A method and apparatus for evaluating the resolving performance of an aperture-encoding imaging system

Abstract

The application relates to a method and device for evaluating the resolution performance of an aperture coding imaging system, which comprises the following steps: obtaining echo signals of a target and parameter data of an aperture coding imaging system with random phase coding, which is to be evaluated in terms of resolution performance, by multiple irradiations of the target by the imaging system; processing the echo signals and the parameter data to obtain a three-dimensional radiation field pattern in an imaging plane and a system energy noise ratio; calculating a threshold constant plane according to the system energy noise ratio, a right tail function of a Gaussian distribution and a preset resolution error probability; the space variable interval corresponding to a cross section of the three-dimensional radiation field pattern is a resolution unit of the system; and finally, the resolution performance of the system is evaluated according to the size of the resolution unit. The method considers noise when evaluating the resolution performance of the system, so that the evaluation scheme is more suitable for actual scenes.

Description

Technical Field

[0001] This application relates to the field of radar imaging technology, and in particular to an evaluation method and measuring device for evaluating the resolution performance of an aperture-coded imaging system. Background Technology

[0002] In recent years, metamaterial aperture-coded imaging systems, as a novel imaging radar technology, have provided an efficient and economical solution for microwave forward-looking and staring high-resolution imaging. Metamaterials refer to artificial composite electromagnetic structures formed by the macroscopic arrangement of subwavelength-scale units, exhibiting unique electromagnetic properties not found in natural electromagnetic materials, allowing for flexible modulation of electromagnetic wave propagation. Aperture coding technology involves randomly modulating electromagnetic waves incident on a coding plate using a coding antenna, creating a non-uniform electromagnetic wavefront in the transmission channel, resulting in a rich random radiation field in the target area. As the coding system develops richer random radiation patterns, the more spatial information of the target can be acquired with a limited number of measurements, increasing the potential for super-resolution imaging using echo signals and super-resolution algorithms. This imaging system uses metamaterials as modulation devices, offering advantages over phased arrays in terms of lower cost and energy consumption, while avoiding the dependence of the imaging system's lateral resolution performance on relative motion, enabling forward-looking and staring imaging. Therefore, metamaterial aperture-coded imaging has significant advantages such as low cost and forward-looking imaging capabilities, complementing traditional radar imaging.

[0003] Due to the flexibility of scheme design and the complexity of the analysis process, aperture-coded imaging has long suffered from fragmented, piecemeal, and one-sided problems in the analysis of resolution and imaging performance. This has limited the development of this imaging system to a localized level, and it currently remains mainly in the laboratory demonstration stage. According to current research results, the resolution performance of metamaterial aperture-coded imaging systems is affected by various factors such as the waveform of the coded signal, imaging distance, array configuration, and super-resolution imaging algorithms. Different scholars often analyze the resolution performance of imaging systems based on some of these factors to derive local quantitative relationships, but none of them consider the influence of random noise, thus limiting their application value. Summary of the Invention

[0004] Therefore, it is necessary to provide an evaluation method and measurement device for assessing the resolution performance of an aperture-coded imaging system, which is used to quantitatively evaluate and analyze the impact of noise on the resolution performance of the system, in order to address the aforementioned technical problems.

[0005] A method for evaluating the resolving performance of an aperture-coded imaging system, the method being applied to an aperture-coded imaging system comprising:

[0006] The target echo signal is acquired by illuminating the target multiple times using an aperture-coded imaging system employing random phase coding, which is to be evaluated for resolution performance.

[0007] Acquire parameter data of the aperture-coded imaging system, including the center frequency of the narrowband signal, the element spacing, the number of elements, the plane where the target is located, and the radial distance between the aperture-coded antennas;

[0008] The parameter data is processed to obtain a stereo pattern of radiation field in the imaging plane.

[0009] The system energy-to-noise ratio is calculated based on the target echo signal.

[0010] The size of the resolving unit is calculated based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability.

[0011] The resolution performance of the system is evaluated on the stereo pattern based on the size of the resolution unit.

[0012] In one embodiment, the parameter data is processed to obtain a stereo pattern related to the radiation field in the imaging plane, and the pattern along the X-axis is represented as follows:

[0013]

[0014] In the above formula, k represents the center frequency of the narrowband signal, d represents the element spacing, N represents the number of elements, and R represents the radial distance between the target plane and the aperture-coded antenna.

[0015] In one embodiment, a threshold is calculated based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and a preset resolution error probability. A spatial variable interval of the radiation field correlated with this threshold is obtained on the radiation field correlation pattern as the resolution cell size. The resolution cell size along the X-direction is calculated using the following formula:

[0016]

[0017] In the above formula, Δx represents the resolution cell size, F represents the radiation field correlation pattern, Q represents the right-tail function of the Gaussian distribution, and P... e The error probability is represented by ENR, and the system energy-to-noise ratio is represented by ENR.

[0018] An evaluation apparatus for assessing the resolving performance of an aperture-coded imaging system, the apparatus comprising:

[0019] The target echo signal acquisition module is used to acquire the target echo signal, which is obtained by irradiating the target multiple times by an aperture-coded imaging system using random phase coding, which is to be evaluated for resolution performance.

[0020] The parameter data acquisition module is used to acquire the parameter data of the aperture-coded imaging system. The parameter data includes the center frequency of the narrowband signal, the element spacing, the number of elements, the plane where the target is located, and the radial distance between the aperture-coded antennas.

[0021] A stereo pattern acquisition module is used to process the parameter data to obtain a stereo pattern related to the radiation field in the imaging plane;

[0022] The system energy-to-noise ratio calculation module is used to calculate the system energy-to-noise ratio based on the target echo signal.

[0023] The resolution cell size acquisition module is used to calculate the resolution cell size based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability.

[0024] A resolution performance evaluation module is used to evaluate the resolution performance of the system based on the size of the resolution unit on the stereo pattern.

[0025] The aforementioned evaluation method and measurement device for assessing the resolving performance of an aperture-coded imaging system involves acquiring target echo signals obtained from multiple illuminations of the target by the aperture-coded imaging system employing random phase coding, along with parameter data of the imaging system. This data is processed to obtain a radiation field correlation pattern and a system energy-to-noise ratio (ENN) within the imaging plane. A threshold is then calculated based on the EMN, the right-tail function of the Gaussian distribution, and a preset resolution error probability. The spatial variable range obtained by aligning the threshold in the stereo pattern is used as the resolving unit size of the aperture-coded imaging system. Finally, the resolving performance of the system is evaluated based on the resolving unit size. This method considers noise when evaluating the system's resolving performance, making the evaluation scheme more relevant to real-world scenarios. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating a method for evaluating the resolution performance of an aperture-coded imaging system in one embodiment.

[0027] Figure 2 This is a schematic diagram of the geometry of a one-dimensional linear array aperture-coded imaging system in one embodiment;

[0028] Figure 3 This is a schematic diagram of the geometry of a two-dimensional linear array aperture-coded imaging system in one embodiment;

[0029] Figure 4 This is a one-dimensional pattern of different random phase coding methods in one embodiment;

[0030] Figure 5This is a schematic diagram illustrating the process of using a detector to distinguish adjacent imaging points in one embodiment;

[0031] Figure 6 This is a schematic diagram illustrating the error detection probability in one embodiment;

[0032] Figure 7 This is a schematic diagram illustrating the distribution of test statistics under two hypotheses in one embodiment.

[0033] Figure 8 This is a schematic diagram of the resolution estimation algorithm in one embodiment;

[0034] Figure 9 This is a schematic diagram illustrating the mapping relationship between a resolution threshold and the error probability, where the left figure is the theoretical curve and the right figure is the Monte Carlo experimental result;

[0035] Figure 10 This is a structural block diagram of an imaging system resolution performance evaluation device in one embodiment. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0037] To address the lack of existing solutions that statistically consider the impact of signal-to-noise ratio on metamaterial aperture-coded imaging systems and propose quantifiable methods, this paper presents a method for evaluating the resolving performance of such imaging systems, including:

[0038] Step S100: Acquire the target echo signal, which is obtained by irradiating the target multiple times by an aperture-coded imaging system using random phase coding, which is to be evaluated for resolution performance.

[0039] Step S110: Obtain parameter data of the aperture-coded imaging system, including the center frequency of the narrowband signal, the spacing between array elements, the number of array elements, the plane where the target is located, and the radial distance between the aperture-coded antennas.

[0040] Step S120: Process the parameter data to obtain a stereo pattern related to the radiation field in the imaging plane;

[0041] Step S130: Calculate the system energy-to-noise ratio based on the target echo signal;

[0042] Step S140: Calculate the size of the resolving unit based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability.

[0043] Step S150: Evaluate the resolution performance of the system based on the resolution cell size on the stereo pattern.

[0044] The imaging system resolution performance evaluation method in this paper mainly focuses on the aperture-coded imaging system. Since this system is a relatively new imaging system, the imaging principle of the aperture-coded imaging system is introduced first here.

[0045] Based on the imaging principle of aperture coding systems, the mathematical model of the imaging problem can be described as follows:

[0046]

[0047] In formula (1), t l For the l-th sampling time, r m Let S(t) be the position vector of the launch array pointing towards the space target. l ,r m ) for t l The time-coded aperture at r m Complex amplitude of random radiation field at location σ m The scattering coefficient of the target in r m The distribution of w(t) l ) refers to t l Time-of-flight noise complex amplitude, S r (t l ) refers to t l The time system receives the echo.

[0048] The matrix consisting of the reference signals at all times and at grid points in the target region is called the reference signal matrix, denoted by S. The imaging problem can then be simplified as follows:

[0049] Sr=S·σ+w (2)

[0050] In existing technologies, correlation matched filtering, also known as the correlation method, is equivalent to the back projection method or the generalized matched filtering algorithm. It is a fundamental imaging algorithm for aperture-coded imaging, namely:

[0051] σ=S H ·Sr (3)

[0052] Correlation methods offer strong noise tolerance and robust imaging results, but their resolution is limited. When the system uses a single-frequency or narrowband signal, a one-dimensional linear array coded aperture imaging system (see reference) is suitable. Figure 2 The analytical expression for the correlation function of the imaging geometry diagram shown is:

[0053]

[0054] Two-dimensional linear array coded aperture imaging system (reference) Figure 3The analytical expression for the correlation function of the imaging geometry diagram shown is:

[0055]

[0056] Since the graph of the above correlation function is similar to an array pattern, this function is also referred to as a correlation pattern in this paper.

[0057] Next, the principle of the resolution performance evaluation method mentioned in this paper will be explained. It should be noted that this paper only uses the following imaging system as an example to illustrate this method. In the embodiments described, this method can also be applied to other aperture-coded imaging system structures.

[0058] The aperture-coded imaging system includes a control terminal, a vector grid analyzer, a transmitter, an encoding module, an aperture-coded antenna, and a receiver. The control terminal controls the vector grid analyzer to transmit microwave signals to the target via the transmitter, while simultaneously controlling the encoding module to drive the aperture-coded antenna to randomly modulate the phase of the transmitted microwave signals. The vector grid analyzer then receives the target echo signal reflected by the target through the receiver. Furthermore, the resolution performance of the aperture-coded imaging system is evaluated using the resolution performance evaluation method proposed in this paper within the control terminal.

[0059] In deriving the method presented in this paper, it is assumed that the aperture-coded imaging system uses random phase coding, transmits narrowband signals, and the system imaging algorithm is not limited. This method is a universally applicable and effective analytical tool independent of specific algorithms. It uses a statistical decision maker to distinguish adjacent point targets in space, introducing the concepts of probability and statistics into the resolution characterization of the aperture-coded imaging system. By measuring appropriate test statistics, this method transforms the problem of resolving two points in space into a threshold decision problem, and by introducing a signal-to-noise ratio (SNR) influence factor, it can quantify the impact of SNR on the resolution threshold of the imaging system.

[0060] To create a highly uncorrelated random radiation field in space, a control terminal needs to perform spatiotemporal random coding on the coding board via a coding module (common random distributions include Bernoulli distribution, Hadamard distribution, Gaussian distribution, uniform distribution, sparse random distribution, etc.) to achieve uncorrelated transmission between different array elements and a spatiotemporally uncorrelated random radiation field in the target area. With an array size of 16×16 and an array spacing of 51m, transmitting a narrowband signal with a center frequency of 10GHz, and a radial distance of 100m from the imaging plane, the correlation pattern of the reference radiation field along the lateral direction within the imaging plane is shown below. Figure 4 As shown, the one-dimensional and two-dimensional related radiation patterns satisfy formulas (4) and (5), respectively.

[0061] When the imaging scene and radar system parameters are determined, the resolution cell size of the system can be estimated based on the minimum error probability detection theory and the aforementioned related radiation patterns. The minimum error probability detector is a Bayesian method of hypothesis testing that selects the decision with the minimum error probability by specifying prior probabilities. The error probability is defined as:

[0062] P e =P(H0|H1)P(H1)+P(H1|H0)P(H0)

[0063]

[0064] The problem of distinguishing two adjacent points in space can be described as the following decision problem:

[0065]

[0066] In formula (7), x[n] is the received signal, s0[n] is the reference signal of the reference cell, and s1[n] is the reference signal immediately adjacent to the reference signal. Assuming that the prior probability from each point in the imaging region is the same, the minimum probability test will select the decision with the maximum likelihood.

[0067] The judgment process is as follows Figure 5 As shown, the error probability is expressed as follows:

[0068]

[0069] To simplify the analysis of the error probability of the test statistic, the test statistic is transformed into:

[0070]

[0071] The simplified decision criterion is: Decision H1 is made when T(x) > 0, and decision H0 is made when T(x) < 0. Furthermore:

[0072]

[0073]

[0074]

[0075] The PDFs of both hypotheses are symmetric about the y-axis, and the error probabilities are as follows: Figure 6 As shown, the error probability can be expressed as:

[0076]

[0077] In formula (13), When implementing this method, the error probability can be set based on empirical values.

[0078] Therefore, the threshold for a suitable imaging unit is:

[0079]

[0080]

[0081] In formulas (14) and (15), k represents the center frequency of the narrowband signal, d represents the element spacing, N represents the number of elements, R represents the radial distance between the target plane and the aperture-coded antenna, Δx represents the threshold interval, F represents the radiation field correlation pattern, Q represents the right-tail function of the Gaussian distribution, and P e The value represents the probability of a resolution error, and ENR represents the system energy-to-noise ratio.

[0082] Furthermore, simulation experiments demonstrate that the target spacing Δx in the imaging space is related to the resolution error probability P. e It follows the relationship shown in formula (14), such as Figure 7 As shown, the distribution of the test statistic is calculated under two hypotheses, where the target echo distribution changes with the change of Δx under the two hypotheses, and the overlap area of ​​the two PDFs is P. e .

[0083] In fact, for a system, the function value corresponding to the inverse function in formula (14) is a constant. The cross section of the plane of this constant and the envelope of the stereo pattern is the size of the system resolution threshold to be sought. In a single dimension (such as the horizontal x-axis), this constant is represented as a range of values. The single dimension of the stereo pattern along the horizontal x-axis is represented by formula (15).

[0084] In the specific implementation process according to the method in this paper, after the aperture coding imaging system is built, it is necessary to first set the minimum resolution error probability required by the system, and then determine the key parameters of the system, that is, the parameter data referred to in step S110, such as the center frequency k of the narrowband signal, the element spacing d, the number of elements N, and the radial distance R between the imaging plane and the coding plate, in order to estimate the correlation coefficient between each spatial position in the imaging plane.

[0085] Next, the system is used to acquire the target echo, and the target (such as a metal patch) is positioned within the imaging plane. The system's control terminal simultaneously controls the vector network analyzer and the encoding module. The vector network analyzer transmits and receives microwave signals via an external transmitter and receiver. The aperture-coded antenna, driven by the encoding module, randomly modulates the phase of the incident wave signal to obtain a spatiotemporally independent random radiation field. The pseudo-random signal reflected by the target is received by the receiver.

[0086] In step S130, the system energy-to-noise ratio (ENR) is calculated based on the target echo data. Specifically, according to experimental and simulation verification, the amplitude of the reference signal based on random phase coding approximately follows a Gaussian distribution; therefore, both the echo signal and random noise can be regarded as random complex Gaussian distributions.

[0087] Before transmitting the signal, the amplitude A of random noise in space is measured using a vector network analyzer. n ,power Among them, L n The number of noise amplitude measurement points. This refers to the square of the noise amplitude obtained in the l-th measurement. After the coded transmission system starts, the echo power is estimated after each acquisition of the echo signal amplitude and phase. Among them, A r This refers to the sampled echo amplitude, L r The number of points for measuring the amplitude of the echo signal. This refers to the square of the echo amplitude obtained in the l-th measurement. Since the received echo S... r [n] = s[n] + w[n], and the signal s[n] and noise w[n] are independent of each other. Therefore, the echo signal power is: The system energy-to-noise ratio measurement results are as follows:

[0088]

[0089] Finally, the resolution cell size of the system can be obtained according to formulas (14) and (15). Subsequently, the resolution performance of the system can be evaluated based on this resolution estimate.

[0090] In this embodiment, the resolution estimation algorithm based on the statistical minimum error probability constraint is as follows: Figure 8 As shown.

[0091] In this paper, the feasibility and effectiveness of the proposed method for evaluating actual resolution are also verified through simulation, such as... Figure 9 The diagram shown illustrates the mapping relationship between the discrimination threshold and the error probability. Figure 9 (a) is P e A schematic diagram of the theoretical curve relating to Δx. Figure 9 (b) is P e A schematic diagram of the simulation results relating to Δx.

[0092] The aforementioned method for evaluating the resolution performance of aperture-coded imaging systems introduces energy-to-noise ratio (ENR) into the quantification process of system resolution performance for the first time, improving the evaluation system for aperture-coded imaging systems and making it more suitable for practical application scenarios. It provides theoretical guidance for the construction of imaging scenarios and the setting of system parameters in practical applications. To quantify the impact of ENR on the imaging system, this method constructs a minimum error probability decision detector, simplifying the decision process to a comparison and counting process between the test statistic and the value of 0. Finally, theoretical and simulation verification demonstrates the mapping relationship between the resolution threshold and the minimum error probability when the system parameters and ENR are determined. To measure the ENR of the imaging system, this method equates the measurement of the reference signal energy of the random phase-coded imaging system to the power measurement of a random Gaussian signal. Through reference signal matrix derivation and simulation statistics, it is concluded that the temporal distribution of the reference signal under this coding method follows a Gaussian distribution. Analytical expressions for the key system parameters k (spatial frequency of the narrowband signal), R (radial distance between the imaging plane and the coding aperture), d (element spacing), N (number of elements), and ENR (system power-to-noise ratio) are given (see equations (19) and (20)). Therefore, in practical applications, the imaging resolution can be directly estimated from the above key system parameters. Furthermore, the resolution performance of the system can be evaluated based on this resolution estimate to assist in issues such as system parameter setting, scene construction, mesh generation during the imaging process, and algorithm optimization.

[0093] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0094] In one embodiment, such as Figure 10 As shown, a measurement device for an aperture-coded imaging system is provided, comprising: a target echo signal acquisition module 200, a parameter data acquisition module 210, a stereo pattern acquisition module 220, a system energy-to-noise ratio calculation module 230, a threshold interval acquisition module 240, and a resolution estimation module 250, wherein:

[0095] The target echo signal acquisition module 200 is used to acquire the target echo signal, which is obtained by the aperture-coded imaging system to be evaluated for resolution performance by scanning the target multiple times.

[0096] The parameter data acquisition module 210 is used to acquire the parameter data of the aperture-coded imaging system. The parameter data includes the center frequency of the narrowband signal, the element spacing, the number of elements, the plane where the target is located, and the radial distance between the aperture-coded antennas.

[0097] The stereo pattern acquisition module 220 is used to process the parameter data to obtain a stereo pattern related to the radiation field in the imaging plane;

[0098] The system energy-to-noise ratio calculation module 230 is used to calculate the system energy-to-noise ratio based on the target echo signal.

[0099] The resolution unit size acquisition module 240 is used to calculate the resolution unit size based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability.

[0100] The resolution performance evaluation module 250 is used to evaluate the resolution performance of the system based on the size of the resolution unit on the stereo pattern.

[0101] Specific limitations regarding the measuring device can be found in the above section on the limitations of the resolution performance evaluation method for aperture-coded imaging systems, and will not be repeated here. Each module in the aforementioned measuring device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0102] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0103] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for evaluating the resolving performance of an aperture-coded imaging system, characterized in that, The method, when applied to an aperture-coded imaging system, includes: The target echo signal is acquired by illuminating the target multiple times using an aperture-coded imaging system employing random phase coding, which is to be evaluated for resolution performance. Acquire parameter data of the aperture-coded imaging system, including the center frequency of the narrowband signal, the element spacing, the number of elements, the plane where the target is located, and the radial distance between the aperture-coded antennas; The parameter data is processed to obtain a stereo pattern of radiation field in the imaging plane. The system energy-to-noise ratio is calculated based on the target echo signal. The size of the resolving unit is calculated based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability. The resolution performance of the system is evaluated on the stereo pattern based on the size of the resolution unit.

2. The method according to claim 1, characterized in that, The parameter data is processed to obtain a stereo pattern of the radiation field in the imaging plane, and the pattern along the X-axis is represented as follows: In the above formula, k represents the center frequency of the narrowband signal, d represents the element spacing, N represents the number of elements, and R represents the radial distance between the target plane and the aperture-coded antenna.

3. The method according to claim 2, characterized in that, A threshold is calculated based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and a preset resolution error probability. The spatial variable interval of the radiation field correlation pattern aligned with this threshold is then used as the resolution cell size. The resolution cell size along the X-direction is calculated using the following formula: In the above formula, Δx represents the resolution cell size, F represents the radiation field correlation pattern, Q represents the right-tail function of the Gaussian distribution, and P... e The error probability is represented by ENR, and the system energy-to-noise ratio is represented by ENR.

4. An evaluation device for assessing the resolving performance of an aperture-coded imaging system, characterized in that, The device includes: The target echo signal acquisition module is used to obtain the target echo signal by irradiating the target multiple times by an aperture-coded imaging system employing random phase coding, which is to be evaluated for resolution performance. The parameter data acquisition module is used to acquire the parameter data of the aperture-coded imaging system. The parameter data includes the center frequency of the narrowband signal, the element spacing, the number of elements, the plane where the target is located, and the radial distance between the aperture-coded antennas. A stereo pattern acquisition module is used to process the parameter data to obtain a stereo pattern related to the radiation field in the imaging plane; The system energy-to-noise ratio calculation module is used to calculate the system energy-to-noise ratio based on the target echo signal. The resolution cell size acquisition module is used to calculate the resolution cell size based on the system energy-to-noise ratio, the right-tail function of the Gaussian distribution, and the preset resolution error probability. A resolution performance evaluation module is used to evaluate the resolution performance of the system based on the size of the resolution unit on the stereo pattern.

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