A jitter auxiliary measurement precision enhancement method for space-based calibration
By injecting a uniformly distributed artificial jitter signal in front of the low-order analog-to-digital converter and performing multiple independent quantization observations and arithmetic averaging, the problem of insufficient accuracy of the low-order analog-to-digital converter under the resource constraints of the satellite platform was solved, and high-precision measurement of the space-based calibration system was realized.
Patent Information
- Application Number
- CN202611115474.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-27
- Publication Date
- 2026-08-25
AI Technical Summary
Due to the strict limitations of satellite platform resources, the inherent quantization accuracy of low-bit analog-to-digital converters is insufficient, which cannot meet the high-precision measurement requirements of space-based calibration systems.
A zero-mean, uniformly distributed artificial jitter signal is injected into the continuous-time analog input signal fed forward by the low-bit analog-to-digital converter to generate a composite analog signal. The measurement accuracy is improved by multiple independent quantization observations and arithmetic mean calculations.
By increasing the number of independent quantization observations, measurement accuracy and resolution are significantly improved without increasing the number of bits and power consumption of the low-bit analog-to-digital converter, thus achieving high-precision calibration.
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Figure CN122632289A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electronic communication and signal processing technology, and in particular to a method for enhancing the accuracy of jitter-assisted measurements for space-based calibration. Background Technology
[0002] Satellite calibration is crucial for ensuring the accuracy, consistency, and reliability of Earth observation data. External calibration primarily involves adjusting radar measurements using ground-based calibration targets, a process that estimates the antenna pattern and gain. However, this ground-based method is highly sensitive to weather, terrain, and climate change, limiting its accuracy and operational flexibility. In recent years, space-based calibration has emerged as a solution to overcome the limitations of traditional ground-based methods, particularly addressing the geographical discontinuity between calibration points and the actual observation area.
[0003] The core of external calibration is the use of active radiometric calibrators with precisely known radiation characteristics. These calibrators complete the calibration process by receiving downlink signals from satellite sensors and then relaying them. This bidirectional process allows for independent and accurate calibration of both the sensor's transmit and receive chains. Calibration is inherently a high-precision metrological task. In resource-rich ground environments, advanced active calibration systems primarily employ high-bit-rate and high-linearity analog-to-digital converters (ADCs) as their core components. This design choice aims to achieve distortion-free quantization of complex radar signals.
[0004] Compared to ground-based calibration, which is susceptible to terrain and atmospheric interference, space-based calibration offers significant advantages: global coverage, immunity to atmospheric interference, and a higher signal-to-noise ratio. However, the stringent payload limitations imposed by satellite platforms necessitate miniaturized and low-power designs for calibration systems. This fundamental constraint creates a core contradiction: the requirement for high-precision space-based calibration clashes with hardware realities. Traditional high-level ADCs are crucial for high-precision measurements, but are often impractical due to size and power consumption issues, while low-level ADCs inherently lack sufficient quantization accuracy to meet stringent accuracy standards. Summary of the Invention
[0005] The purpose of this invention is to provide a method for enhancing the accuracy of jitter-assisted measurements in space-based calibration, in order to solve the problem that, under the strict constraints of satellite platform resources, low-bit analog-to-digital converters cannot meet the high-precision measurement requirements of space-based calibration systems due to their inherent insufficient quantization accuracy.
[0006] To achieve the above objectives, the present invention provides a method for enhancing the accuracy of jitter-assisted measurements in space-based calibration, comprising the following steps: S1. Receive continuous-time analog input signals from the space-based calibration system; the space-based calibration system is mounted on the satellite platform and, due to the strict limitations of the payload, uses a low-bit analog-to-digital converter for signal quantization; S2. Inject a zero-mean artificial jitter signal that follows a uniform distribution into the continuous-time analog input signal. The artificial jitter signal is independent of the continuous-time analog input signal to generate a composite analog signal. The amplitude range of the artificial jitter signal is equal to one quantization step of the low-order analog-to-digital converter. S3. Use a low-bit analog-to-digital converter to perform multiple independent quantization observations on the composite analog signal to obtain multiple quantized output values corresponding to discrete levels; S4. Calculate the arithmetic mean of multiple quantized output values, and use the arithmetic mean as a high-precision estimate of the amplitude of the continuous-time analog input signal; the variance of the arithmetic mean is given by the following formula: ; in, Represents variance. This represents a quantization step size of a low-order analog-to-digital converter, achieved by increasing the number of independent quantization observations. Arithmetic mean The measurement accuracy is improved without the need to increase the number of bits in the low-bit analog-to-digital converter.
[0007] Preferably, the distribution of the artificial jitter signal in S2 is represented as follows: ; in, Indicates artificial jitter signal. Indicates uniform distribution. This represents a quantization step size of the low-order analog-to-digital converter.
[0008] Preferably, the relationship between the single-quantization output value and the composite analog signal in S3 is expressed as follows: ; in, Indicates the first Quantization output value of each independent quantization observation This indicates the continuous-time analog input signal at the 1st... The amplitude value of each sampling point Indicates the first Artificial jitter signal injected during each independent quantization observation Indicates step size is Uniform midline quantizer, This represents a quantization step size of the low-order analog-to-digital converter.
[0009] Preferably, the formula for calculating the arithmetic mean in S4 is: ; in, Represents the arithmetic mean. Indicates the number of independent quantitative observations. Indicates the first The quantization output value of each independent quantization observation.
[0010] Preferably, for any independent quantization observation, the single quantization output value Only two adjacent discrete levels can be selected. and One of them, and the probabilities of taking these two discrete levels are respectively: ; ; in, Indicates the first Discrete level, It is an integer. Represents conditional probability. This represents the normalized bias, and , This indicates the bias introduced by the uniform centerline quantizer.
[0011] Preferred, single quantization output value The conditional expectation is equal to the amplitude of the simulator input signal, satisfying the following formula: ; in, It represents conditional expectation.
[0012] Preferably, in S4, according to the law of large numbers, the arithmetic mean converges with probability to the amplitude of the continuous-time analog input signal: ; in, It represents the arithmetic mean.
[0013] Therefore, the present invention employs the above-mentioned method for enhancing the accuracy of jitter-assisted measurements for space-based calibration, which has the following beneficial effects: (1) Improved accuracy: standard deviation of the estimator By increasing The standard deviation can be significantly smaller than the inherent resolution of the low-bit analog-to-digital converter. This results in a significant improvement in measurement accuracy.
[0014] (2) Resolution Improvement: The effective quantization step size of this method is Compared to a native low-bit analog-to-digital converter, the effective number of bits increases by approximately 12. The system resolution increases with the square root of the logarithm of the number of observations.
[0015] (3) Error convergence characteristics: The estimation error increases with the number of observations. The increase is based on The rate of decay; to double the measurement accuracy (i.e., halve the error), the number of independent quantized observations needs to be increased. It has been increased to four times its original size.
[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0017] Figure 1 This is a flowchart of a method for enhancing the accuracy of jitter-assisted measurements for space-based calibration according to the present invention; Figure 2 This is a schematic diagram of the signal processing link used in the embodiments of the present invention; Figure 3 This is a comparison chart of the original signal, single quantization output, and 100-times average quantization output after using a 4-bit analog-to-digital converter and adding random jitter in an embodiment of the present invention. Figure 4 This is a graph showing the relationship between the standard deviation of the error and the number of observations M in an embodiment of the present invention. Detailed Implementation
[0018] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely illustrates selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0019] Example like Figure 1 As shown, this invention provides a jitter-assisted measurement accuracy enhancement method for space-based calibration, which can be applied to the signal reception and processing stage of a space-based calibration system to improve the effective measurement accuracy of low-bit analog-to-digital converters, thereby meeting high-precision calibration requirements without increasing hardware power consumption and size. The method includes the following steps: S1. Receive continuous-time analog input signals from the space-based calibration system, which is mounted on the satellite platform. Due to the strict limitations of the payload, a low-bit analog-to-digital converter is used for signal quantization.
[0020] Let the continuous-time analog input signal be , This indicates the continuous-time analog input signal at the 1st... Without manual jitter, the amplitude value of each sampling point will produce a large quantization error when the low-bit analog-to-digital converter directly quantizes the continuous-time analog input signal, which limits the measurement accuracy.
[0021] like Figure 2 As shown, the received radio frequency signal passes through an antenna, a matched filter, and a down-conversion frequency in sequence to obtain a continuous-time analog input signal. .
[0022] S2. Inject a zero-mean artificial jitter signal that follows a uniform distribution into the continuous-time analog input signal to generate a composite analog signal. The amplitude range of the artificial jitter signal is equal to one quantization step of the low-order analog-to-digital converter.
[0023] like Figure 2 As shown, before analog-to-digital conversion, the artificially jittered signal is... Superimposed by adder The composite analog signal is obtained. Among them, artificial jitter signal The simulated noise is zero-mean, follows a uniform distribution, and and The distribution of mutually independent artificial jitter signals is represented as follows: ; in, Indicates uniform distribution. This represents a quantization step size of the low-order analog-to-digital converter.
[0024] S3. Use a low-bit analog-to-digital converter to perform multiple independent quantization observations on the composite analog signal to obtain multiple quantized output values corresponding to discrete levels; like Figure 2 As shown, the superimposed composite analog signal is sampled and quantized by a low-order analog-to-digital converter. Without artificial jitter, the... The amplitude of the continuous-time analog input signal at each sampling point The quantized output is denoted as , is represented as: ; in, This indicates the continuous-time analog input signal at the 1st... The amplitude value of each sampling point Indicates step size is A uniform centerline quantizer corresponds to the value of one least significant bit (LSB). Due to the bias of low-precision quantization, the amplitude of the continuous-time analog input signal is... With the output discrete level of the low-bit analog-to-digital converter The relationship between them can be represented as: ; in, , For the first low-bit analog-to-digital converter Discrete level, , The bias introduced by the uniform centerline quantizer is used to change the quantization behavior. An artificial dither signal with a known statistical distribution is injected. Adding this artificial dither signal can significantly improve the accuracy of the estimation. By adding artificial dither to the simulator of the low-bit analog-to-digital converter, the output of the i-th independent quantized observation can be expressed as: ; in, Indicates the first Quantization output value of each independent quantization observation Indicates the first Artificial jitter signals injected during each independent quantization observation.
[0025] because Corresponding to discrete levels, It can be rewritten as: ; The above surface, the quantized output value after adding artificial jitter. It is equal to the discrete level without artificial jitter. With a disturbance term sum.
[0026] S4. Calculate the arithmetic mean of multiple quantized output values and use the arithmetic mean as a high-precision estimate of the amplitude of the continuous-time analog input signal.
[0027] The quantized output value is then processed by arithmetic averaging to obtain a high-precision signal, denoted as . Arithmetic mean The calculation formula is: ; in, Represents the arithmetic mean. This represents the number of independent quantized observations, which is increased by adding the number of independent quantized observations. Arithmetic mean The measurement accuracy is improved without the need to increase the number of bits in the low-bit analog-to-digital converter.
[0028] Because the composite signal received by the uniform midline quantizer is Meanwhile, the amplitude range of the artificially jittered signal is limited to one quantization step, and the single quantization output value is... Only two adjacent discrete levels can be selected. and One of them, namely .
[0029] For any single independent quantization observation The conditional probability analysis for these two discrete levels is as follows: for The probability, that is, when At that time, there were: ; in It is the normalized bias, representing exist and The relative positions between them. Given a uniform distribution. The probability is: ; for The probabilities are: ; in, Indicates the first Discrete level, It is an integer. Represents conditional probability. This represents the normalized bias, and , This indicates the bias introduced by the uniform centerline quantizer.
[0030] Calculate conditional expectation : ; in, It represents conditional expectation.
[0031] The above formula shows that, under uniformly distributed artificial jitter injection, the conditional expectation of the quantized output value is equal to the amplitude of the original continuous-time analog input signal. That is, the estimator is unbiased.
[0032] According to the law of large numbers, when the number of independent quantified observations... When sufficiently large, the arithmetic mean converges with probability to the amplitude of the continuous-time analog input signal: ; in, It represents the arithmetic mean.
[0033] The precision of an estimator is quantified by its mean square error; for an unbiased estimator, the mean square error is equal to its variance. .
[0034] Given that jitter is uncorrelated with quantization error, a single observation value The variance is given by the sum of the jitter variance and the original quantization error variance: ; in, It is the variance of the uniform quantization error. It is an artificial shaking signal. The variance, therefore: ; because The observations are independent and uniformly distributed, and their sample mean variance is: ; in, Indicates variance.
[0035] The effects of this embodiment will be illustrated below through a specific simulation example.
[0036] The simulation scenario is configured as follows: a 4-bit low-order analog-to-digital converter is used, with a scale range of [0, 5]V and a quantization step size of... The input signal is a composite sine wave with a fundamental frequency of... sampling frequency Sampling time Seconds, each time data is collected Each sampling point has [number] sampling points. Before quantization, an independent artificial jitter signal is added to each sampling point, with the amplitude range of the artificial jitter signal being [[...]. ].
[0037] Figure 3 This demonstrates the impact of adding artificial jitter on signal averaging of a 4-bit low-order analog-to-digital converter (ADC) quantization. The original polytone signal (blue curve) is corrupted by quantization noise during a single sampling, exhibiting typical step-like distortion (red step curve). After 100 independent quantization observations and arithmetic averaging, the reconstructed signal (green step) maintains its basic signal shape while significantly reducing quantization artifacts. Figure 3 The gray dashed line represents the discrete quantization level. It can be seen that the arithmetic averaging process enables the system to effectively distinguish the intermediate voltage between two adjacent discrete levels, thus breaking through the nominal 4-bit resolution limit.
[0038] Figure 4 This shows the standard deviation of the error and the number of independent quantized observations. The experimental results (red curve) closely follow the theoretical relationship. Attenuation trend (blue dashed line), standard deviation of error from The voltage dropped from 0.1269V to The value was 0.0128V. This result is in high agreement with the theoretical analysis, verifying that the method in this embodiment can effectively suppress quantization error and achieve a significant improvement in measurement accuracy through manual jitter and multiple arithmetic averages.
[0039] Therefore, this invention employs the aforementioned method for enhancing the accuracy of space-based calibration measurements through jitter-assisted measurement. By injecting a uniformly distributed artificial jitter signal before the low-bit analog-to-digital converter (ADC) and performing multiple independent quantization observations and arithmetic averaging, the measurement accuracy of the space-based calibration system can be significantly improved without increasing the number of bits or power consumption of the ADC. This method is particularly suitable for resource-constrained satellite platforms and has significant engineering application value.
[0040] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A method for enhancing the accuracy of jitter-assisted measurements in space-based calibration, characterized in that, Includes the following steps: S1. Receive continuous-time analog input signals from the space-based calibration system; the space-based calibration system is mounted on the satellite platform and, due to the strict limitations of the payload, uses a low-bit analog-to-digital converter for signal quantization; S2. Inject a zero-mean artificial jitter signal that follows a uniform distribution into the continuous-time analog input signal. The artificial jitter signal is independent of the continuous-time analog input signal to generate a composite analog signal. The amplitude range of the artificial jitter signal is equal to one quantization step of the low-order analog-to-digital converter. S3. Use a low-bit analog-to-digital converter to perform multiple independent quantization observations on the composite analog signal to obtain multiple quantized output values corresponding to discrete levels; S4. Calculate the arithmetic mean of multiple quantized output values, and use the arithmetic mean as a high-precision estimate of the amplitude of the continuous-time analog input signal; the variance of the arithmetic mean is given by the following formula: ； in, Represents variance. This represents a quantization step size of a low-order analog-to-digital converter, achieved by increasing the number of independent quantization observations. Arithmetic mean The measurement accuracy is improved without the need to increase the number of bits in the low-bit analog-to-digital converter.
2. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 1, characterized in that, The distribution of the artificial jitter signal in S2 is represented as follows: ； in, Indicates artificial jitter signal, Indicates uniform distribution. This represents a quantization step size of the low-order analog-to-digital converter.
3. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 1, characterized in that, The relationship between the single-quantization output value and the composite analog signal in S3 is expressed as follows: ； in, Indicates the first Quantization output value of each independent quantization observation This indicates the continuous-time analog input signal at the 1st... The amplitude value of each sampling point Indicates the first Artificial jitter signal injected during each independent quantization observation Indicates step size is Uniform midline quantizer, This represents a quantization step size of the low-order analog-to-digital converter.
4. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 1, characterized in that, The formula for calculating the arithmetic mean in S4 is: ； in, Represents the arithmetic mean. Indicates the number of independent quantitative observations. Indicates the first The quantization output value of each independent quantization observation.
5. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 3, characterized in that, For any independent quantized observation, the single quantized output value Only two adjacent discrete levels can be selected. and One of them, and the probabilities of taking these two discrete levels are respectively: ； ； in, Indicates the first Discrete level, It is an integer. Represents conditional probability. This represents the normalized bias, and , This indicates the bias introduced by the uniform centerline quantizer.
6. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 5, characterized in that, Single quantization output value The conditional expectation is equal to the amplitude of the simulator input signal, satisfying the following formula: ； in, It represents conditional expectation.
7. The method for enhancing the accuracy of jitter-assisted measurement in space-based calibration according to claim 6, characterized in that, In S4, according to the law of large numbers, the arithmetic mean converges with probability to the amplitude of the continuous-time analog input signal: ； in, It represents the arithmetic mean.