A complementary waveform design method for SAR range sidelobe suppression

Abstract

The application discloses a complementary waveform design method for SAR range sidelobe suppression, and is applied to the technical field of radars, so as to solve the adverse effects caused by waveform agility, explore the feasibility of waveform agility in improving the performance of SAR range sidelobe suppression, and meanwhile, maintain the range resolution, wherein the concept of complementary sequences is introduced. The sidelobes of the complementary sequences can theoretically offset each other in any non-zero phase lag. However, directly applying the complementary sequences to SAR may cause the quality of SAR images to decrease. Therefore, the amplitude and phase modulation effects introduced by waveform agility are jointly considered, and the low sidelobe waveform design for SAR imaging is realized without expanding the main lobe.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a complementary waveform design technique for suppressing range sidelobes in SAR imaging. Background Technology

[0002] Synthetic Aperture Radar (SAR) is a radar system capable of achieving high-resolution imaging under various weather conditions. SAR achieves high resolution in the range direction by transmitting a linearly frequency-modulated signal with a large time-width product and compressing the pulse through matched filtering at the receiver. Utilizing synthetic aperture technology, SAR can also achieve high resolution in the azimuth direction, thus finding wide applications in disaster monitoring, resource exploration, geological mapping, and military reconnaissance.

[0003] Range sidelobes are a common concern in SAR imaging. Sidelobes from strongly scattering targets can obscure weak targets, degrading SAR image quality and increasing the difficulty of image interpretation. Traditional single-waveform designs, limited by the principle of energy conservation, reduce range resolution while reducing sidelobes. Typical methods for suppressing range sidelobes can be categorized into two main types: receiver processing and waveform optimization. Among these, the Spatial Variation Apodization (SVA) method eliminates sidelobes through different weighting functions, but this nonlinear processing can reduce the signal-to-noise ratio (SNR) and lead to the loss of phase information. Nonlinear Frequency Modulation (NLFM) signals have attracted widespread attention due to their potential in reducing sidelobes, but their design remains constrained by energy conservation.

[0004] The paper "First demonstration of echo separation for orthogonal waveform encoding MIMO-SAR based on airborne experiments" (IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–16, 2022) proposes using chaotic frequency modulation (CFM) signals to overcome this limitation, achieving range sidelobe cancellation by transmitting different CFM signals between different pulses. However, waveforms transmitted in different azimuth directions also bring new challenges, such as energy spikes caused by Doppler spectrum aliasing and incoherent azimuth compression. The paper "New insights into SAR alternate transmitting mode based on waveform diversity" (IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–9, 2022) proposes an azimuth compensation algorithm to eliminate azimuth ambiguity caused by waveform agility, but this process reduces the signal-to-noise ratio and compensates different waveforms to the same waveform. Summary of the Invention

[0005] In existing SAR imaging technologies, the range sidelobe problem can cause sidelobes of strong scattering targets to cover weak targets, reducing SAR image quality and increasing the difficulty of image interpretation. To overcome the energy conservation limitations of traditional single-waveform designs, this invention proposes a SAR range sidelobe suppression method based on complementary waveform design. This method fully utilizes the transmitter's degrees of freedom to transmit multiple waveforms and leverages the information differences between different pulses to reduce the sidelobe level while maintaining constant range resolution.

[0006] The technical solution adopted in this invention is: a complementary waveform design method for SAR range sidelobe suppression, comprising:

[0007] S1. Transmit complementary waveforms between different pulses;

[0008] S2. Based on the complementary waveforms of step S1, with the goal of minimizing the integral sidelobe level of the point spread function weighted, spectral constraints and constant mode constraints are introduced to construct a waveform optimization problem.

[0009] S3. Introduce two auxiliary variables to replace the variables in the spectrum constraint and the constant mode constraint respectively; and use the auxiliary variables to reconstruct the waveform optimization problem in step S2.

[0010] S4. Minimize the augmented Lagrangian function by iteratively optimizing the waveform parameters to obtain the final transmitted signal.

[0011] The beneficial effects of this invention are as follows: This invention proposes a complementary waveform design method to suppress range sidelobes in SAR imaging. This method overcomes the limitations of traditional single-waveform design by transmitting multiple complementary waveforms and utilizing the information differences between them. The SAR waveform optimization problem is formulated as a non-convex optimization problem and solved using the Inaccurate Alternating Direction Penalty Method (IADPM) framework. This method can effectively handle complex optimization problems and find approximate solutions. The augmented Lagrangian function is used to handle constraints in the optimization problem, enabling the algorithm to satisfy spectral constraints while maintaining constant waveform amplitude, thus improving the algorithm's practicality and flexibility. Iterative Sequential Quadratic Optimization (ISQO) is employed to solve the non-convex quartic optimization subproblem. This method effectively approximates the optimal solution by sequentially solving a series of approximate problems. Adaptive Lagrangian multiplier and penalty function parameter update rules are introduced into the algorithm. These rules dynamically adjust the parameters according to the changes in the residuals, thereby promoting the convergence of the algorithm. Attached Figure Description

[0012] Figure 1 It is a single waveform limitation diagram.

[0013] Figure 2 This is a schematic diagram of waveform agility.

[0014] Figure 3 This is a flowchart of the SAR-PSFS method.

[0015] Figure 4 This is a comparison chart of the autocorrelation function (ACF) of different waveform designs.

[0016] Figure 5 These are images showing the compression results of point target imaging distances under different waveforms;

[0017] Among them, (a) is the point target imaging range compression result corresponding to LFM, (b) is the point target imaging range compression result corresponding to NLFM, (c) is the point target imaging range compression result corresponding to MM-WPSL, and (d) is the point target imaging range compression result corresponding to SAR-PSFS.

[0018] Figure 6 These are images showing the frequency-Doppler domain imaging results under different waveforms;

[0019] Among them, (a) is the frequency-Doppler domain imaging result corresponding to LFM, (b) is the frequency-Doppler domain imaging result corresponding to NLFM, (c) is the frequency-Doppler domain imaging result corresponding to MM-WPSL, and (d) is the frequency-Doppler domain imaging result corresponding to SAR-PSFS.

[0020] Figure 7 These are images of point targets under different waveforms;

[0021] Among them, (a) is the point target imaging result corresponding to LFM, (b) is the point target imaging result corresponding to NLFM, (c) is the point target imaging result corresponding to MM-WPSL, and (d) is the point target imaging result corresponding to SAR-PSFS.

[0022] Figure 8 This is a comparison chart of the distance profiles of different waveforms.

[0023] Figure 9 This is a distributed scene imaging result image;

[0024] Among them, (a) is the distributed scene imaging result corresponding to LFM, (b) is the distributed scene imaging result corresponding to NLFM, (c) is the distributed scene imaging result corresponding to MM-WPSL, and (d) is the distributed scene imaging result corresponding to SAR-PSFS. Detailed Implementation

[0025] This invention is mainly verified by simulation experiments, and all steps and conclusions are verified by simulation in Matlab.

[0026] Step 1: Establish the signal model. Based on the parameters of the SAR system, such as carrier frequency f0 and pulse repetition frequency f... a A SAR signal model is established, which considers target scattering characteristics and waveform transmission characteristics. For example... Figure 1 As shown, the limitations of a single waveform design are illustrated, thus prompting consideration of complementary waveform design.

[0027] In SAR signal models, target scattering is considered to remain unchanged within small variations in the observation angle. In side-look focus mode, the expected echo of a point target can be expressed as:

[0028]

[0029] Where t and η represent the fast and slow time variables, respectively, σ0 represents the radar cross-section of the point target, and ω r (t) and ω a (η) represent the fast time envelope and the slow time envelope, respectively, where f0 is the carrier frequency, and η c R(η) represents the zero Doppler time, R(η) is the slant range between the radar and the target at slow time η, c is the speed of light, and f is the speed of light. a δ is the pulse repetition frequency (PRF) and the Dirac function.

[0030] Consider ωr If (t) is a rectangular window, then the distance-compressed echo signal s0(t,η) can be expressed as:

[0031]

[0032] in For transmitting signal x m The distance compression result of (t).

[0033] make For deterministic signals The distance compression result (such as LFM) is then It can be represented as:

[0034]

[0035] Where u m (t) represents the value in the m-th pulse. Modulation; deterministic signals, such as LFM (Linear Frequency Modulation).

[0036] Therefore, the expression for the original pulse compression result can be reformulated as:

[0037]

[0038] make The above equation is then broken down into the sum of the main lobe region and the side lobe regions:

[0039]

[0040] Where b0 is the maximum value of the matched filter, and w(t) is a rectangular window with 1 in the main lobe region and 0 in other regions. It is the complementary window function of w(t), satisfying

[0041] Due to the law of conservation of energy, the matched filter value is the same for different waveforms within the main lobe, so d(t,η) in the expression can be simplified to b0. From s3(t,η), it can be seen that the imaging expression for the main lobe region is consistent with the traditional transmission mode. However, due to the additional term d(t,η) introduced by waveform agility in the side lobe region, amplitude and phase modulation are added in the azimuth dimension. Therefore, the SAR image can be expressed as:

[0042]

[0043] in R0 represents the slant range at the zero Doppler moment, p a (η) is the amplitude of the impulse response in the azimuth dimension, while h(t,η) is the compression result. Specifically, pa (η) is ω a (η-η c This is a manifestation of the relationship in the direction dimension, and it is reflected in p. a (η) as The multiplier factor of the window function directly affects the signal amplitude in the main lobe region; h(t,η) is In orientation processing, this relationship is reflected in h(t,η) as... The multiplier factor of the window function directly affects the signal amplitude and phase in the sidelobe region.

[0044] While maintaining consistent waveform energy, waveform agility does not affect the energy accumulation of SAR. However, in the sidelobe region, waveform agility adds an azimuth modulation term. Therefore, by jointly optimizing all transmitted waveforms, it is theoretically possible to suppress both range sidelobes and amplitude-phase modulation simultaneously.

[0045] Step 2, Complementary Waveform Design. Introducing the concept of complementary sequences, a waveform optimization problem is constructed, aiming to minimize the point spread function weighted integrated sidelobe level (PSFWISL). Waveform agility methods for range sidelobe suppression are implemented by transmitting different waveforms between different pulses, such as… Figure 2 As shown.

[0046] First, we introduce the concept of complementary sequences, and let the sequence set be... Indicates the transmitted signal x m Discrete form of (t), where Let m = 1, ..., M represent the set of complex numbers, where m = 1, ..., M represents the discrete-phase coded signal transmitted at the m-th pulse time, M is the total number of pulse times, and N is the number of coded sub-pulses. The sequence set... When the sum of the autocorrelation of the sequences at any non-phase lag k is zero, the sequence set is called a complementary sequence, i.e.:

[0047]

[0048] in It represents the sequence x m The aperiodic autocorrelation function at lag k yes The discrete form of .

[0049] Combining the concept of complementary sequences and the azimuth characteristics of SAR echoes, a waveform optimization problem was constructed. The optimization objective is to minimize the point spread function weighted integral sidelobe level (PSFWISL), which is defined as:

[0050]

[0051] Where ω(k,a) represents the weights of the SAR imaging results at lag k and the a-th azimuth angle, h m (a) represents the response at the a-th azimuth angle.

[0052] Step 3, Problem Construction. The waveform optimization problem is formulated as a non-convex optimization problem with a fourth-order objective function.

[0053] To improve the adaptability of the designed phase-coded signal and prevent interpolation operations from affecting signal performance, spectral constraints are introduced:

[0054]

[0055] Where f l Let be the discrete Fourier transform vector of the l-th frequency point. f l The conjugate transpose of q(l,m) represents the value of the m-th spectral mask at the l-th frequency. Specifically, q(l,m) is a window in the frequency domain, which can be a rectangular window, Hanning window, or other window functions.

[0056] To avoid degradation or distortion when generating waveforms in a SAR system, constant mode constraints are considered:

[0057]

[0058] Considering the above factors, the waveform optimization problem can be described as follows:

[0059]

[0060] Among them, J k Let J represent a matrix. k (i,j)=1 if ji=k, else J k (i,j)=0, this optimization problem is a non-convex optimization problem with a fourth-order objective function.

[0061] Step four involves employing the Inexact Alternating Direction Penalty Method (IADPM). An auxiliary variable is introduced, transforming the original problem into a minimization problem of the augmented Lagrangian function. The discretized set of transmitted signals is then iteratively updated using the IADPM framework. Auxiliary variable Y (t) Lagrange multipliers Sum of penalty function parameters

[0062] To solve the above fourth-order nonconvex optimization problem, and considering that directly solving the original problem is very challenging, the Alternating Direction Penalty Method (IADPM) framework is adopted. The original problem is decomposed into several easier-to-solve subproblems, and the solution to the original problem is approximated by alternating iteration.

[0063] 41 Introduction of Auxiliary Variables

[0064] To simplify the problem, we introduce auxiliary variables y(l,m) and z, defined as follows:

[0065]

[0066] The spectral constraints and norm constraints of y(l,m) can be decomposed into two subproblems through the IADPM framework. z converts the sequence set into a vector, thereby simplifying the original problem.

[0067] 42 Reconstruction of the Optimization Problem

[0068] Using auxiliary variables, problem (11) can be restructured as follows:

[0069]

[0070] Among them, B k,a =J k Diag(c a Diag(c) a ) represents c a diagonal matrix,

[0071] Step 5: Iteratively solve the subproblem. The non-convex quartic optimization subproblem is solved using Iterative Sequential Quadratic Optimization (ISQO). By sequentially solving the approximate problem, the optimal solution is approximated. After each iteration, the discretized set of the transmitted signal is updated. and auxiliary variable Y (t) The iteration is then checked for convergence. If the preset exit condition is met, the iteration terminates. The output is the discretized set of the finally converged transmitted signals. like Figure 3 As shown, the iterative solution process includes the following steps:

[0072] 51 Initialization Parameters

[0073] Set the initial set of discretized transmitted signals.

[0074] Initial auxiliary variable Y (0)

[0075] Initial Lagrange multipliers

[0076] Initial penalty function parameters

[0077] Weighting coefficients ω(k,a), k=1,…,N-1

[0078] Convergence parameter δ 1,c ,δ 2,c ,v

[0079] Initial iteration counter t=0

[0080] 52 Update waveform parameters

[0081] Using the current auxiliary variable Y (t) Lagrange multipliers Sum of penalty function parameters The waveform parameters are updated by minimizing the augmented Lagrange function. As shown in equation (15).

[0082]

[0083] And ensure that the updated waveform parameters satisfy the constant mode constraint |x m (n)|=1.

[0084] Solve (15) using the Iterative Sequential Quadratic Optimization (ISQO) technique:

[0085] enter

[0086] ω(k), k=1,…,N-1,i=0,Y (t) ,

[0087] initialization

[0088]

[0089] repeat

[0090] 1: Calculate Υ(z) and λ

[0091] in λ = max{eig(Υ(z))}, where λ is the largest eigenvalue of Υ(z).

[0092] 2: Update I N It is the identity matrix

[0093] 3: Calculation in, It is a vector, defined as follows during iteration t: It is a vector, defined as follows during iteration t: and Used to handle spectral constraints in augmented Lagrange functions; ⊙ denotes the Hadamard product;

[0094] 4: According to the formula Update x m(i+1)

[0095] 5: Update z i+\

[0096] 6: Increase the iteration counter i = i + 1

[0097] Final output

[0098] 53 Update auxiliary variables

[0099] Based on the latest discretization set of transmitted signals Update the auxiliary variable Y by minimizing the augmented Lagrangian function. (t+1) , as in equation (16).

[0100]

[0101] Ensure that the updated auxiliary variables satisfy the spectral constraints The objective function of problem (16) omitting the relationship between y and m For irrelevant constant terms, by using the method of square completion, problem (16) becomes

[0102]

[0103] in,

[0104] Therefore, the solution is

[0105]

[0106] 54. Update Lagrange multipliers and penalty function parameters

[0107] According to the latest auxiliary variable Y (t+1) The Lagrange multipliers are updated using formulas (19) and (20). Sum of penalty function parameters

[0108]

[0109] in δ is the residual of the m-th waveform at the t-th iteration. 1,c and δ 2,c Here is the convergence parameter, 0 < δ 1,c <1,δ 2,c >1 but close to 1.

[0110]

[0111] in It is an intermediate update value of the penalty function parameter.

[0112] Intermediate update value The maximum absolute value.

[0113] 55 Iteration Counter Update

[0114] Update the iteration counter t = t + 1.

[0115] 56 Exit Iteration Condition Check

[0116] Check if the preset exit condition is met, i.e., the L2 norm of the difference between two iterations is less than a threshold or the maximum number of iterations has been reached. If the condition is met, stop the iteration and output the converged discretized set of the transmitted signal.

[0117] Step Six, Performance Evaluation. The proposed waveform design method is evaluated for its effectiveness in SAR imaging by simulating point targets and distributed scenarios. For example... Figure 4 As shown, the autocorrelation function (ACF) of different waveforms is presented, and the linear frequency modulation (LFM), non-linear frequency modulation (NLFM), minimum-maximum weighted peak sidelobe level (MM-WPSL), and the complementary waveform design method proposed in this invention are compared. Figure 6 The frequency-Doppler domain performance of different waveforms was demonstrated. Figure 6 (a) shows that the Doppler bandwidth of the LFM signal is approximately 500 Hz, with the energy mainly concentrated in the main lobe region. Figure 6 Figure (b) shows that, compared to the LFM signal, the spectrum of the NLFM signal is no longer rectangular in order to suppress the peak sidelobe level (PSL). Figure 6 (c) indicates that aliasing occurred in the Doppler domain of the MM-WPSL waveform, the energy diffused outside the Doppler bandwidth, and the signal within the Doppler bandwidth was severely modulated along the azimuth dimension. Figure 6(d) indicates that the proposed SAR-PSFS (pointspread function shaping) waveform significantly reduces aliasing within the Doppler bandwidth, with energy mainly concentrated in the main lobe region. This demonstrates that the proposed waveform optimization method can effectively reduce Doppler aliasing, highlighting the better sidelobe suppression effect of the proposed method. Figure 7 (a) shows the imaging results of the LFM signal, where the sidelobe level is relatively high, resulting in more stray energy around the target and poor imaging quality. Figure 7 In (b), it is shown that the imaging results of the NLFM signal are improved compared to LFM, and the sidelobe level is reduced. However, due to the limitations of its single waveform design, there is still a certain sidelobe level. Figure 7 The imaging results of the MM-WPSL waveform in (c) show the effect of waveform agility, but due to the lack of joint optimization, energy spikes appear outside the main energy region, resulting in poor imaging quality. Figure 7 The imaging results of the SAR-PSFS waveform proposed in (d) effectively suppress energy spikes while reducing sidelobe levels, thus improving imaging quality and making the target clearer. Figure 8 The range profiles of different waveforms are shown. The LFM signal range profile exhibits a high sidelobe level, resulting in strong energy outside the main lobe region, affecting target sharpness. The NLFM signal range profile shows a lower sidelobe level compared to the LFM signal, indicating that the NLFM signal has some effect on sidelobe suppression, but the effect is not significant. The MM-WPSL waveform profile shows a reduction in sidelobe level, but some sidelobe energy still exists, especially in regions far from the main lobe. The Hanning window provides good sidelobe suppression, but may lead to an increase in the main lobe width. The SAR-PSFS waveform exhibits the lowest sidelobe level in the range profile, showing a significant sidelobe suppression effect, while maintaining the same main lobe width as the Hanning window. This indicates that the proposed method suppresses sidelobes without sacrificing range resolution. Figure 9 The imaging results of the distributed scene were demonstrated, and the application effect of the proposed waveform design method in the real scene was verified.

[0118] Through these steps, this invention provides an effective SAR waveform optimization method that can significantly suppress range sidelobes while maintaining high resolution, thereby improving the quality of SAR imaging. The flexibility and adaptability of this method make it suitable for different application scenarios and SAR system configurations. The performance of the proposed waveform was verified through simulation experiments. The experiments included both point targets and distributed scenarios. Simulation results show that, compared with traditional linear frequency modulated (LFM) signals, NLFM signals, and minimum maximum weighted peak sidelobe level (MM-WPSL), the waveform designed in this invention achieves a lower sidelobe level while maintaining the same main lobe width, and can effectively mitigate energy spikes caused by waveform agility.

[0119] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A complementary waveform design method for SAR range sidelobe suppression, characterized in that, include: S1. Transmit complementary waveforms between different pulses; S2. Based on the complementary waveforms from step S1, and with the objective of minimizing the weighted integral sidelobe level of the point spread function, spectral constraints and constant mode constraints are introduced to construct a waveform optimization problem. First, the concept of complementary sequences is introduced, and the sequence set is defined as follows: Indicates the transmission signal The discrete form, where , Represents the set of complex numbers. Indicates the first A discrete-phase encoded signal transmitted at each pulse time point, where M is the total number of pulse times and N is the number of encoded sub-pulses, if and only if the sequence set The autocorrelation and in any non-phase lag When the sum of all elements is zero, the set of sequences is called a complementary sequence, i.e.: ； in It represents a sequence Lag The nonperiodic autocorrelation function at time , yes Discrete form; Combining the concept of complementary sequences and the azimuth characteristics of SAR echoes, a waveform optimization problem is constructed; the optimization objective is to minimize the point spread function weighted integral sidelobe level PSFWISL, which is defined as: ； in In lag and the The weights of SAR imaging results at each azimuth angle. For the first Response at each azimuth angle; The optimization problem is formulated by describing the waveform optimization problem as a non-convex optimization problem with a fourth-order objective function. To improve the adaptability of the designed phase-coded signal and prevent interpolation operations from affecting signal performance, spectral constraints are introduced: ； in For the first Discrete Fourier transform vectors at frequency points express The conjugate transpose of . For the first The spectral mask at the ... The value of each frequency point, , ; To avoid degradation or distortion when generating waveforms in a SAR system, constant mode constraints are considered: ； Considering the above factors, the waveform optimization problem can be described as follows: ； in, Represent a matrix, ; S3. Introduce two auxiliary variables to replace the variables in the spectrum constraint and the constant mode constraint respectively; and use the auxiliary variables to reconstruct the waveform optimization problem in step S2. S4. Minimize the augmented Lagrangian function by iteratively optimizing the waveform parameters to obtain the final transmitted signal.

2. The complementary waveform design method for SAR range sidelobe suppression according to claim 1, characterized in that, In step S1, if and only if The autocorrelation and any non-zero phase lag When the sum is zero, it is called They are complementary sequences, that is: ； Where M is the total number of pulse moments. Represents a set of sequences, containing from arrive All , , This represents the set of complex numbers, where N is the number of coded sub-pulses. Indicates the first One transmitted signal Discrete form; Represents a sequence Lag The non-periodic autocorrelation function over time.

3. The complementary waveform design method for SAR range sidelobe suppression according to claim 2, characterized in that, Introducing auxiliary variables Replace the variables in the spectrum constraints, that is: ; Introducing auxiliary variables Replace the variables in the constant constraint, that is: The superscript T denotes transpose, thus converting the sequence set into a vector and simplifying the original problem. The optimization problem is refactored as follows: in, , express diagonal matrix, .

4. The complementary waveform design method for SAR range sidelobe suppression according to claim 3, characterized in that, The implementation process of step S4 includes: S41. Set the initial set of discretized transmitted signals. Initial auxiliary variables Initial Lagrange multipliers Initial penalty function parameters Weighting coefficients Convergence parameters Initial iteration counter ; S42. Use the current auxiliary variable. Lagrange multipliers Sum of penalty function parameters The following equation is solved using iterative sequential quadratic optimization techniques to update the discretized set of the transmitted signal. : 。 5. The complementary waveform design method for SAR range sidelobe suppression according to claim 4, characterized in that, During the iteration process, based on the latest waveform parameters The auxiliary variable is updated by minimizing the augmented Lagrange function. , yes The combined form of the matrices is as follows: 。 6. The complementary waveform design method for SAR range sidelobe suppression according to claim 5, characterized in that, During the iteration process, based on the latest auxiliary variables Update Lagrange multipliers : ； in yes In the The residual at the next iteration and For convergence parameters, .

7. The complementary waveform design method for SAR range sidelobe suppression according to claim 5, characterized in that, During the iteration process, based on the latest auxiliary variables Update penalty function parameters : ； in It is an intermediate update value of the penalty function parameter. Intermediate update value The maximum absolute value.

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