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CN120275708A - Radio frequency signal processing system based on microwave broadband instantaneous frequency measurement receiver - Google Patents

Radio frequency signal processing system based on microwave broadband instantaneous frequency measurement receiver
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CN120275708A
CN120275708ACN202510764163.5ACN202510764163ACN120275708ACN 120275708 ACN120275708 ACN 120275708ACN 202510764163 ACN202510764163 ACN 202510764163ACN 120275708 ACN120275708 ACN 120275708A
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CN120275708B (en
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王晓平
刘昆
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Shanghai Pinyu Electronic Technology Co ltd
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Shanghai Pinyu Electronic Technology Co ltd
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Abstract

The invention discloses a radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver, in particular to the field of electromagnetic frequency measurement of radio frequency signals, which comprises an identification extraction module, a track reconstruction module, a path switching module and a prediction compensation module; the identification extraction module is used for dividing the original radio frequency data stream into long-time fragments, extracting a frequency response sequence from each time fragment, and marking the time fragments meeting the conditions as frequency shielding response sections according to the threshold judgment results of the frequency change speed and the amplitude change slope. By constructing a joint judging mechanism of the frequency change speed and the amplitude change slope and combining a frequency hopping trend fitting and track connection point reconstruction method, the frequency shielding response section is dynamically identified and the internal frequency evolution path is restored, so that the problem that a frequency blind area caused by geomagnetic disturbance cannot be demodulated is solved.

Description

Radio frequency signal processing system based on microwave broadband instantaneous frequency measurement receiver
Technical Field
The invention relates to the technical field of electromagnetic frequency measurement of radio frequency signals, in particular to a radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver.
Background
In space electromagnetic tomography and geomagnetic anomaly monitoring tasks, an orbit satellite usually needs to conduct high-sensitivity radio frequency measurement and spectrum evolution analysis on electromagnetic disturbance caused by events such as solar activity, plasma fluctuation, corona projection and the like, and especially relies on capturing transient frequency response of weak continuous wave signals in a specific frequency band;
However, in actual observation, the low-frequency macro-amplitude electromagnetic disturbance from a geomagnetic girdle is often affected, the disturbance has strong periodicity and long wave characteristics, wide-area interference background noise is formed by continuous superposition in a space electromagnetic environment, and low-frequency tailing and frequency baseline deviation are caused in a frequency measurement system, so that target frequency which can be demodulated is passively 'sunk' or fused with a background, and is integrally submerged from the aspect of frequency measurement judgment;
Because the existing broadband instantaneous frequency measurement receiving mechanism generally depends on a band-pass window function and a linear frequency response model, a hidden frequency point structure cannot be recovered from the large-scale disturbance, and finally a stable blind area is generated in a key detection frequency band by a frequency measurement channel, so that important weak signals cannot be identified or reset to zero by mistake;
Therefore, in the complex geomagnetic background, how to recover the phagocytized target frequency track from the frequency shielding phenomenon caused by the continuous disturbance becomes a core problem for restricting the performance of the spatial electromagnetic frequency measurement system.
Disclosure of Invention
In order to overcome the defects in the prior art, the embodiment of the invention provides a radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver, which is used for dynamically identifying a frequency shielding response section and recovering an internal frequency evolution path thereof by constructing a joint judging mechanism of a frequency change speed and an amplitude change slope and combining a frequency hopping trend fitting and track connection point reconstruction method so as to solve the problem that a frequency blind area caused by geomagnetic disturbance cannot be demodulated.
In order to achieve the aim, the invention provides the technical scheme that the radio frequency signal processing system based on the microwave broadband instantaneous frequency measurement receiver comprises an identification extraction module, a track reconstruction module, a path switching module and a prediction compensation module;
The identification extraction module is used for dividing the original radio frequency data stream into long-time fragments, extracting a frequency response sequence from each time fragment, and marking the time fragments meeting the conditions as frequency shielding response sections according to the threshold judgment results of the frequency change speed and the amplitude change slope;
The track reconstruction module is used for extracting and judging frequency direction jump trend of a frequency shielding response section in disturbance response description data, constructing a frequency track connection point by fitting a frequency direction trend line, complementing the frequency track connection point into a continuous frequency evolution track by interpolation, and forming a target frequency recovery result;
The path switching module is used for comparing the target frequency recovery result with the original frequency response sequence, replacing the original frequency response sequence in a time segment meeting the condition according to the judging result of the frequency difference sequence, judging whether to execute frequency measurement path switching or not through the shielding compensation mark, and generating a replaced frequency measurement result in the geomagnetic disturbance environment;
The prediction compensation module is used for extracting frequency hopping errors in the alternative frequency measurement result, constructing a frequency disturbance prediction template, generating a frequency shielding prediction window, constructing a predicted frequency track according to the frequency direction change trend, and generating an advanced frequency recovery result.
In a preferred embodiment, the identification extraction module is configured to divide an original radio frequency data stream acquired by the microwave broadband instantaneous frequency measurement receiver into long-time segments, and perform discrete extraction on a frequency response in each time segment;
calculating the frequency change speed and the amplitude change slope of the frequency response sequence extracted from each time segment to be used as quantitative expression of frequency behaviors in the time segment;
Judging whether the frequency change speed is in a preset frequency change speed threshold range in at least three continuous time points, and the amplitude change slope is in a preset amplitude change slope threshold range in at least three corresponding continuous time points, if so, marking the time segment as a frequency gradual change response section, otherwise, skipping the current time segment, and continuing to process the next time segment;
judging whether the center frequency of the frequency gradual change response section is smaller than a preset center frequency threshold value, judging whether the duration of the frequency gradual change response section is larger than a preset duration threshold value, if so, marking the frequency gradual change response section as a frequency shielding response section, otherwise, skipping the current frequency gradual change response section, not marking the frequency shielding response section, and continuing to process the next time slice;
After the marking is completed, the time index, center frequency, frequency change speed and amplitude change slope of the frequency mask response section are output and used as disturbance response description data.
In a preferred embodiment, the track reconstruction module is used for extracting frequency direction jump trend of each frequency shielding response section in the disturbance response description data and calculating an incremental change curve between adjacent frequency values;
Judging whether a change section with the frequency increment direction reversing times larger than a preset reversing times threshold value exists in the increment change curve, if the change section meets the condition, marking the change section as a suspected frequency evolution inflection point region, otherwise, marking the frequency shielding response section as a track-free jump characteristic and stopping;
The method comprises the steps of performing forward and backward frequency trend line fitting on a suspected frequency evolution inflection point region to respectively obtain a frequency direction trend line before a shielding section and a frequency direction trend line after the shielding section, extending the frequency direction trend line before the shielding section backwards to a preset appointed fitting time interval according to the termination time of the frequency direction trend line before the shielding section, extending the frequency direction trend line after the shielding section forwards to the preset appointed fitting time interval according to the starting time of the frequency direction trend line after the shielding section, and searching an intersection position point of the lower limit of a frequency difference in an extending overlapping interval of the two frequency direction trend lines to serve as a frequency track connecting point of a frequency shielding response section;
And supplementing the frequency track connection point into a continuous frequency evolution track through interpolation by a fitting function of the frequency track connection point and the frequency direction trend lines at two sides of the frequency shielding response section, and taking the continuous frequency evolution track as a target frequency recovery result.
In a preferred embodiment, the path switching module is configured to perform one-to-one comparison between the target frequency recovery result and the original frequency response sequence output by the microwave broadband instantaneous frequency measurement receiver, and extract a frequency difference sequence between the target frequency recovery result and the original frequency response sequence in the frequency shielding response section;
judging whether the frequency difference value in the continuous time segment in the frequency difference value sequence is larger than a preset tolerance threshold value, if so, replacing the original frequency response sequence with a target frequency recovery result in the time segment to form an updated frequency output sequence;
matching the updated frequency output sequence with the time index of the frequency mask response section to generate a frequency correction output section with a mask compensation mark;
judging whether more than three sections of frequency correction output sections with shielding compensation marks continuously appear in the updated frequency output sequence, if the conditions are met, executing a frequency shielding adaptation switching flow, and switching a frequency measurement path from an original frequency response sequence to a target frequency recovery result;
And marking the frequency measurement path output result after the frequency shielding adaptation switching process as a substitute frequency measurement result in the geomagnetic disturbance environment, and storing the substitute frequency measurement result in the disturbance environment frequency response recording sequence.
In a preferred embodiment, the prediction compensation module is configured to extract all frequency hopping position points from the alternative frequency measurement result, and calculate a frequency hopping error corresponding to each frequency hopping position point to form a frequency hopping error sequence;
judging whether error paragraphs with consistent error directions and time intervals smaller than a preset interval threshold exist in the frequency hopping error sequence, if the error paragraphs meet the conditions, marking the error paragraphs as a frequency disturbance prediction template, otherwise, storing the frequency hopping error sequence as a frequency measurement error record into an error cache;
taking the time interval in the frequency disturbance prediction template as a prediction window period parameter, taking the end time index of the frequency disturbance prediction template as a prediction window starting point, and generating a frequency shielding prediction window;
and the time index covered by the frequency shielding prediction window is used for extracting a corresponding time period in the original frequency response sequence, a predicted frequency track is constructed according to the frequency direction change trend extracted from the frequency disturbance prediction template, and the predicted frequency track is stored in a frequency track cache and marked as an advanced frequency recovery result generated based on disturbance prediction.
In a preferred embodiment, the identification extraction module is defined in the identification extraction moduleFor time slicesWhether marked as a frequency mask response section;
;
Wherein the method comprises the steps ofFor time slicesInner time pointA corresponding frequency response value; For time slicesInner time pointA corresponding amplitude response value; indicating the rate of change of frequency; representing the slope of the amplitude change; For time slicesIs a set of sampling time points; A lower threshold value for the rate of frequency change; an upper threshold value for the rate of change of frequency; a lower threshold value for the slope of the amplitude variation; an upper threshold value which is the slope of the amplitude variation; For time slicesIs a center frequency of (a); Is the upper threshold of the center frequency; Representing time slicesDuration of (2); Is a duration threshold; the logic judgment function is a logic judgment function, wherein the logic judgment function is established as1, otherwise, the logic judgment function is 0; Representing a logical relationship and; Indicating all.
In a preferred embodiment, in the trajectory reconstruction module, a definition is made ofTime for reconstructed frequency evolution traceA value of (a);
;
;
Wherein the method comprises the steps ofThe interpolation function is used for connecting the frequency direction trend line with the frequency track connection point to form a continuous track; Is an interpolation starting point; extending a function of a frequency direction trend line prior to frequency masking the response section; extending a function of a frequency direction trend line after the frequency masking response section; Searching a time index set of interpolation starting points; representing absolute value symbols; representing a time point corresponding to the lower limit of the difference value;
;
Wherein the method comprises the steps ofExtending the function of the trend line in the frequency direction before the frequency mask response section at the interpolation starting pointThe function value of the upper part; Extending the function of the trend line in the frequency direction after the frequency mask response segment at the interpolation starting pointThe function value of the above formulaLinear weighting function representing a continuous multiplication symbol, interpolation sectionThe definition is as follows:
;
Wherein the method comprises the steps ofFor interpolating the duration of the transition interval; the condition range in which the formula is established is expressed.
In a preferred embodiment, the frequency direction trend line extension function preceding the frequency mask response segmentExpressed as:
;
frequency direction trend line extension function after frequency mask response segmentExpressed as:
;
Wherein the method comprises the steps ofTime ofAn original frequency response value thereon; For sliding the width of the time windowRepresenting a continuous multiplication symbol; Second derivative in time of the frequency response; coefficients representing the second derivative of the frequency response in the trend line before the masking segment; Representing a suppression coefficient for the second derivative of the frequency response in the trend line after the masking segment; is an exponential decay factor in the time direction before the masking period; Adding a weight factor to the index in the time direction after the shielding section; an exponential decay function.
In a preferred embodiment, in the path switching module, a path is definedExpressed in timeJudging whether the original result is replaced by the recovery result;
;
;
;
Wherein the method comprises the steps ofTime for the original frequency response sequenceA value of (a); Recovering the result in time for the target frequencyA value of (a); Replacing the threshold value for the frequency difference value; The frequency output value is updated; Is the firstA frequency correction output section with a shading compensation flag; Representing the total number of corrected sections in the current judgment period; Indicating whether to trigger path switching, wherein 1 is switching and 0 is holding; as a logic decision function, the logic decision function is established as 1, otherwise is 0, whereRepresenting a continuous multiplication symbol; Representing absolute value symbols.
In a preferred embodiment, the prediction compensation module is defined inA set of time points in a prediction template;
;
;
Wherein the method comprises the steps ofIs the firstTime index of the jump error; Time for frequency hopping errorThe values above; Representation ofWhen the symbol of (b)The value is +1 whenWhen the value is-1, whenThe value is 0; is the upper threshold of the time interval; Expressed in timeRecovering the result of the predicted frequency; representing a frequency prediction track generation function constructed based on a prediction template and a fitting trend function; Representing a frequency direction change function obtained by historical trend fitting; Is a collective symbol representing all of the conditions satisfiedA set of components; Representing a logical relationship and.
The invention has the technical effects and advantages that:
Aiming at the problems that a weak continuous wave signal is easy to be covered by geomagnetic disturbance background and cannot be demodulated by a traditional frequency measurement structure in a space electromagnetic chromatography task, the invention constructs a low-frequency disturbance response extraction mechanism in the electromagnetic frequency measurement process through a combined threshold recognition mechanism of the frequency change speed and the amplitude change slope, and can judge a shielding section under the condition of not only relying on the center frequency, thereby effectively recovering a blind area signal in a frequency measurement channel;
By analyzing frequency increment inversion behavior in the identified frequency shielding response section, fitting front and back trend lines and connecting point interpolation calculation are executed, a complete frequency evolution track is constructed, a truncated frequency measurement path can be recovered under the nonlinear jump condition, and track integrity and time consistency under continuous frequency measurement are improved;
The triggering conditions of the multi-section shielding compensation marks are designed by adopting a difference comparison and frequency correction output section accumulation judgment strategy between the target frequency recovery result and the original frequency measurement result, so that the dynamic frequency measurement path replacement is realized on the premise of avoiding path oscillation, and the self-adaptive robustness of frequency measurement output in an electromagnetic disturbance environment is effectively enhanced;
The disturbance prediction template and the frequency shielding prediction window are constructed through time distribution and direction trend analysis of the frequency hopping errors, the generation of the predicted frequency track is completed before the frequency measurement processing system enters the shielding state, a predicted compensation path based on a disturbance behavior mode is formed, and the frequency measurement early warning and advanced modeling capacity of the frequency measurement processing system in a periodic disturbance scene is improved.
Drawings
FIG. 1 is a schematic diagram of a system module according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1 of the specification, a radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to an embodiment of the present invention includes an identification extraction module, a track reconstruction module, a path switching module, and a prediction compensation module;
The identification extraction module is used for dividing the original radio frequency data stream into long-time fragments, extracting a frequency response sequence from each time fragment, and marking the time fragments meeting the conditions as frequency shielding response sections according to the threshold judgment results of the frequency change speed and the amplitude change slope;
The track reconstruction module is used for extracting and judging frequency direction jump trend of a frequency shielding response section in disturbance response description data, constructing a frequency track connection point by fitting a frequency direction trend line, complementing the frequency track connection point into a continuous frequency evolution track by interpolation, and forming a target frequency recovery result;
The path switching module is used for comparing the target frequency recovery result with the original frequency response sequence, replacing the original frequency response sequence in a time segment meeting the condition according to the judging result of the frequency difference sequence, judging whether to execute frequency measurement path switching or not through the shielding compensation mark, and generating a replaced frequency measurement result in the geomagnetic disturbance environment;
The prediction compensation module is used for extracting frequency hopping errors in the alternative frequency measurement result, constructing a frequency disturbance prediction template, generating a frequency shielding prediction window, constructing a predicted frequency track according to the frequency direction change trend, and generating an advanced frequency recovery result.
The identification extraction module is used for dividing an original radio frequency data stream acquired by the microwave broadband instantaneous frequency measurement receiver into long-time fragments, and performing discrete extraction on frequency response in each time fragment;
calculating the frequency change speed and the amplitude change slope of the frequency response sequence extracted from each time segment to be used as quantitative expression of frequency behaviors in the time segment;
Judging whether the frequency change speed is in a preset frequency change speed threshold range in at least three continuous time points, and the amplitude change slope is in a preset amplitude change slope threshold range in at least three corresponding continuous time points, if so, marking the time segment as a frequency gradual change response section, otherwise, skipping the current time segment, and continuing to process the next time segment;
judging whether the center frequency of the frequency gradual change response section is smaller than a preset center frequency threshold value, judging whether the duration of the frequency gradual change response section is larger than a preset duration threshold value, if so, marking the frequency gradual change response section as a frequency shielding response section, otherwise, skipping the current frequency gradual change response section, not marking the frequency shielding response section, and continuing to process the next time slice;
After the marking is completed, the time index, center frequency, frequency change speed and amplitude change slope of the frequency mask response section are output and used as disturbance response description data.
The track reconstruction module is used for extracting frequency direction jump trend of each frequency shielding response section in the disturbance response description data and calculating an incremental change curve between adjacent frequency values;
judging whether a change section with the frequency increment direction reversing times larger than a preset reversing times threshold value exists in the increment change curve, if the change section meets the conditions, marking the change section as a suspected frequency evolution inflection point region, otherwise, marking the frequency shielding response section as a track-free jump characteristic, and terminating the subsequent flow;
The method comprises the steps of performing forward and backward frequency trend line fitting on a suspected frequency evolution inflection point region to respectively obtain a frequency direction trend line before a shielding section and a frequency direction trend line after the shielding section, extending the frequency direction trend line before the shielding section backwards to a preset appointed fitting time interval according to the termination time of the frequency direction trend line before the shielding section, extending the frequency direction trend line after the shielding section forwards to the preset appointed fitting time interval according to the starting time of the frequency direction trend line after the shielding section, and searching an intersection position point of the lower limit of a frequency difference in an extending overlapping interval of the two frequency direction trend lines to serve as a frequency track connecting point of a frequency shielding response section;
And supplementing the frequency track connection point into a continuous frequency evolution track through interpolation by a fitting function of the frequency track connection point and the frequency direction trend lines at two sides of the frequency shielding response section, and taking the continuous frequency evolution track as a target frequency recovery result.
The path switching module is used for carrying out one-to-one comparison on the target frequency recovery result and an original frequency response sequence output by the microwave broadband instantaneous frequency measurement receiver, and extracting a frequency difference value sequence of the target frequency recovery result and the original frequency response sequence in the frequency shielding response section;
judging whether the frequency difference value in the continuous time segment in the frequency difference value sequence is larger than a preset tolerance threshold value, if so, replacing the original frequency response sequence with a target frequency recovery result in the time segment to form an updated frequency output sequence;
matching the updated frequency output sequence with the time index of the frequency mask response section to generate a frequency correction output section with a mask compensation mark;
judging whether more than three sections of frequency correction output sections with shielding compensation marks continuously appear in the updated frequency output sequence, if the conditions are met, executing a frequency shielding adaptation switching flow, and switching a frequency measurement path from an original frequency response sequence to a target frequency recovery result;
And marking the frequency measurement path output result after the frequency shielding adaptation switching process as a substitute frequency measurement result in the geomagnetic disturbance environment, and storing the substitute frequency measurement result in the disturbance environment frequency response recording sequence.
The prediction compensation module is used for extracting all frequency hopping position points from the alternative frequency measurement result, calculating the frequency hopping error corresponding to each frequency hopping position point and forming a frequency hopping error sequence;
judging whether error paragraphs with consistent error directions and time intervals smaller than a preset interval threshold exist in the frequency hopping error sequence, if the error paragraphs meet the conditions, marking the error paragraphs as a frequency disturbance prediction template, otherwise, storing the frequency hopping error sequence as a frequency measurement error record into an error cache;
taking the time interval in the frequency disturbance prediction template as a prediction window period parameter, taking the end time index of the frequency disturbance prediction template as a prediction window starting point, and generating a frequency shielding prediction window;
and the time index covered by the frequency shielding prediction window is used for extracting a corresponding time period in the original frequency response sequence, a predicted frequency track is constructed according to the frequency direction change trend extracted from the frequency disturbance prediction template, and the predicted frequency track is stored in a frequency track cache and marked as an advanced frequency recovery result generated based on disturbance prediction.
It should be noted that, in the formula structure related to the scheme, the dimensionless terms can be used as proportional or structural adjusting factors, and only play a role of numerical scaling when being combined with the unit-containing quantity, and a new physical dimension is not introduced, so that the whole expressed unit system is not changed or confused;
secondly, in the formula structure of the scheme, if a plurality of variable items with different physical units are involved, including but not limited to time type, quality type or energy type variables, the joint occurrence of the variable items is a collaborative modeling relation for expressing multiple physical mechanisms, each variable can form a unified structure through function mapping, ratio combination or normalization adjustment, the units are clear, the meaning is clear, and the whole expression accords with a dimension consistency principle and an engineering modeling routine paradigm;
If constants, weights, adjustment factors, threshold parameters, proportion coefficients and the like are designed, the parameters belong to adjustable control parameters oriented to different application environments, the values of the parameters depend on target equipment configuration, data input characteristics and performance optimization targets, and the parameters are converged and set in a reasonable range in a mode of model verification, performance constraint or engineering calibration and the like in an implementation stage;
Definition in an identification extraction moduleFor time slicesWhether marked as frequency mask response segment (yes, 0 no);
;
Wherein the method comprises the steps ofFor time slicesInner time pointA corresponding frequency response value; For time slicesInner time pointA corresponding amplitude response value; Indicating the rate of change of frequency (derivative over time); representing the slope of the amplitude change (derivative over time); For time slicesIs a set of sampling time points; A lower threshold value for the rate of frequency change; an upper threshold value for the rate of change of frequency; a lower threshold value for the slope of the amplitude variation; an upper threshold value of the slope of the amplitude change during the time segmentOn the premise of being identified as a frequency ramp response segment,For time slicesIs a center frequency of (a); Is the upper threshold of the center frequency, and is in the time segmentOn the premise of being identified as a frequency ramp response segment,Representing time slicesDuration of (2); Is a duration threshold; the logic judgment function is a logic judgment function, wherein the logic judgment function is established as1, otherwise, the logic judgment function is 0; representing a logical relationship AND; all are represented, each element in the set satisfying a certain condition for expression.
In the track reconstruction module, definitionTime for reconstructed frequency evolution traceA value of (a);
;
;
Wherein the method comprises the steps ofThe interpolation function is used for connecting the frequency direction trend line with the frequency track connection point to form a continuous track; for the interpolation starting point, the interpolation starting point is the time point corresponding to the minimum difference value of the trend line functions in the two frequency directions in the search interval; extending a function of a frequency direction trend line prior to frequency masking the response section; extending a function of a frequency direction trend line after the frequency masking response section; Searching a time index set of interpolation starting points; representing absolute value symbols; representing a time point corresponding to the lower limit of the difference value;
;
Wherein the method comprises the steps ofExtending the function of the trend line in the frequency direction before the frequency mask response section at the interpolation starting pointThe function value of the upper part; Extending the function of the trend line in the frequency direction after the frequency mask response segment at the interpolation starting pointThe function value of the above formulaLinear weighting function representing a continuous multiplication symbol, interpolation sectionThe definition is as follows:
;
Wherein the method comprises the steps ofFor interpolating the duration of the transition interval; the condition range that the formula holds is expressed for defining that the variable is valid for the formula within the specific interval.
Frequency direction trend line extension function before frequency mask response sectionExpressed as:
;
frequency direction trend line extension function after frequency mask response segmentExpressed as:
;
Wherein the method comprises the steps ofTime ofThe original frequency response value, additionally time in the above formulaThe point in time, representing the current calculated trendRepresenting points in time used to traverse the integration window; For sliding time window width, the sliding time window width is used for constructing trend intervalRepresenting a continuous multiplication symbol; For the second derivative of the frequency response in time, the second derivative of the frequency response in time represents the varying acceleration and is used for judging the smoothness or the sharpness of the trend; The enhancement coefficient of the second derivative of the frequency response in the trend line before the shielding section is represented, the enhancement coefficient of the second derivative of the frequency response in the trend line before the shielding section is used for highlighting the rapid inflection point change in the track before the shielding, in practical application, the value of the enhancement coefficient can be combined with the change steepness degree of the frequency response in a history interval, the enhancement coefficient should be larger when the fluctuation of the response curvature is obvious, and the enhancement coefficient should be moderately reduced when the response is more gentle so as to avoid overfitting; The suppression coefficient of the second derivative of the frequency response in the trend line after the shielding section is represented, the suppression coefficient of the second derivative of the frequency response in the trend line after the shielding section is used for smoothing trend change after the transition section, misleading of local severe disturbance on fitting results is prevented, in practical application, the value is based on fluctuation stability of frequency response data after the shielding section, the suppression capability is properly enhanced when fluctuation is severe, and the limit can be relaxed when the fluctuation rule is clear; For the exponential decay factor in the time direction before the shielding section, the exponential decay factor in the time direction before the shielding section is used for determining the retention degree of the historical frequency response value in trend calculation, the value of the exponential decay factor can be adjusted according to a historical time window covered by trend analysis, if the historical track information is more critical, the decay rate is slowed down, and if only the short-term direction is required to be captured, the decay rate can be increased to increase the responsiveness; The index weighting factors in the time direction behind the shielding section are used for controlling the attention degree of frequency trend modeling to the recent response point, the value of the index weighting factors can be determined according to the predictability of the frequency trend behind the shielding section, the weighting degree is properly increased when the trend is strong in continuity, and the weighting is kept gentle when the trend is uncertain or the oscillation is strong so as to prevent errors; An exponential decay function, wherein the exponential decay function is used for simulating the sensitivity reduction of the distance to the time, and the formula structure in the formula is as follows: is shown in the intervalInternal pair variableFor reflecting trend accumulation.
In the path switching module, definitionExpressed in timeJudging whether the original result is replaced by the recovery result (1 is replaced, and 0 is reserved);
;
;
;
Wherein the method comprises the steps ofTime for the original frequency response sequenceA value of (a); Recovering the result in time for the target frequencyA value of (a); Replacing the threshold value for the frequency difference value; The frequency output value is updated; Is the firstA frequency correction output section with a shading compensation flag; Representing the total number of corrected sections in the current judgment period; Indicating whether to trigger path switching, wherein 1 is switching and 0 is holding; as a logic decision function, the logic decision function is established as 1, otherwise is 0, whereRepresenting a continuous multiplication symbol; Representing absolute value symbols.
Definition in prediction Compensation ModuleA set of time points in a prediction template;
;
;
Wherein the method comprises the steps ofIs the firstTime index of the jump error; Time for frequency hopping errorThe values above; Representation ofWhen the symbol of (b)The value is +1 whenWhen the value is-1, whenThe value is 0; is the upper threshold of the time interval; Expressed in timeRecovering the result of the predicted frequency; representing a frequency prediction track generation function constructed based on a prediction template and a fitting trend function; Representing a frequency direction change function obtained by historical trend fitting; Is a collective symbol representing all of the conditions satisfiedA set of components; Representing a logical relationship AND (AND).
The technical scheme of the invention aims at solving the problem of frequency measurement blind areas caused by frequency shielding phenomenon of weak radio frequency signals due to geomagnetic disturbance in a track observation task, wherein a common frequency measurement model in the prior art adopts a fixed frequency window or linear filter structure, and can not accurately recover signal tracks under strong background interference, and particularly, when nonlinear jump behaviors such as interruption, drift or fall-back occur in a frequency evolution process, the conventional means can not judge whether the frequency continuity is truly interrupted or only shielded by background signals;
The method comprises the steps of firstly identifying an extraction module for bearing the entrance task of a scheme, namely identifying a time segment with frequency shielding characteristics from an original radio frequency data stream acquired by a microwave broadband instantaneous frequency measurement receiver, adopting combined threshold judgment of frequency change speed and amplitude change slope for executing logic, wherein in the stage of frequency shielding, the signal usually presents two characteristics, namely narrowing a frequency fluctuation range, stabilizing amplitude change, keeping continuity of local slope in time dimension even if a weak signal is 'suppressed' to the vicinity of a frequency response base line by background disturbance, and selecting to establish a composite threshold for the speed and direction of a change trend without using a frequency value as a judgment basis in design so as to reduce sensitivity to amplitude and central value deviation;
After the preliminary identification of the shielding response section is completed, the core task of the track reconstruction module is to judge whether the frequency track has the evolution trend of being broken or not, and construct a continuous track at the jump point; in a real scene, the frequency direction change before and after a weak signal is shielded is generally inconsistent, for example, a slowly rising target signal can slide down or stagnate rapidly after being interfered and is easy to be fitted or misjudged after being pressed, so that the model designs a bidirectional fitting structure of forward and backward trend lines, sets a controllable fitting extension time range, searches the minimum frequency difference point in the overlapping area of the trend lines at two sides as a track connecting point, essentially surrounds a shielding section by a known trend, presumes frequency change logic in a frequency area which is not directly observed, and finally reconstructs the shielding section into a continuous track by using a fitting function so as to recover a target frequency path;
The task of the path switching module is not just to output a recovery result, but to judge whether to incorporate the recovery result into the frequency measurement path for replacing the original frequency response sequence; the method comprises the steps of determining a frequency difference value of a frequency correction output section, determining a frequency difference value of a frequency correction output section, and judging whether the frequency difference value exceeds a preset tolerance threshold value or not according to the frequency difference value of the frequency correction output section, wherein the frequency difference value is equal to or less than a preset tolerance threshold value;
The structure is provided for solving the problem that frequency shielding has periodicity or predictability in a track long-term running task, and because a plurality of geomagnetic disturbances have relatively regular behaviors, such as polar disturbance excited by solar wind usually repeatedly occurs at certain track heights, frequency jump error directions and time intervals are extracted from historical substitution frequency measurement results, an error paragraph is constructed, a prediction window can be generated in advance, the prediction window can be used for directly constructing a frequency track for advanced compensation without waiting for explicit identification of a shielding period once the shielding period is covered in an original frequency response sequence, and the structure improves passive compensation into active prediction and is a prospective part in practical application and suitable for the frequency measurement guarantee task in multi-track long-term running.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (10)

Translated fromChinese
1.一种基于微波宽带瞬时测频接收机的射频信号处理系统,包括识别提取模块、轨迹重建模块、路径切换模块、预测补偿模块,其特征在于:1. A radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver, comprising an identification and extraction module, a trajectory reconstruction module, a path switching module, and a prediction and compensation module, characterized in that:识别提取模块用于将原始射频数据流划分为等长时间片段,并在每个时间片段中提取频率响应序列,依据频率变化速度与幅值变化斜率的阈值判断结果,标记满足条件的时间片段为频率遮蔽响应区段;The identification and extraction module is used to divide the original RF data stream into equal time segments, and extract the frequency response sequence in each time segment, and mark the time segment that meets the conditions as the frequency masking response segment according to the threshold judgment results of the frequency change speed and the amplitude change slope;轨迹重建模块用于对扰动响应描述数据中的频率遮蔽响应区段进行频率方向跳变趋势提取与判断,并通过拟合频率方向趋势线构建频率轨迹连接点,将频率轨迹连接点通过插值补全为连续频率演化轨迹,形成目标频率恢复结果;The trajectory reconstruction module is used to extract and judge the frequency direction jump trend of the frequency masking response section in the disturbance response description data, and construct the frequency trajectory connection points by fitting the frequency direction trend line, and interpolate the frequency trajectory connection points into a continuous frequency evolution trajectory to form the target frequency recovery result;路径切换模块用于将目标频率恢复结果与原始频率响应序列进行比对,依据频率差值序列的判断结果在满足条件的时间片段内替代原始频率响应序列,并通过遮蔽补偿标记判定是否执行测频路径切换,生成地磁扰动环境下的替代测频结果;The path switching module is used to compare the target frequency recovery result with the original frequency response sequence, replace the original frequency response sequence in the time segment that meets the conditions according to the judgment result of the frequency difference sequence, and determine whether to perform the frequency measurement path switching through the masking compensation mark to generate the alternative frequency measurement result under the geomagnetic disturbance environment;预测补偿模块用于提取替代测频结果中的频率跳变误差,构建频率扰动预测模板并生成频率遮蔽预测窗口,依据频率方向变化趋势构建预测频率轨迹,生成提前频率恢复结果。The prediction compensation module is used to extract the frequency jump error in the alternative frequency measurement result, construct a frequency disturbance prediction template and generate a frequency masking prediction window, construct a predicted frequency trajectory according to the frequency direction change trend, and generate an early frequency recovery result.2.根据权利要求1所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:2. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 1, characterized in that:识别提取模块用于将微波宽带瞬时测频接收机所获取的原始射频数据流划分为等长时间片段,并对每个时间片段中的频率响应进行离散提取;The identification and extraction module is used to divide the original radio frequency data stream obtained by the microwave broadband instantaneous frequency measurement receiver into equal time segments, and to perform discrete extraction of the frequency response in each time segment;对每个时间片段中提取的频率响应序列计算频率变化速度与幅值变化斜率,作为该时间片段中频率行为的定量表达;The frequency change speed and amplitude change slope are calculated for the frequency response sequence extracted from each time segment as a quantitative expression of the frequency behavior in the time segment;判断频率变化速度是否在不少于三个连续时间点内均处于预设的频率变化速度阈值范围内,且幅值变化斜率在对应的不少于三个连续时间点内均处于预设的幅值变化斜率阈值范围内,若满足,则标记该时间片段为频率缓变响应区段,否则跳过当前时间片段,继续处理下一时间片段;Determine whether the frequency change speed is within the preset frequency change speed threshold range in at least three consecutive time points, and whether the amplitude change slope is within the preset amplitude change slope threshold range in at least three consecutive time points. If so, mark the time segment as a frequency slow change response segment, otherwise skip the current time segment and continue to process the next time segment;判断频率缓变响应区段的中心频率是否小于预设的中心频率阈值,且该频率缓变响应区段的持续时间是否大于预设的持续时间阈值,若均满足,则标记为频率遮蔽响应区段,否则跳过当前频率缓变响应区段,不标记为频率遮蔽响应区段,并继续处理下一时间片段;Determine whether the center frequency of the frequency slowly varying response section is less than a preset center frequency threshold, and whether the duration of the frequency slowly varying response section is greater than a preset duration threshold. If both conditions are met, mark it as a frequency masking response section. Otherwise, skip the current frequency slowly varying response section, do not mark it as a frequency masking response section, and continue to process the next time segment.在完成标记后,输出频率遮蔽响应区段的时间索引、中心频率、频率变化速度与幅值变化斜率,用作扰动响应描述数据。After the marking is completed, the time index, center frequency, frequency change speed and amplitude change slope of the frequency masking response segment are output and used as disturbance response description data.3.根据权利要求2所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:3. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 2, characterized in that:轨迹重建模块用于对扰动响应描述数据中各频率遮蔽响应区段进行频率方向跳变趋势提取,计算相邻频率值之间的增量变化曲线;The trajectory reconstruction module is used to extract the frequency direction jump trend of each frequency masking response segment in the disturbance response description data and calculate the incremental change curve between adjacent frequency values;判断增量变化曲线中是否存在连续时间区间内频率增量方向的反转次数大于预设反转次数阈值的变化段,若满足条件,则将该变化段标记为疑似频率演化拐点区,否则将该频率遮蔽响应区段标记为无轨迹跳变特征并终止;Determine whether there is a change segment in the incremental change curve in which the number of reversals in the frequency increment direction within a continuous time interval is greater than a preset reversal number threshold. If the condition is met, mark the change segment as a suspected frequency evolution inflection point area; otherwise, mark the frequency masking response section as having no trajectory jump feature and terminate;对疑似频率演化拐点区执行前向与后向的频率趋势线拟合,分别得到遮蔽段前的频率方向趋势线与遮蔽段后的频率方向趋势线;将遮蔽段前的频率方向趋势线按照其终止时间向后延伸至预设的指定拟合时间区间,将遮蔽段后的频率方向趋势线按照其起始时间向前延伸至预设的指定拟合时间区间,在两条频率方向趋势线的延伸重叠区间内搜索频率差下限的交汇位置点,作为频率遮蔽响应区段的频率轨迹连接点;Perform forward and backward frequency trend line fitting on the suspected frequency evolution inflection point area to obtain the frequency direction trend line before the masking section and the frequency direction trend line after the masking section respectively; extend the frequency direction trend line before the masking section backward to a preset specified fitting time interval according to its end time, and extend the frequency direction trend line after the masking section forward to a preset specified fitting time interval according to its start time, and search for the intersection point of the lower limit of the frequency difference in the extended overlapping interval of the two frequency direction trend lines as the frequency trajectory connection point of the frequency masking response section;通过频率轨迹连接点与频率遮蔽响应区段两侧的频率方向趋势线的拟合函数,将频率轨迹连接点通过插值补全为一条连续频率演化轨迹,作为目标频率恢复结果。Through the fitting function of the frequency trajectory connection points and the frequency direction trend lines on both sides of the frequency masking response segment, the frequency trajectory connection points are interpolated to form a continuous frequency evolution trajectory as the target frequency recovery result.4.根据权利要求3所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:4. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 3, characterized in that:路径切换模块用于将目标频率恢复结果与微波宽带瞬时测频接收机输出的原始频率响应序列进行一对一比对,提取目标频率恢复结果与原始频率响应序列在频率遮蔽响应区段内的频率差值序列;The path switching module is used to perform a one-to-one comparison between the target frequency recovery result and the original frequency response sequence output by the microwave broadband instantaneous frequency measurement receiver, and extract the frequency difference sequence between the target frequency recovery result and the original frequency response sequence in the frequency masking response section;判断频率差值序列中是否存在连续时间片段内的频率差值大于预设的容差阈值,若满足,则将目标频率恢复结果在该时间片段内替代原始频率响应序列形成更新频率输出序列;Determine whether there is a frequency difference in a continuous time segment in the frequency difference sequence that is greater than a preset tolerance threshold. If so, replace the original frequency response sequence with the target frequency recovery result in the time segment to form an updated frequency output sequence;将更新频率输出序列与频率遮蔽响应区段的时间索引进行匹配,生成带有遮蔽补偿标记的频率修正输出区段;Matching the updated frequency output sequence with the time index of the frequency masking response segment to generate a frequency correction output segment with a masking compensation mark;判断更新频率输出序列中是否连续出现三段以上带有遮蔽补偿标记的频率修正输出区段,若满足条件,则执行频率遮蔽适配切换流程,将测频路径由原始频率响应序列切换为目标频率恢复结果;否则,保持测频路径为原始频率响应序列并终止适配切换流程;Determine whether there are three or more frequency correction output segments with masking compensation marks in succession in the updated frequency output sequence. If the condition is met, execute the frequency masking adaptive switching process to switch the frequency measurement path from the original frequency response sequence to the target frequency recovery result; otherwise, keep the frequency measurement path as the original frequency response sequence and terminate the adaptive switching process;将处于频率遮蔽适配切换流程后的测频路径输出结果标记为地磁扰动环境下的替代测频结果,并存入干扰环境频率响应记录序列中。The frequency measurement path output result after the frequency masking adaptation switching process is marked as an alternative frequency measurement result under the geomagnetic disturbance environment and stored in the interference environment frequency response record sequence.5.根据权利要求4所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:5. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 4, characterized in that:预测补偿模块用于从替代测频结果中提取所有频率跳变位置点,并计算每个频率跳变位置点对应的频率跳变误差,构成频率跳变误差序列;The prediction compensation module is used to extract all frequency jump position points from the alternative frequency measurement results, and calculate the frequency jump error corresponding to each frequency jump position point to form a frequency jump error sequence;判断频率跳变误差序列中是否存在误差方向一致且时间间隔小于预设间隔阈值的误差段落,若满足条件,则标记该误差段落为频率扰动预测模板,否则,将频率跳变误差序列作为测频误差记录存入误差缓存;Determine whether there is an error segment with consistent error direction and time interval less than a preset interval threshold in the frequency hopping error sequence. If the condition is met, mark the error segment as a frequency disturbance prediction template. Otherwise, store the frequency hopping error sequence as a frequency measurement error record in the error cache.将频率扰动预测模板中的时间间隔作为预测窗口周期参数,将频率扰动预测模板末端时间索引作为预测窗口起始点,生成频率遮蔽预测窗口;The time interval in the frequency disturbance prediction template is used as the prediction window period parameter, and the end time index of the frequency disturbance prediction template is used as the prediction window starting point to generate a frequency masking prediction window;将频率遮蔽预测窗口所覆盖的时间索引用于提取原始频率响应序列中的对应时间段,依据频率扰动预测模板中提取的频率方向变化趋势构建预测频率轨迹,并将该预测频率轨迹存入频率轨迹缓存,标记为基于扰动预测生成的提前频率恢复结果。The time index covered by the frequency masking prediction window is used to extract the corresponding time period in the original frequency response sequence, and the predicted frequency trajectory is constructed according to the frequency direction change trend extracted from the frequency disturbance prediction template. The predicted frequency trajectory is stored in the frequency trajectory cache and marked as the early frequency recovery result generated based on disturbance prediction.6.根据权利要求5所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:6. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 5, characterized in that:在识别提取模块中定义为时间片段是否标记为频率遮蔽响应区段;Defined in the recognition extraction module For time segment Whether to mark as frequency masking response section; ;其中为时间片段内时间点对应的频率响应值;为时间片段内时间点对应的幅值响应值;表示频率变化速度;表示幅值变化斜率;为时间片段的采样时间点集合;为频率变化速度的下限阈值;为频率变化速度的上限阈值;为幅值变化斜率的下限阈值;为幅值变化斜率的上限阈值;为时间片段的中心频率;为中心频率上限阈值;表示时间片段的持续时间;为持续时间阈值;为逻辑判定函数,逻辑判定函数成立为1,否则为0;表示逻辑关系与;表示所有。in For time segment Internal time point The corresponding frequency response value; For time segment Internal time point The corresponding amplitude response value; Indicates the frequency change speed; Indicates the slope of amplitude change; For time segment The set of sampling time points; is the lower limit threshold of the frequency change speed; is the upper threshold of the frequency change speed; is the lower threshold of the amplitude change slope; is the upper threshold of the amplitude change slope; For time segment The center frequency of is the upper limit threshold of the center frequency; Represents a time segment Duration of is the duration threshold; is a logic decision function, if the logic decision function is established, it is 1, otherwise it is 0; Indicates logical relationship and; Indicates all.7.根据权利要求6所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:7. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 6, characterized in that:在轨迹重建模块中,定义为重建后的频率演化轨迹在时间上的值;In the trajectory reconstruction module, define is the reconstructed frequency evolution trajectory in time The value on ; ;其中为插值函数,插值函数用于连接频率方向趋势线与频率轨迹连接点形成连续轨迹;为插值起始点;为频率遮蔽响应区段之前的频率方向趋势线延伸函数;为频率遮蔽响应区段之后的频率方向趋势线延伸函数;为搜索插值起始点的时间索引集合;表示绝对值符号;表示取差值下限对应的时间点;in is an interpolation function, which is used to connect the frequency direction trend line and the frequency trajectory connection point to form a continuous trajectory; is the interpolation starting point; It is the frequency direction trend line extension function before the frequency masking response section; It is the frequency direction trend line extension function after the frequency masking response section; A time index set for searching the interpolation starting point; Indicates the absolute value symbol; Indicates the time point corresponding to the lower limit of the difference; ;其中为频率遮蔽响应区段之前的频率方向趋势线延伸函数在插值起始点上的函数值;为频率遮蔽响应区段之后的频率方向趋势线延伸函数在插值起始点上的函数值;式中的表示连乘符号;插值区段的线性权重函数定义为:in The frequency direction trend line extension function before the frequency masking response segment is at the interpolation starting point Function value on ; The frequency direction trend line extension function after the frequency masking response segment is at the interpolation starting point The function value on Indicates the multiplication symbol; linear weight function of the interpolation segment Defined as: ;其中为插值过渡区间的持续时间;表示公式成立的条件范围。in is the duration of the interpolation transition interval; Indicates the range of conditions under which the formula is true.8.根据权利要求7所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:8. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 7, characterized in that:频率遮蔽响应区段之前的频率方向趋势线延伸函数表示为:Frequency direction trend line extension function before the frequency masking response segment It is expressed as: ;频率遮蔽响应区段之后的频率方向趋势线延伸函数表示为:Frequency-direction trendline extension function after the frequency masking response segment It is expressed as: ;其中时间上的原始频率响应值;为滑动时间窗口宽度;式中的表示连乘符号;为频率响应在时间上的二阶导数;表示遮蔽段前趋势线中对频率响应二阶导数的系数;表示遮蔽段后趋势线中对频率响应二阶导数的抑制系数;为遮蔽段前时间方向上的指数衰减因子;为遮蔽段后时间方向上的指数增权因子;指数衰减函数。in time The original frequency response value on ; is the sliding time window width; Indicates the symbol for continuous multiplication; is the second-order derivative of the frequency response in time; represents the coefficient of the second derivative of the frequency response in the trend line before the masking segment; It represents the suppression coefficient of the second-order derivative of the frequency response in the trend line after the masking segment; is the exponential decay factor in the time direction before the masking stage; is the exponential weighting factor in the time direction after the masking period; Exponential decay function.9.根据权利要求8所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:9. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 8, characterized in that:在路径切换模块中,定义表示在时间判断是否使用恢复结果替代原始结果;In the path switching module, define Indicates at time Determine whether to use the restored result to replace the original result; ; ; ;其中为原始频率响应序列在时间上的值;为目标频率恢复结果在时间上的值;为频率差值替代阈值;为更新后的频率输出值;为第段带有遮蔽补偿标记的频率修正输出区段;表示在当前判断周期内的修正区段总数;表示是否触发路径切换,其中1为切换,0为保持;为逻辑判定函数,逻辑判定函数成立为1,否则为0;式中的表示连乘符号;表示绝对值符号。in is the original frequency response sequence in time The value on The target frequency is recovered in time The value on Replace the threshold value with the frequency difference; is the updated frequency output value; For the A frequency correction output section with a masking compensation mark; Indicates the total number of correction segments in the current judgment cycle; Indicates whether to trigger path switching, where 1 means switching and 0 means keeping; is a logic decision function, which is 1 if it is established, otherwise it is 0; Indicates the symbol for continuous multiplication; Represents the absolute value symbol.10.根据权利要求9所述的一种基于微波宽带瞬时测频接收机的射频信号处理系统,其特征在于:10. The radio frequency signal processing system based on a microwave broadband instantaneous frequency measurement receiver according to claim 9, characterized in that:在预测补偿模块中定义为预测模板中的时间点集合;Defined in the prediction compensation module is the set of time points in the prediction template; ; ;其中为第个跳变误差的时间索引;为频率跳变误差在时间上的数值;表示的符号,当时取值为+1,当时取值为-1,当时取值为0;为时间间隔的阈值上限;表示在时间上的预测频率恢复结果;表示基于预测模板与拟合趋势函数构建的频率预测轨迹生成函数;表示由历史趋势拟合得到的频率方向变化函数;是集合符号,表示满足条件的所有组成的集合;表示逻辑关系与。in For the The time index of the jump error; is the frequency jump error in time The value on ; express The symbol, when When the value is +1, The value is -1 when When the value is 0; is the upper threshold of the time interval; Indicates at time The predicted frequency recovery results on; represents the frequency prediction trajectory generation function constructed based on the prediction template and the fitting trend function; Represents the frequency direction change function obtained by fitting the historical trend; It is a set symbol, indicating all A collection of components; Represents logical relationship.
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