objects and advantages of the present application will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0055] Figure 1 It is a flow chart of a method for predicting signals under a carrier spin state based on a stochastic differential equation according to the present invention;

[0056] Figure 2 It is a structural diagram of a computer system of a server for implementing the method, system, and device embodiments of the present application. DETAILED DESCRIPTION

[0057] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are intended only to illustrate the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the relevant invention are shown in the accompanying drawings.

[0058] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0059] To address the above issues, this paper proposes a signal prediction method for the carrier spin state based on stochastic differential equations. First, the problem is transformed into a stochastic differential equation containing noise, and the frequency parameter is linearized and reparameterized, which greatly accelerates the solution speed and accuracy. Second, the covariance matrix of the noise vector after quadratic difference is calculated. By establishing an accurate model, the accuracy of frequency and other parameter estimation is further improved. Finally, fast parameter estimation is achieved through iterative weighted least squares, and the theoretical derivation of the error range of frequency and other parameter estimation is given. This method can be used to estimate frequency and other parameters in non-stationary signals containing regression terms such as trends, and can also be applied to estimate frequency and other parameters of stationary signals. It has broad application value in related fields such as aerospace electronics, unmanned system equipment, the Internet of Things, and high-end intelligent equipment.

[0060] The first embodiment of the present invention provides a method for predicting signals in a carrier spin state based on a stochastic differential equation, the method comprising the following steps:

[0061] Step S1, constructing an initial mathematical model of the signal in continuous time based on the real signal and the observation noise, wherein the initial mathematical model includes a plurality of pre-constructed signal parameters to be solved;

[0062] Step S2, based on the initial mathematical model, sampling the signal at equal time intervals to obtain N groups of observation vectors;

[0063] Step S3, calculating the signal parameter to be solved based on the observation vector and the stochastic differential equation of the signal;

[0064] Step S4, combining the solved signal parameters and the initial mathematical model to obtain a signal prediction mathematical model;

[0065] Step S5, processing the signal at any time based on the prediction mathematical model to obtain the position, speed or posture of the carrier after processing; the processing method includes prediction, interpolation, smoothing or filtering.

[0066] In order to more clearly illustrate the signal prediction method of the carrier spin state based on the stochastic differential equation of the present invention, the following is combined with Figure 1 Each step in the embodiment of the present invention is described in detail as follows:

[0067] Step S1, constructing an initial mathematical model of the signal in continuous time based on the real signal and the observation noise, wherein the initial mathematical model includes a plurality of pre-constructed signal parameters to be solved;

[0068] The initial mathematical model y(t) described in the present invention is constructed by:

[0069] y(t)=x(t)+ε(t), t∈R;

[0070] Where x(t) is the true signal and ε(t) is the observation noise.

[0071] The true signal x(t) and the observation noise ε(t) are calculated as follows:

[0072]

[0073] in, are the signal parameters to be solved, t is the time when the signal is observed; the non-periodic part of the signal is represented by a second-order polynomial in a short time, and its constant term, first-order and second-order coefficients are (b, c, d) respectively. The amplitude, frequency and phase parameters of the periodic part of the signal are

[0074] ε(t)~N(0,σ 2 );

[0075] Among them, σ2 is the variance of the signal noise. A larger value indicates a larger signal noise.

[0076] In this embodiment, Gaussian white noise is used as an assumption, which can meet the needs of most scenarios. For special cases, such as random processes in which the noise changes over time and is non-white noise, such as Brownian motion or ARIMA process, corresponding mathematical models can be used for parameterization, and steps S2-S5 can still be used with slight modifications.

[0077] In step S1, the actual signal is assumed to be a linear trend plus a periodic signal over a period of time. This is because the receiver samples the signal at a high frequency, thus obtaining a large number of observations in a very short period of time. This allows the linear trend to approximate the slowly varying signal in a very short period of time. In practical applications, this can be replaced with a polynomial or other functional form. After linearizing the parameters, steps S2-S6 can be used to estimate and solve the parameters.

[0078] Based on the initial mathematical model, the signal is sampled at equal time intervals to obtain N groups of observation vectors;

[0079] Step S2, the observation vector (i, y i ), which is calculated as follows:

[0080] y i =y(iΔt)=x i +ε i ;

[0081] Where, i∈{1,2,Λ,N}, Δt is the equal time interval.

[0082] Step S3, calculating the signal parameter to be solved based on the observation vector and the stochastic differential equation of the signal;

[0083] In this embodiment, the signal parameter to be solved is calculated as follows:

[0084] Step S31: Calculate the matrix Z and the matrix H according to the stochastic differential equation of the signal:

[0085] from We can get (y n+1 -ε n+1 +y n-1 -ε n-1 -2y n +2ε n )=-f 2 (2πΔt) 2 (y n -ε n -b-cn-dn 2 ), and then there is So the parameters to be solved is reparameterized and linearized to have

[0086]

[0087]

[0088] Among them, β1, β2, β3, and β4 are the parameters corresponding to the weighted parameters of f, b, c, and d respectively and the parameters after linearization.

[0089] Step S32: Calculate the signal parameter β based on the matrix Z and the matrix H, and iterate β to obtain according to Calculate the signal parameters to be solved

[0090] Z=Hβ+e,e~N(0,σ 2 Σ); where β represents the reparameterization of (f,b,c,d), The estimated value obtained by solving for β;

[0091] e~N(0,σ 2 Σ) where Σ is the exact covariance matrix of the noise e about Z = Hβ + e, Σ∈Σ ij ,Σ ij is the element corresponding to the i-th row and j-th column of the Σ matrix;

[0092]

[0093] Step S33, based on the solved signal parameters Calculate the signal parameters to be solved

[0094] In this embodiment, the signal parameters to be solved are The calculation method is:

[0095] Step S321 , constructing a matrix Σ by using a priori values ​​or empirical values ​​as initial values, wherein the signal parameter f to be solved is initialized;

[0096] Step S322, calculate Then get

[0097] Step S323, the signal parameter f is based on the initialization signal parameter f to be solved or the signal parameter f in step S322. Update and loop step S321-step S322 until two consecutive The cycle stops when the change is less than the preset threshold. The given threshold can be used according to The allowable error range is determined, such as 0.001.

[0098] The present invention provides a given frequency initial value, and iteratively updates the covariance matrix related to the frequency. In actual calculations, for most cases, it can converge after 2-3 iterations. The innovation of the present invention is that, in the discrete model of the stochastic differential equation, the temporal correlation of the noise is taken into account, and the covariance matrix of the noise is used to perform weighted least squares iterative estimation. By accurately calculating the covariance matrix, the accuracy of the estimated value of the frequency parameter is greatly improved. In scenarios such as high-speed spinning of the carrier, the frequency value is large, and its small error will cause signal smoothing or a large offset in the predicted value. Therefore, improving the accuracy of frequency parameter estimation is of great significance in practical applications.

[0099] Signal parameters to be solved The calculation method is:

[0100] Step S331, calculate

[0101] in, and Respectively represent the estimated values ​​of the signal amplitudes of the cosine function corresponding to the first column and the sine function corresponding to the second column in the matrix X, for and A 2D column vector composed of , X is an N×2 dimensional matrix, Among them, X ij is the element corresponding to the i-th row and j-th column of matrix X;

[0102] Step S332, based on and Calculated

[0103]

[0104] Among them, ||·||2 is the L2 norm.

[0105] Linearizing the amplitude, phase and other parameters of the periodic signal improves the calculation speed of parameter estimation, which is particularly suitable for scenarios with high real-time requirements.

[0106] Existing frequency estimation methods for periodic signals use frequency parameters that are nonlinear with respect to the objective function, resulting in slow solution and computational convergence and low accuracy. The innovation of this method lies in the introduction of stochastic differential equations, which reparameterize and linearize originally nonlinear parameters such as frequency. This significantly reduces computational complexity, enables rapid solution, and significantly improves computational accuracy, making it particularly suitable for applications requiring high real-time performance and precision.

[0107] Step S4, combining the solved signal parameters and the initial mathematical model to obtain a signal prediction mathematical model;

[0108] In the present invention, the signal prediction mathematical model is:

[0109]

[0110] is the predicted value of the future moment or the interpolated value of the past unobserved moment or the smoothed value or filtered value of the observed moment. When t is greater than NΔt, The value is the predicted value of the signal at time t in the future. When t is less than or equal to NΔt, The value is the interpolated value of the past unobserved time or the smoothed value or filtered value of the observed time, that is, the real signal obtained after removing the noise.

[0111] This method differs from other positioning methods in that it linearizes the frequency parameters, thereby improving the solution speed and parameter estimation accuracy. Furthermore, it further expands its applicable scenarios, eliminating the need for signal stationarity assumptions. When the signal contains long-term trends over a period of time, such as linear or other functional forms, this method can simultaneously estimate the parameters of the long-term trend and the periodic signal quickly and accurately.

[0112] Based on existing theories, the present invention demonstrates through experiments that a signal parameter estimation method based on stochastic differential equations under the carrier spin state can quickly and accurately solve parameters such as the signal frequency and long-term trend, thereby obtaining highly reliable predictions or smoothed values. This method can also be widely used in various scenarios.

[0113] Although the various steps in the above embodiment are described in the above-mentioned order, those skilled in the art will understand that in order to achieve the effect of this embodiment, different steps do not have to be executed in such an order. They can be executed simultaneously (in parallel) or in a reverse order. These simple changes are within the scope of protection of the present invention.

[0114] A second embodiment of the present invention provides a signal prediction system for a carrier spin state based on a stochastic differential equation, based on a signal prediction method for a carrier spin state based on a stochastic differential equation of the first embodiment, comprising:

[0115] A model building module is configured to build an initial mathematical model of the signal in continuous time based on the real signal and the observation noise, wherein the initial mathematical model includes a plurality of pre-built signal parameters to be solved;

[0116] an observation vector calculation module configured to sample the signal at equal time intervals based on the initial mathematical model to obtain N groups of observation vectors;

[0117] a parameter solving module configured to calculate the signal parameter to be solved based on the observation vector and the stochastic differential equation of the signal;

[0118] A prediction model building module configured to combine the solved signal parameters and the initial mathematical model to obtain a prediction mathematical model of the signal;

[0119] A signal processing module is configured to predict, interpolate, smooth or filter the signal at any time based on the prediction mathematical model.

[0120] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working process and related instructions of the system described above can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here.

[0121] It should be noted that the above embodiment provides a signal prediction system for a carrier spin state based on a stochastic differential equation, and only illustrates the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the modules or steps in the embodiments of the present invention can be further decomposed or combined. For example, the modules in the above embodiment can be combined into one module, or further divided into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are merely for the purpose of distinguishing the modules or steps and are not to be considered as improper limitations of the present invention.

[0122] An electronic device according to a third embodiment of the present invention includes:

[0123] at least one processor; and

[0124] a memory communicatively connected to at least one of the processors; wherein,

[0125] The memory stores instructions that can be executed by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned signal prediction method under the carrier spin state based on stochastic differential equations.

[0126] A fourth embodiment of the present invention provides a computer-readable storage medium storing computer instructions, wherein the computer instructions are configured to be executed by the computer to implement the above-mentioned method for predicting signals under a carrier spin state based on stochastic differential equations.

[0127] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes and related instructions of the storage device and processing device described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0128] Those skilled in the art should be able to appreciate that, in conjunction with the modules and method steps of each example described in the embodiments disclosed herein, it is possible to implement them with electronic hardware, computer software, or a combination of the two, and the programs corresponding to the software modules and method steps can be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disks, removable disks, CD-ROMs, or any other form of storage medium known in the art. In order to clearly illustrate the interchangeability of electronic hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in electronic hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0129] Reference below Figure 2 , which shows a structural diagram of a computer system of a server for implementing the method, system, and device embodiments of the present application. Figure 2 The server shown is merely an example and should not limit the functions and scope of use of the embodiments of the present application.

[0130] like Figure 2 As shown, the computer system includes a central processing unit (CPU) 201, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 202 or the program loaded from the storage part 208 to the random access memory (RAM) 203. Various programs and data required for system operation are also stored in the RAM 203. The CPU 201, ROM 202, and RAM 203 are connected to each other via a bus 204. An input / output (I / O) interface 205 is also connected to the bus 204.

[0131] The following components are connected to the I / O interface 205: an input section 206 including a keyboard, a mouse, and the like; an output section 207 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and a speaker; a storage section 208 including a hard disk and the like; and a communication section 209 including a network interface card such as a LAN (Local Area Network) card or a modem. The communication section 209 performs communication processing via a network such as the Internet. A drive 210 is also connected to the I / O interface 205 as needed. A removable medium 211, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 210 as needed, so that a computer program read therefrom can be installed into the storage section 208 as needed.

[0132] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 209, and / or installed from the removable medium 211. When the computer program is executed by the central processing unit (CPU) 201, the above-mentioned functions defined in the method of the present application are executed. It should be noted that the computer-readable medium mentioned above in the present application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take a variety of forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code embodied on a computer-readable medium may be transmitted using any suitable medium, including, but not limited to, wireless, wire, optical cable, RF, etc., or any suitable combination thereof.

[0133] Computer program code for performing the operations of the present application may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0134] The flow charts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present application. In this regard, each box in the flow chart or block diagram can represent a module, program segment or a part of code, and the module, program segment or a part of code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order than that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the specified function or operation, or can be implemented by a combination of dedicated hardware and computer instructions.

[0135] The terms "first", "second", etc. are used to distinguish similar objects, rather than to describe or indicate a particular order or sequence.

[0136] The term "comprise" or any other similar term is intended to cover non-exclusive inclusion such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0137] Thus far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art may make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will fall within the scope of protection of the present invention.

Claims

1. A method for predicting signals in a carrier spin state based on stochastic differential equations, characterized in that: The method comprises the following steps: Step S1, constructing an initial mathematical model of the signal in continuous time based on the real signal and the observation noise, wherein the initial mathematical model includes a plurality of pre-constructed signal parameters to be solved; Step S2, based on the initial mathematical model, sampling the signal at equal time intervals to obtain N groups of observation vectors; Step S3, calculating the signal parameter to be solved based on the observation vector and the stochastic differential equation of the signal; Step S4, combining the solved signal parameters and the initial mathematical model to obtain a signal prediction mathematical model; Step S5, processing the signal at any time based on the prediction mathematical model to obtain the position, speed or posture of the carrier; the processing method includes prediction, interpolation, smoothing or filtering.

2. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 1, characterized in that: The initial mathematical model y(t) is constructed as follows: y(t)=x(t)+ε(t), t∈R; Where x(t) is the true signal and ε(t) is the observation noise.

3. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 2, characterized in that: The true signal x(t) and the observation noise ε(t) are calculated as follows: Among them, (a,f, b, c, d) are the signal parameters to be solved, t is the time when the signal is observed; the non-periodic part of the signal is represented by a second-order polynomial in a short time, and its constant term, first-order and second-order coefficients are (b, c, d) respectively, and the amplitude, frequency and phase parameters of the periodic part of the signal are (a, f, ); ε(t)~N(0,σ 2 ); Among them, σ 2 is the variance of the signal noise. A larger value indicates a larger signal noise.

4. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 3, characterized in that: The observation vector (i,y i ), which is calculated as follows: and i =y(i△t)=x i +ε i ; Where i∈{1,2,…,N}, △t is the equal time interval.

5. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 4, characterized in that: The signal parameter to be solved is calculated as follows: Step S31: Calculate the matrix Z and the matrix H according to the stochastic differential equation of the signal: Step S32: Calculate the signal parameter β based on the matrix Z and the matrix H, and iterate β to obtain according to Calculate the signal parameters to be solved Z=Hβ+e,e~N(0,σ 2 Σ); Where β represents the reparameterization of (f,b,c,d), To solve for the estimated value of β, Σ is the exact covariance matrix of the noise e with respect to Z = Hβ + e; Step S33, based on the solved signal parameters Calculate the signal parameters to be solved 6. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 5, characterized in that: Use stochastic differential equations to model the signal parameters (f, b, c, d) to be solved, reparameterize and linearize them before solving. (f, b, c, d) is reparameterized and linearized as follows: Among them, β1, β2, β3, and β4 are the parameters corresponding to the weighted parameters of f, b, c, and d respectively and the parameters after linearization.

7. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 6, characterized in that: e~N(0,σ 2 Σ∈Σ in Σ) ij ,Σ ij is the element corresponding to the i-th row and j-th column of the Σ matrix; 8. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 7, characterized in that: Signal parameters to be solved The calculation method is: Step S321 , constructing a matrix Σ by using a priori values ​​or empirical values ​​as initial values, wherein the signal parameter f to be solved is initialized; Step S322, calculate Then get Step S323, the signal parameter f is based on the initialization signal parameter f to be solved or the signal parameter f in step S322. Update and loop step S321-step S322 until two consecutive The loop stops when the change is less than the preset threshold.

9. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 8, characterized in that: Signal parameters to be solved The calculation method is: Step S331, calculate in, and Respectively represent the estimated values ​​of the signal amplitudes of the cosine function corresponding to the first column and the sine function corresponding to the second column in the matrix X, for and A 2D column vector composed of X is an N×2 dimensional matrix, Among them, X ij is the element corresponding to the i-th row and j-th column of matrix X; Step S332, based on and Calculated Among them, ||·||2 is the L2 norm.

10. The method for predicting signals under carrier spin states based on stochastic differential equations according to claim 9, characterized in that: The signal prediction mathematical model is: is the predicted value of the future moment or the interpolated value of the past unobserved moment or the smoothed value or filtered value of the observed moment. When t is greater than N△t, The value is the predicted value of the signal at time t in the future. When t is less than or equal to N△t, The value is an interpolation of past unobserved moments or a smoothed or filtered value of observed moments.

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