A simulation method for medium-wave navigation based on Hilbert-variable analog signals

Abstract

This invention discloses a mid-wave navigation simulation method based on Hilbert-variant analog signals, relating to the field of radio navigation. The method includes the following steps: S1, setting working signal parameters and initializing the radio compass azimuth; S2, calculating the signal amplitude and phase information received by the omnidirectional antenna and the loop antenna under the current aircraft attitude using an electromagnetic propagation model; S3, carrier reconstruction to generate a loop modulation signal; S4, signal superposition; S5, calculating the envelope modulation depth, and determining whether the current loop antenna pointing is the true azimuth angle of the navigation station based on whether the modulation depth approaches zero; S6, if satisfied, outputting the azimuth angle; if not satisfied, adjusting the loop antenna pointing angle and repeating steps S2 to S5. This invention reconstructs the fundamental process of direction finding logic at the phase level, thereby enabling the simulation system to maintain stable direction finding performance in complex multipath environments, enhancing the method's engineering practicality and environmental adaptability.

Description

Technical Field

[0001] This invention relates to the field of radio navigation technology, and in particular to a medium-wave navigation simulation method based on Hilbert variation analog signals. Background Technology

[0002] Medium-wave navigation systems, as a key component of traditional aviation radio navigation systems, have long played an irreplaceable role in scenarios such as airport approach, en-route guidance, and low-visibility flight support. This system consists of a ground-based omnidirectional beacon and an airborne radio compass. Its basic operating principle relies on the ground station transmitting continuous intermediate-frequency, non-amplified carrier signals, while the airborne equipment uses a combination of loop and omnidirectional antennas to receive the signals and utilizes the amplitude modulation characteristics of the two signals to determine the beacon's azimuth. Given its simple structure, wide coverage, and low dependence on infrastructure, medium-wave navigation systems are still widely used in some areas and specific flight missions. However, as modern aviation operations place higher demands on navigation accuracy, calibration efficiency, and environmental adaptability, the traditional operation and maintenance model relying on actual flight calibration has shown many bottlenecks, necessitating the introduction of high-fidelity virtual simulation methods to support navigation beacon performance evaluation and parameter optimization.

[0003] In existing technologies, some studies have attempted to conduct simulation verification of medium-wave navigation stations by combining electromagnetic wave propagation modeling with signal strength compensation. Chinese invention patent CN117629253A discloses a verification method for a moving platform medium-wave navigation station. This method constructs a three-dimensional propagation environment including terrain, obstacles, and flight trajectory, calculates the received signal strength based on models such as ray tracing, and then corrects the simulation results using empirical compensation coefficients to approximate measured data. This method reduces reliance on actual flight to some extent, providing an auxiliary tool for navigation station layout planning and preliminary parameter verification. Its technical logic is based on macroscopic fitting of signal attenuation characteristics, focusing on energy-level matching rather than precise reproduction of the internal physical processes of airborne direction-finding mechanisms. In a specific historical period, such methods were practically valuable due to their high computational efficiency and relatively simple engineering implementation, especially suitable for large-scale coverage assessment or coarse performance screening.

[0004] However, with increasingly stringent navigation verification standards and rising demands for adaptability analysis in complex electromagnetic environments, the aforementioned simulation paradigm based on signal strength compensation reveals deep-seated, fundamental limitations. The direction-finding function of a radio compass does not simply rely on the absolute amplitude of the received signal. Instead, it determines the azimuth angle based on the phase and amplitude coupling relationship between the loop antenna's induced signal and the omnidirectional antenna's reference signal. This is achieved through simulation processes such as balanced modulation, signal superposition, and envelope detection, ultimately based on the criterion of zero modulation depth. This process is essentially a highly nonlinear dynamic signal processing chain, and its output is extremely sensitive to signal phase continuity, modulation waveform integrity, and antenna pattern phase reversal characteristics. If only the average signal strength is used as the simulation target, it cannot accurately reflect the signal polarity reversal caused by a phase abrupt change near a specific azimuth of the loop antenna, nor can it capture the subtle changes in the modulation envelope at different azimuth angles. Furthermore, in complex propagation scenarios involving multipath, diffraction, or terrain occlusion, the signal not only experiences amplitude attenuation but also suffers from non-negligible phase distortion and time delay spread. This factor directly interferes with the logic for determining modulation depth, and existing intensity compensation models completely lack the ability to model such phase-related effects.

[0005] Therefore, although it has some reference value in macro coverage prediction, when it comes to key verification tasks such as direction finding accuracy verification, antenna pointing calibration, or robustness analysis of edge conditions, there is a significant systematic deviation between its simulation results and the actual airborne equipment response. Summary of the Invention

[0006] This invention overcomes the shortcomings of the prior art and provides a mid-wave navigation simulation method based on Hilbert variation analog signals.

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: This invention provides a medium-wave navigation simulation method based on Hilbert-varying analog signals, comprising the following steps:

[0008] S1. Set the operating signal parameters of the medium-wave navigation station and initialize the initial position and orientation of the radio compass;

[0009] S2. Using an electromagnetic propagation model, calculate the signal amplitude and phase information received by the omnidirectional antenna and the loop antenna under the current aircraft attitude; wherein, the signal received by the loop antenna carries a phase symbol determined by its directivity function;

[0010] S3. Perform carrier reconstruction on the omnidirectional antenna received signal to obtain an omnidirectional reference signal; perform carrier reconstruction on the loop antenna received signal and apply balanced modulation at a preset frequency to generate a loop modulation signal;

[0011] S4. Perform Hilbert transform on the omnidirectional reference signal and the ring modulation signal respectively to generate the corresponding analytic signals; superimpose the two analytic signals in the complex domain to obtain the composite complex signal;

[0012] S5. Extract the envelope of the synthesized complex signal, calculate the modulation depth of the envelope, and determine whether the current ring antenna pointing is the true azimuth of the navigation station based on whether the modulation depth approaches zero.

[0013] S6. If the modulation depth meets the direction finding conditions, output the current ring antenna pointing angle as the azimuth angle of the navigation station relative to the aircraft; if not, adjust the pointing angle of the ring antenna with a preset step size, and repeat steps S2 to S5 until the azimuth angle that meets the conditions is obtained.

[0014] In a preferred embodiment of the present invention, in step S1, the working signal parameters include a carrier frequency range of 0.15-1.7 MHz, a modulation frequency of 135 Hz, and the initial azimuth angle of the radio compass is consistent with the heading of the aircraft.

[0015] In a preferred embodiment of the present invention, in step S2, the electromagnetic propagation model is a simulation calculation model for radio wave propagation channels, which comprehensively considers the vector superposition of direct waves, ground reflected waves, diffracted waves and obstacle shielding effects.

[0016] In a preferred embodiment of the present invention, in step S2, the phase sign of the signal received by the loop antenna is determined by the quadrant in which the azimuth angle lies: if the azimuth angle The amplitude sequence of the signal received by the loop antenna is negative; otherwise, it is non-negative.

[0017] In a preferred embodiment of the present invention, in step S3, the signal expression for carrier reconstruction is:

[0018] ;in, f c This refers to the actual operating frequency of the navigation station; A r ( t The received amplitude is the time-varying amplitude calculated using the propagation model.

[0019] The expression for the ring modulation signal is:

[0020] ;in, f m =135 Hz; A l ( t ) represents the amplitude sequence of the signal received by the loop antenna.

[0021] In a preferred embodiment of the present invention, in step S4, the Hilbert transform is implemented using a fast Fourier transform: the real signal is subjected to... N Point FFT sets the negative frequency components to zero and multiplies the positive frequency components by 2, while keeping the DC component unchanged. Then, inverse FFT is performed to obtain the imaginary part of the analytic signal.

[0022] In a preferred embodiment of the present invention, in step S4, the two analytical signals are superimposed in the complex domain by adding the analytical signal of the omnidirectional reference signal and the analytical signal of the ring modulation signal point by point, according to the real part and the imaginary part.

[0023] In a preferred embodiment of the present invention, in step S5, the modulation depth D The formula for calculation is:

[0024] ;in, A max This represents the maximum value of the envelope; A min This is the minimum value of the envelope;

[0025] Direction finding condition is modulation depth D The absolute value is less than the preset threshold and the envelope waveform exhibits stable plateau characteristics.

[0026] In a preferred embodiment of the present invention, in step S6, the step size of adjusting the pointing angle of the loop antenna is 5°, or a binary search strategy is used to reduce the search interval by half until the step size is less than 1°.

[0027] In a preferred embodiment of the present invention, in step S6, the first-order difference at the envelope initiation time is calculated. The symbol eliminates the ambiguity between 0° and 180° in direction finding: if The true location is in the first semicircle; if Then it is located in the second half of the circle.

[0028] This invention addresses the shortcomings of the prior art and has the following beneficial effects:

[0029] (1) This invention provides a mid-wave navigation simulation method based on Hilbert transform analog signals. By introducing Hilbert transform and complex signal processing mechanism, it can accurately model the phase jump characteristics caused by the radiation pattern of the loop antenna, so that the simulation system can accurately capture the phase reversal phenomenon of the signal in a specific azimuth interval, and thus truly reflect the nonlinear change of modulation depth in the signal superposition stage. It can effectively eliminate the direction finding error caused by phase ambiguity near 90° and 270° in the traditional method, and improve the accuracy of azimuth determination. Compared with the simulation method in the prior art that only relies on signal strength compensation, this invention reconstructs the fundamental process of direction finding logic from the phase level, so that it can overcome its inherent defect of not being able to handle signal polarity changes, so that the simulation system can still maintain stable direction finding performance in complex multipath environments, and enhance the engineering practicality and environmental adaptability of the method.

[0030] (2) In this invention, the analytical signals of the omnidirectional antenna and the loop antenna are superimposed point by point according to the real part and the imaginary part. The modulation depth is calculated by envelope detection and used as the basis for azimuth angle determination. The superposition of complex signals can completely preserve the phase amplitude coupling relationship of the two signals. The criterion of zero modulation depth conforms to the real direction finding logic of the airborne radio compass. This enables the simulation process to accurately reproduce the internal process of the nonlinear dynamic signal processing chain and accurately determine the azimuth angle of the navigation station relative to the aircraft. Compared with the existing methods that lack phase distortion and time delay extension modeling capabilities, this invention can still achieve high confidence direction finding simulation in complex propagation environments such as multipath diffraction, thereby meeting the accuracy requirements of key verification tasks such as direction finding accuracy verification and antenna pointing calibration.

[0031] (3) In this invention, the determination criterion based on the modulation depth approaching zero is adopted, and the azimuth ambiguity is eliminated by combining the envelope initial phase information. The antenna pointing is determined by analyzing the dynamic characteristics of the synthesized signal envelope, and the 0° and 180° azimuths are distinguished by the initial change direction of the envelope. This can improve the uniqueness and reliability of the direction finding results and avoid misjudgment of the reverse azimuth. Compared with the lack of an effective ambiguity resolution mechanism in the prior art, this invention completely reproduces the demodulation and judgment logic in the actual equipment at the simulation level, effectively solving the technical deficiency of the device that is prone to incorrect pointing in the back area, thereby enhancing the simulation robustness under various flight attitudes and terrain conditions and reducing the risk of false alarms and false alarms. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram illustrating the working mode of a medium-wave navigation station;

[0034] Figure 2 This is a schematic diagram of an antenna;

[0035] Figure 3 This is a schematic diagram of the working principle of a medium-wave navigation station;

[0036] Figure 4 This is a flowchart of the medium-wave navigation simulation method based on Hilbert variation analog signals of the present invention;

[0037] Figure 5 This is a flowchart of the simulation data of the medium-wave navigation station in this invention;

[0038] Figure 6 This is a schematic diagram of the oscillating loop antenna signal (a), omnidirectional antenna signal (b), and superimposed signal (c) of the present invention;

[0039] Figure 7 This is an example diagram of the virtual verification result data of the wave navigation station in this invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein. Therefore, the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0042] It should be noted that the relevant terms and technical background mentioned in the embodiments of the present invention are explained as follows:

[0043] Radio wave propagation simulation: The performance of wireless communication systems is primarily constrained by mobile wireless channels. The propagation path between the transmitter and receiver is highly complex, ranging from simple line-of-sight propagation to encountering various complex terrain features such as buildings, mountains, and foliage. Unlike wired channels, which are fixed and predictable, wireless channels exhibit extreme randomness, making them particularly difficult to analyze. Even the speed of the mobile station can affect signal fading.

[0044] Wireless channel modeling has always been a challenging aspect of mobile wireless system design and a crucial foundation of modern radio engineering, proving invaluable for mission planning and network design. Wireless channel modeling primarily involves studying the various propagation effects of wireless signals. Radio wave propagation simulation, based on transmitter and receiver parameter modeling, simulates the radio wave propagation channel, taking into account the influence of geographical environment, buildings, and atmospheric factors, and using simulation methods to analyze the communication system.

[0045] Hilbert Transform for Signals: In mathematics and signal processing, the Hilbert transform is a transform of a function... u ( t Generate functions with the same domain. H ( u ()( t The Hilbert transform is a linear operator. It is important in signal processing as it derives the linear operators of a signal. u ( t The analytical representation of ) means that the real signal u ( t Extending this to the complex plane, it satisfies the Cauchy-Riemann equations.

[0046] Amplitude Detection Simulation: The basic principle of an amplitude detection circuit is to use the characteristics of nonlinear components to convert a modulated signal into a DC signal with varying amplitude. Simulated amplitude detection involves calculating the envelope of the signal amplitude to obtain the changes in the signal amplitude.

[0047] Understandably, a medium-wave navigation system consists of two main parts: ground equipment and airborne equipment, such as... Figure 1 As shown; the ground equipment is a medium-wave navigation unit, also commonly called a non-directional radio beacon (NDB). The medium-wave navigation unit and its auxiliary facilities constitute a medium-wave navigation station. The airborne equipment is a radio compass (a device that indicates a fixed direction), which is essentially a receiver that measures the direction of incoming radio waves. The medium-wave navigation unit provides direction-finding radio signals for the radio compass by transmitting non-directional intermediate frequency signals.

[0048] Medium-wave navigation systems obtain the relative azimuth information of ground navigation stations by measuring the direction of arrival of radio waves using an airborne radio compass. This type of system belongs to amplitude-based angle measurement navigation systems. The mathematical model of the amplitude-based M-mode angle measurement method is as follows:

[0049] ;

[0050] An electrical signal expression represents an amplitude-modulated wave signal, where, E m It is the signal amplitude;m It is the modulation depth; sin(Ω) t ) is a low-frequency modulated signal; sin( ωt () is a high-frequency carrier signal; m ( θ The modulation depth is a function of the measured angle, and the angle is established accordingly. θ With electrical parameters m The relationship.

[0051] like Figure 2 As shown, due to the figure-eight antenna pattern of the transmitting antenna, the periodic rotation of the transmitting antenna (135Hz) causes the signal received in a fixed receiving direction to present a figure-eight signal with a modulation depth in the low-frequency envelope. The frequency of the change is the antenna pattern rotation frequency (135Hz). After processing to obtain the changes of a complete cycle, the zero-crossing point within this cycle is found. The angle of the receiving position relative to the medium-wave navigation station can be calculated from the phase of the zero-crossing point.

[0052] The working principle block diagram of a radio compass is as follows: Figure 3 As shown; according to the antenna pattern of the loop antenna, when the antenna is directly facing the medium-wave navigation station, the received signal is minimal, resulting in a modulation depth of 0 for the superimposed signal. Similarly, when the antenna is facing away from the medium-wave navigation station, the received signal also reaches its minimum. However, since a stable modulation signal cannot be formed at this position, the received composite signal can be demodulated. When a stable signal with a modulation depth of 0 is obtained, the angle through which the servo rotates is the relative azimuth angle of the navigation station.

[0053] Medium-wave navigation systems possess advantages such as simple structure, convenient use and maintenance, and low cost. Their onboard radio compass operates within the 100-1800 kHz frequency band, utilizing numerous civilian radio stations and dedicated ground navigation stations (NDBs) for aircraft orientation and positioning. They can also be integrated with radio altimeters, pointing beacons, and other equipment to guide aircraft approach and landing. Therefore, although the medium-wave navigation system was first used on aircraft in 1937, its unique advantages have made it popular among pilots, resulting in its enduring application. The main performance characteristics of a medium-wave navigation system are as follows: 1. Operating frequency: 150-1700 kHz band, channel spacing 1 kHz. 2. Effective range: Not less than 100 km. 3. System capacity: Unlimited. 4. Absolute accuracy: 5°~10°.

[0054] Based on the working principle of medium-wave navigation stations, this invention provides a medium-wave navigation simulation method based on Hilbert-varying analog signals for the virtual verification process of airport medium-wave navigation systems. By virtually simulating airport medium-wave navigation equipment, the simulation results of medium-wave navigation along flight paths are analyzed, thus providing a reference for parameter settings and actual flight verification of medium-wave navigation stations and airborne navigation equipment. Figure 4 The simulation method flow, and Figure 5 As shown in the data flow diagram of the simulation method, the medium-wave navigation simulation method includes the following steps:

[0055] S1. Set the operating signal parameters of the medium-wave navigation station and initialize the initial position and orientation of the radio compass;

[0056] S2. Using an electromagnetic propagation model, calculate the signal amplitude and phase information received by the omnidirectional antenna and the loop antenna under the current aircraft attitude; wherein, the signal received by the loop antenna carries a phase symbol determined by its directivity function;

[0057] S3. Perform carrier reconstruction on the omnidirectional antenna received signal to obtain an omnidirectional reference signal; perform carrier reconstruction on the loop antenna received signal and apply balanced modulation at a preset frequency to generate a loop modulation signal;

[0058] S4. Perform Hilbert transform on the omnidirectional reference signal and the ring modulation signal respectively to generate the corresponding analytic signals; superimpose the two analytic signals in the complex domain to obtain the composite complex signal;

[0059] S5. Extract the envelope of the synthesized complex signal, calculate the modulation depth of the envelope, and determine whether the current ring antenna pointing is the true azimuth of the navigation station based on whether the modulation depth approaches zero.

[0060] S6. If the modulation depth meets the direction finding conditions, output the current ring antenna pointing angle as the azimuth angle of the navigation station relative to the aircraft; if not, adjust the pointing angle of the ring antenna with a preset step size, and repeat steps S2 to S5 until the azimuth angle that meets the conditions is obtained.

[0061] In this embodiment, in step S1, the operating signal parameters of the medium-wave navigation station are first set; the navigation station operates in the medium-wave band, with a carrier frequency range of 0.15-1.7 MHz, and a typical operating frequency of 150 kHz; the modulation frequency is fixed at 135 Hz, and the signal is transmitted externally in the form of an unmodulated continuous wave.

[0062] Furthermore, the initial position and orientation of the airborne radio compass are initialized so that its initial azimuth angle is consistent with the aircraft's heading, i.e., the zero-degree pointing of the loop antenna is aligned with the aircraft's longitudinal axis. The aircraft's three-dimensional trajectory data is provided by an external flight mission planning module, including timestamps, latitude and longitude coordinates, and altitude information. Simultaneously, the system loads a Digital Elevation Model (DEM) containing elements such as geographic elevation, topography, building distribution, and vegetation cover for subsequent accurate modeling of the electromagnetic propagation path.

[0063] In this embodiment, during step S2, in the electromagnetic propagation modeling stage, the electromagnetic wave propagation model is used to calculate the signal amplitude and phase information received by the omnidirectional antenna and the loop antenna respectively under the current flight attitude. Based on the principles of geometric optics, the electromagnetic wave engine comprehensively considers direct waves, ground-reflected waves, diffracted waves, and obstacle shielding effects, performing vector superposition on each effective propagation path to output the received signal in complex baseband form. The sampling interval strictly satisfies the Nyquist sampling theorem requirement.

[0064] For example, if the carrier frequency is 1 MHz, a sampling rate of 2.5 MHz can be used, and the sampling time... t The range is 0 to (1 / 135*3) s, and the sampling interval is... s, resulting in approximately 556 sampling points. Based on the amplitude sampling calculation, the function is obtained. ,in, The amplitude of the balanced modulated signal can be specifically represented as: ,in, This represents the maximum amplitude of the signal. Therefore, the balanced modulation signal expression can be expressed as:

[0065] ;

[0066] in, rand This represents random amplitude fluctuations caused by noise. The signal that produces balanced modulation is as follows: Figure 6 (a) provides an example.

[0067] For a typical scenario with a carrier frequency of 150 kHz, the sampling rate is set to 500 kHz to generate a cosine signal within the sampling time. This signal is then multiplied by the received amplitude data to obtain the generated signal data. Figure 6 (b) provides an example.

[0068] Furthermore, the omnidirectional antenna receiving module is modeled based on the characteristics of the omnidirectional radiation pattern; the antenna gain is defined as a fixed positive value, and the radiation pattern function is always equal to 1, meaning that regardless of the receiving azimuth, its output amplitude is only affected by path loss, multipath fading, and terrain obstruction. Specifically, the amplitude sequence of the signal received by the omnidirectional antenna...A o ( t Output by the TacanPropModelManager module, this sequence directly reflects the signal strength after propagation channel correction, without containing any directional modulation or phase reversal.

[0069] The loop antenna receiving module is modeled based on its figure-eight directivity function. This directivity function is defined as:

[0070] ;

[0071] in, λ For the operating wavelength, θ This is the azimuth angle of the aircraft relative to the navigation station (0° is due north, increasing clockwise). When θ When the angle is between 90° and 270°, the directivity function is negative, corresponding to a 180° phase flip in the received signal. This phase sign is explicitly recorded and used as a criterion for signal polarity, which is then used in subsequent symbol processing of the modulated signal. Therefore, the amplitude sequence output by the loop antenna is a signed sequence. A l ( t Its absolute value is calculated by the propagation model, and its sign is determined by the quadrant in which the azimuth angle is located: if ,but A l ( t )<0; otherwise A l ( t ) ≥0.

[0072] In this embodiment, in step S3, the signal processing stage first maps the amplitude sequences output by the omnidirectional antenna and the loop antenna onto the carrier signal respectively. The carrier frequency is taken from the actual operating frequency of the navigation station, and the sampling rate is not less than 2.5 times the carrier frequency. For the loop antenna signal, a 135 Hz balanced modulation is further applied. The modulation method is to multiply the original carrier signal by a sine wave with an amplitude of 1 and a frequency of 135 Hz to form an oscillating modulation signal.

[0073] Specifically, carrier modulation is applied to the received amplitude sequences of both the omnidirectional and loop antennas. The carrier signal is generated using a cosine function, expressed as:

[0074] ;

[0075] in, f c This refers to the actual operating frequency of the navigation station; A r ( tThe received amplitude is calculated using the propagation model. For an omnidirectional antenna signal, since there is no modulation term, the reconstructed signal is:

[0076] .

[0077] For the loop antenna signal, a 135 Hz balanced modulation is applied, with a modulation index of [insert value here]. m =1, the modulation method is to multiply the original carrier signal by a sine wave with an amplitude of 1 and a frequency of 135 Hz to form an oscillating modulation signal, the expression of which is:

[0078] ;

[0079] in, f m =135 Hz. It is worth noting that, due to A l ( t The signal itself carries symbolic information. When it is negative, it is equivalent to superimposing a 180° phase shift on the modulated signal, thereby accurately reproducing the signal polarity reversal phenomenon of the loop antenna in the back region.

[0080] In this embodiment, in step S4, for s o ( t )and s l ( t Perform Hilbert transforms on the real signals respectively to generate the corresponding analytic signals; the Hilbert transform is implemented using Fast Fourier Transform (FFT): first, the real signals are processed... N Point FFT ( N (≥1024), set the negative frequency components to zero, multiply the positive frequency components by 2 (keeping the DC component unchanged), and then perform an inverse FFT (IFFT) to obtain the imaginary part of the analytic signal. Therefore, the analytic signal representation of the omnidirectional antenna signal is:

[0081] ;

[0082] in, j The imaginary unit is used. The analytic signal representation of a loop antenna signal is:

[0083] .

[0084] Furthermore, the two complex signals are added point by point, with their real parts and imaginary parts added together, to form a superimposed composite complex signal:

[0085] .

[0086] In this embodiment, in step S5, the envelope of the synthesized complex signal is obtained by taking the modulus of each sampling point, i.e., calculated as follows:

[0087] ;

[0088] Where Re represents the real part of the complex signal; Im represents the imaginary part of the complex signal. For example... Figure 6 (c) provides a schematic diagram of the envelope result of the superimposed signal, which is... A ( t The signal exhibits a periodic fluctuation of 135 Hz over time, and its modulation depth directly reflects the deviation between the current pointing of the loop antenna and the true azimuth of the navigation station. The envelope signal is then sent to the amplitude detection module, which employs a sliding window extreme value detection algorithm. The window length covers at least two complete modulation cycles (i.e., 720 sampling points) to suppress transient noise interference.

[0089] Furthermore, within the window, the maximum value of the envelope is detected. A max and minimum value A min And calculate the modulation depth D :

[0090] .

[0091] Among them, when the modulation depth D When the absolute value is less than a preset threshold (e.g., 0.01) and the envelope waveform exhibits stable platform characteristics within the window (i.e., standard deviation less than 0.005), the current ring antenna pointing is determined to be the true azimuth angle of the navigation station relative to the aircraft.

[0092] In this embodiment, if the judgment condition of step S5 is not met in step S6, the system rotates the loop antenna in 5° increments to update the azimuth angle and repeats steps S2 to S5. This iterative process continues until an azimuth angle that makes the modulation depth approach zero is found. To improve convergence efficiency, the system can adopt a binary search strategy: the initial search range is 0° to 360°, and the search interval is halved in each iteration until the step size is less than 1°.

[0093] It should be noted that, to resolve the ambiguity in direction finding between 0° and 180°, the system records the historical modulation depth sequence and its envelope start phase at different azimuth angles. Specifically, in t At time 0 (i.e., the first sampling point), calculate the first-order difference of the envelope. Its symbol is the initial slope symbol of the envelope.

[0094] Specifically, when the modulation depth changes from positive to negative or from negative to positive, the half-plane containing the true azimuth can be determined by combining the slope sign: if The true orientation is located in the first semicircle (0°-180°); if It is located in the rear semicircle (180°-360°).

[0095] The proposed method is based on the working principle of medium-wave navigation stations. It uses methods such as simulating the generation and transmission of navigation station signals, radio wave propagation simulation, simulating loop antenna and omnidirectional antenna reception, and analyzing the received signals for navigation to realize the virtual simulation verification process of medium-wave navigation stations. It can obtain the virtual verification results of medium-wave navigation stations, thus providing a reference for the verification and adjustment of medium-wave navigation station parameters. Figure 7 The results of the virtual calibration of the medium-wave navigation station are shown.

[0096] Furthermore, because the proposed method uses radio wave propagation model simulation to simulate the signal propagation process, it can accurately reflect the impact of terrain and other obstructions on navigation signals. Therefore, it can simulate and analyze whether the navigation environment meets protection requirements, providing a theoretical basis for site selection for medium-wave navigation stations.

[0097] The above description is based on the preferred embodiments of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of the invention is defined by the appended claims rather than the foregoing description, and all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0098] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A mid-wave navigation simulation method based on Hilbert-variant analog signals, characterized in that, Includes the following steps: S1. Set the operating signal parameters of the medium-wave navigation station and initialize the initial position and orientation of the radio compass; S2. Using an electromagnetic propagation model, calculate the signal amplitude and phase information received by the omnidirectional antenna and the loop antenna under the current aircraft attitude; wherein, the signal received by the loop antenna carries a phase symbol determined by its directivity function; S3. Perform carrier reconstruction on the omnidirectional antenna received signal to obtain an omnidirectional reference signal; perform carrier reconstruction on the loop antenna received signal and apply balanced modulation at a preset frequency to generate a loop modulation signal; S4. Perform Hilbert transform on the omnidirectional reference signal and the ring modulation signal respectively to generate the corresponding analytic signals; superimpose the two analytic signals in the complex domain to obtain the composite complex signal; S5. Extract the envelope of the synthesized complex signal, calculate the modulation depth of the envelope, and determine whether the current ring antenna pointing is the true azimuth of the navigation station based on whether the modulation depth approaches zero. S6. If the modulation depth meets the direction finding conditions, output the current ring antenna pointing angle as the azimuth angle of the navigation station relative to the aircraft; if not, adjust the pointing angle of the ring antenna with a preset step size, and repeat steps S2 to S5 until the azimuth angle that meets the conditions is obtained.

2. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S1, the operating signal parameters include a carrier frequency range of 0.15-1.7 MHz, a modulation frequency of 135 Hz, and the initial azimuth angle of the radio compass is consistent with the aircraft's heading.

3. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S2, the electromagnetic propagation model is an electromagnetic wave propagation model that comprehensively considers the vector superposition of direct waves, ground-reflected waves, diffracted waves, and obstacle shielding effects.

4. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S2, the phase sign of the signal received by the loop antenna is determined by the quadrant in which the azimuth angle lies: if the azimuth angle The amplitude sequence of the signal received by the loop antenna is negative; otherwise, it is non-negative.

5. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S3, the signal expression for carrier reconstruction is: ; in, f c This refers to the actual operating frequency of the navigation station; A r ( t The received amplitude is the time-varying amplitude calculated using the propagation model. The expression for the ring modulation signal is: ; in, f m =135 Hz; A l ( t ) represents the amplitude sequence of the signal received by the loop antenna.

6. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S4, the Hilbert transform is implemented using a fast Fourier transform: the real signal is subjected to... N Point FFT sets the negative frequency components to zero and multiplies the positive frequency components by 2, while keeping the DC component unchanged. Then, inverse FFT is performed to obtain the imaginary part of the analytic signal.

7. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S4, the two analytical signals are superimposed in the complex domain by adding the analytical signal of the omnidirectional reference signal and the analytical signal of the ring modulation signal point by point, according to the real part and the imaginary part.

8. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S5, the modulation depth D The formula for calculation is: ; in, A max This represents the maximum value of the envelope; A min This is the minimum value of the envelope; Direction finding condition is modulation depth D The absolute value is less than the preset threshold and the envelope waveform exhibits stable plateau characteristics.

9. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S6, the step size for adjusting the pointing angle of the loop antenna is 5°, or a binary search strategy is used to reduce the search interval by half until the step size is less than 1°.

10. The medium-wave navigation simulation method based on Hilbert variation analog signals according to claim 1, characterized in that: In step S6, the first-order difference at the start time of the envelope is calculated. The symbol eliminates the ambiguity between 0° and 180° in direction finding: if , The true location is in the first semicircle; if , It is located in the second half of the circle.

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