A method for estimating the time of flight of a chirp signal

Abstract

The application discloses a Chirp signal stable transmission time estimation method, and relates to the technical field of signal parameter estimation. The method comprises the following steps: establishing a Chirp signal model; establishing a Chirp signal arrival time estimation principle; constructing a Chirp signal continuous arrival time estimation cost function; constructing a Chirp signal stable arrival time estimation objective function; setting an estimation interval and calculating the objective function; golden section updating an iteration interval; convergence criterion and stage switching; parabolic interpolation refinement and accelerated iteration. Through the method, high-precision estimation of the Chirp signal arrival time can be realized, the continuity and stability of the arrival time estimation can be effectively ensured, the adverse effects caused by sampling frequency quantization errors and noise interference can be overcome, and the precision and reliability of ranging and positioning are improved.

Description

Technical Field

[0001] This invention belongs to the field of signal parameter estimation technology, specifically relating to a design method for achieving stable transmission time estimation of Chirp signals. Background Technology

[0002] In modern communication, radar, sonar, positioning, and detection technologies, accurate estimation of signal transmission time is crucial for achieving functions such as ranging, velocity measurement, target identification, and positioning and navigation. A sound source emits a chirp signal at time t1, and after a period of time, it arrives at the sound signal receiver at time t2. t2-t1 is the transmission time of the sound signal. Figure 1 As shown. By accurately obtaining the arrival time of the target signal, the propagation path length can be further calculated, thereby achieving distance measurement; combined with observations from multiple receivers, two-dimensional or three-dimensional positioning of the target can also be achieved. Therefore, the accuracy and stability of the transmission time estimation directly determine the performance and reliability of the entire test system.

[0003] Chirp signals are widely used in ultra-wideband communication, synthetic aperture radar, underwater acoustic communication, medical ultrasound imaging, and indoor / outdoor positioning systems due to their excellent time-frequency characteristics and pulse compression gain, enabling high range resolution within limited bandwidth. The linear frequency-time characteristic of chirp signals, after matched filtering or cross-correlation processing, produces sharp correlation peaks, facilitating high-precision transmission time estimation. However, the high-resolution characteristics under ideal conditions are often affected by various uncertainties in practical applications, leading to a significant decrease in estimation performance. First, channel noise is a crucial factor affecting the stability of transmission time estimation. In low signal-to-noise ratio environments, waveform distortion and noise interference in the received signal directly reduce the significance of correlation peaks, even leading to spurious peaks and consequently causing transmission time estimation errors. Second, multipath effects are prevalent in most application scenarios, such as indoor environments, urban streets, underwater environments, or complex geological environments, where signals often undergo reflection, refraction, or scattering to form multiple paths. The superposition of multipath components results in multiple peaks in the correlation output, making it difficult to identify the true direct path, thus severely impacting the accuracy and stability of transmission time estimation. Furthermore, practical system factors such as clock skew at the transmitter and receiver, unstable hardware sampling rates, bandwidth limitations, and nonlinear distortion can also disrupt the ideal pulse compression characteristics to varying degrees. These problems can lead to the accumulation of estimation bias over time, resulting in significant positioning errors during long-term operation. Especially in applications requiring high-precision ranging and continuous positioning, the cumulative effect of such errors directly impacts system availability. To address these issues, academia and industry have proposed various transmission time estimation methods. For example, threshold-based detection methods, while simple to implement, are sensitive to noise and multipath propagation, exhibiting poor robustness. Methods based on cross-correlation or matched filtering can effectively improve detection accuracy, but may still fail in strong multipath environments. Statistical methods based on maximum likelihood estimation and Bayesian inference can improve performance to some extent, but their computational complexity is high, making them unsuitable for real-time processing. In recent years, transmission time estimation methods combining signal subspace decomposition, wavelet transform, sparse reconstruction, and machine learning have also gained attention. However, these methods often require large amounts of prior information or training samples, and their stability in dynamic and complex environments remains insufficient. Patent application literature, "Design Method for Meshless Delay Estimation of Linear Frequency Modulated Signals Using Matched Integrator Estimators," discloses a method for meshless delay estimation of linear frequency modulated signals using matched integrator estimators. This method primarily addresses the problems of quantization errors and poor delay estimation accuracy in existing delay estimation methods. However, this method suffers from unstable estimation results under small sample sizes and low signal-to-noise ratios, significantly degrading system performance. Therefore, achieving stable and accurate estimation of chirp signal transmission time in complex environments has become a research hotspot and technical challenge in this field.On the one hand, it is necessary to make full use of the frequency modulation characteristics and pulse compression advantages of the Chirp signal and improve the ability to suppress noise and multipath through reasonable algorithm design; on the other hand, it is also necessary to take into account the complexity and real-time performance of the algorithm implementation so that it can run efficiently in the actual system.

[0004] Existing technologies still struggle to simultaneously meet the requirements for high-precision and high-stability transmission time estimation of chirp signals under conditions such as low signal-to-noise ratio, multipath interference, and hardware constraints. This restricts the further expansion of chirp signal applications in ranging and positioning, limiting its application in practical engineering. Summary of the Invention

[0005] To address the shortcomings of existing methods, this invention discloses a stable transmission time estimation method for Chirp signals, achieving high-precision estimation of Chirp signal arrival time. This method effectively ensures the continuity and stability of arrival time estimation, overcomes the adverse effects of sampling frequency quantization errors and noise interference, and improves the accuracy and reliability of ranging and positioning.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for estimating the stable transmission time of a Chirp signal, comprising the following steps:

[0008] Step 1: Establish the Chirp signal model;

[0009] Step 2: Establish the principle of chirp signal arrival time estimation;

[0010] Step 3: Construct the cost function for estimating the continuous arrival time of the Chirp signal;

[0011] Step 4: Construct the objective function for stable arrival time estimation of the Chirp signal;

[0012] Step 5: Define the estimation interval and calculate the objective function

[0013] Step 6: Update the golden ratio iteration interval;

[0014] Step 7: Convergence Criteria and Stage Switching;

[0015] Step 8: Refinement and accelerated iteration of parabolic interpolation.

[0016] Preferably, in step 2, the energy sequence of the sampled signal can be mean-reduced during the time delay estimation process.

[0017] The specific process of mean removal is as follows: First, the energy of each sample point in a frame of sampled signal is calculated. Then, the average value of these energy values ​​is subtracted from the average value to obtain the mean-removed energy sequence. In this way, the influence of background noise and other interference signals on the calculation results can be reduced to a certain extent, making the solution to the extremum of the cost function more stable and reliable, thereby improving the accuracy and robustness of time delay estimation.

[0018] Preferably, in step 8, the estimated time interval is narrowed down to a preset range ε. t At this point, a parabolic interpolation step is introduced, selecting three distinct points within the interval. The corresponding function values ​​(η1, η2, η3) are calculated to construct a quadratic interpolation polynomial. The vertex of the polynomial is taken as a new test point. If the point falls within the current search interval and satisfies the stability condition, the test point generated by the golden section is replaced by the point and the iteration continues.

[0019] The beneficial effects of this invention are as follows:

[0020] (1) The Chirp signal transmission time stability estimation method proposed in this invention introduces a continuous estimation and stability constraint mechanism in the signal processing process, breaking through the time quantization limitation caused by the sampling frequency, and can achieve sub-sampling accuracy continuous transmission time estimation under low sampling rate conditions. By constructing a stable objective function structure and denoising and normalizing the cost function, the estimation results remain highly stable in complex channel environments such as strong noise, ensuring the continuity of the estimation curve, thereby significantly improving the reliability and environmental adaptability of the estimation.

[0021] (2) In the implementation of the algorithm, this invention introduces a strategy that combines hierarchical iterative optimization with parabolic interpolation, which enables the objective function to converge to the true optimum quickly during the iteration process. Compared with traditional search-type or pure correlation-type algorithms, this method significantly reduces the number of iterations and greatly improves the convergence speed. It can obtain high-precision transmission time estimation results in a short time, which meets the needs of real-time signal processing and dynamic target tracking. Attached Figure Description

[0022] Figure 1 This is a diagram illustrating the principle of chirp signal transmission time estimation in related technologies;

[0023] Figure 2 This is a schematic diagram showing the results of the Chirp signal continuous transmission time estimation of the present invention;

[0024] Figure 3 This is a schematic diagram showing the result of the objective function of the Chirp signal stable transmission time estimation method of the present invention having a unique maximum value with respect to the value to be estimated;

[0025] Figure 4This is a schematic diagram showing the objective function of the Chirp signal stabilization transmission time estimation method of the present invention with respect to the objective function of the value to be estimated under noisy conditions;

[0026] Figure 5 This is a schematic diagram of the transmission time estimation result of the Chirp signal stabilization transmission time estimation method of the present invention. Detailed Implementation

[0027] The following is in conjunction with the appendix Figure 2-5 The present invention will be described in detail below with reference to specific embodiments.

[0028] This invention relates to a design method for stable transmission time estimation of Chirp signals. Please refer to [link / reference]. Figures 2-5 By utilizing the matching correlation between the Chirp signal source signal and the Chirp signal received at the receiver, the signal transmission time estimation problem is transformed into an optimization problem of the objective function, thus solving the problem that the time delay estimation accuracy in signal parameter estimation is limited by the quantization error of the signal sampling frequency. Then, a nonlinear transformation is used to transform the parameter estimation problem into an optimization problem, and an iterative solution method is used to stably calculate the signal transmission time value to be estimated.

[0029] The specific implementation process is as follows:

[0030] Step 1: Establish the Chirp signal model

[0031] The sound source emits a chirp signal, and the real passband chirp signal model is as follows:

[0032] s pb (t)=Aω(t)cos(2πf c t+φ(t)), 0≤t≤T (1)

[0033] Where A is the amplitude, ω(t) is the time window, usually a rectangular window, a Hamming window, etc., and φ(t) is the baseband phase.

[0034] After removing the carrier frequency and transferring it to baseband, the corresponding complex baseband Chirp analytic signal is obtained, with the complex envelope being...

[0035] s(t)=Aω(t)e jφ(t) ,0≤t≤T (2)

[0036] Let the sampling frequency f s =1 / T s Discrete time n = 0, ..., N-1, where but

[0037]

[0038] Where j represents the imaginary unit, satisfying j2 =-1, used to simultaneously represent the amplitude and phase information of the signal, facilitating frequency domain analysis and filtering operations. K represents the frequency modulation slope, used to describe the linear rate of change of the signal frequency over time, expressed as... f1 is the termination frequency, f0 is the start frequency, and T is the signal duration. s The sampling time interval is the time interval between two adjacent sampling points, expressed as... This reflects the time resolution of signal discretization.

[0039] Step 2: Establish the principle of Chirp signal arrival time estimation

[0040] The sound source emits a Chirp signal at time t1, and the corresponding baseband model is represented as follows:

[0041]

[0042] The sound signal travels at a speed of c in the medium, and the distance between the sound source and the receiver is d. After a period of propagation, the signal arrives at the receiver at time t2. The signal propagation time is...

[0043]

[0044] The signal arriving at the receiving end is an attenuated, noise-delayed signal from the sound source, denoted as:

[0045] r(t)=αs(t-τ)+n(t),t≥t2 (6)

[0046] Where α is the propagation attenuation or channel gain factor, and n(t) is the receiver noise.

[0047] Substituting into the form of s(t), the received signal can be expressed as

[0048]

[0049] The received signal is the transmitted signal delayed by τ = t2 - t1 in time, and is superimposed with noise and channel effects.

[0050] Step 3: Construct the cost function for estimating the continuous arrival time of the Chirp signal;

[0051] Based on the waveform of the emitted Chirp signal, a corresponding matching template time series is designed, denoted as follows:

[0052]

[0053] Wherein, the variable corresponding to the time series of the matching template is t+τ x , τ x This is the time matching amount corresponding to the received signal in the matching template time series.

[0054] The received signal r(t) is compared with the matching template time series r b (t+τ x Perform time alignment, then multiply the signals at the corresponding time points to obtain the matching template time product sequence, represented as:

[0055]

[0056] Integrating the time-product sequence of the matching template over the sampling time interval yields the time-product sequence of the matching template, expressed as:

[0057]

[0058] Calculate the average value of the time-multiplied cumulative product sequence of the matched template over the time integration interval, expressed as:

[0059]

[0060] The time-multiplied cumulative product sequence of the mean-matched template is calculated as follows:

[0061]

[0062] In the process of time delay estimation, the energy sequence of the sampled signal can be mean-reduced. Specifically, the energy of each sample point in a frame of the sampled signal is first calculated, and then the average value is subtracted from these energy values ​​to obtain the mean-reduced energy sequence. In this way, the influence of background noise and other interference signals on the calculation results can be reduced to a certain extent, making the solution to the extremum of the cost function more stable and reliable, thereby improving the accuracy and robustness of time delay estimation.

[0063] Step 4: Construct the objective function for stable arrival time estimation of the Chirp signal;

[0064] For mean-matched template time-multiplied cumulative product sequence c ave (t|τ) is accumulated over the time interval and expressed as:

[0065]

[0066] The corresponding discrete form, at sampling points n = 0, 1, ..., N-1, with a sampling interval of Δt, is expressed as:

[0067]

[0068] Simultaneously, within the time interval, the time-multiplied cumulative product sequence c of the mean-matched template is processed. ave (t|τ) multiplied point by point, expressed as

[0069]

[0070] Strict continuous-time product is generally represented by logarithmic integral, i.e.:

[0071]

[0072] The corresponding discrete-time form is,

[0073]

[0074] Calculate the time-multiplied cumulative sequence c of the mean-matched template. ave The cumulative product-cumulative ratio of (t|τ) is expressed as:

[0075] ρ(τ)=C ∏ (τ) / C Σ (τ) (18)

[0076] The contribution factor in solving the objective function is expressed as:

[0077] η(τ)=ρ(τ)ln(ρ(τ)) (19)

[0078] Given that ρ(τ) represents the energy value, ln(ρ(τ)) is used to perform logarithmic compression or scaling of the energy. From the perspective of information entropy, p(x)ln(p(x)) represents the product of the probability value and its logarithm, reflecting the contribution of the probabilistic event to the overall uncertainty. Then η is a non-linear weighting, and as τ increases, ln(ρ(τ)) grows more slowly. Therefore, the overall growth is sublinear, which can be used to balance the characteristics of "growth trend" and "logarithmic scaling".

[0079] Step 5: Define the estimation interval and calculate the objective function

[0080] Set the estimation interval [t] for the Chirp signal transmission time estimate. min ,t max ], where t min The minimum value of the time interval, t max This represents the maximum value of the time interval, typically the time width of the chirp signal emitted by the sound source.

[0081] Set the initial iteration time interval [t] min ,t max The corresponding objective function interval is [η]. min ,η max ], in the given interval [t min ,t max Within [the scope of the problem], the objective function η(τ) with a unique maximum value is solved iteratively, with a tolerance ε set. t >0 initializes the endpoints of the time interval, represented as:

[0082]

[0083] Step 6: Golden Section Update Iteration Interval

[0084] In the current iteration k-th iteration, let [a k ,b k [This represents the current interval; internal sampling points are taken.]

[0085]

[0086] in,

[0087] Calculate c respectively k and d k The corresponding objective function value η(c) k ) and η(d k If η(c) k )<η(d k If ), then the maximum point is located in [c k ,b k ], update [a k+1 ,b k+1 ] = [c k ,b k Otherwise, the maximum point is located in [a]. k ,d k ], update [a k+1 ,b k+1 ] = [a k ,d k Subsequently, the internal points and function values ​​are recalculated according to formula (21), and the iteration continues.

[0088] Step 7: Convergence Criteria and Phase Switching

[0089] When the interval length satisfies |b k -a k |≤ε t

[0090] |b k -a k |≤ε t (twenty two)

[0091] It is then assumed that the golden section stage has converged, and the process enters the stage of accelerated iterative calculation of parabolic interpolation.

[0092] Step 8: Refinement and Accelerated Iteration of Parabolic Interpolation

[0093] Parabolic interpolation is used to accelerate the approximation of the maximum point at point [a]. k ,b k Select three different points within. And calculate the corresponding function values ​​(η1, η2, η3) to construct a quadratic interpolation polynomial, and take its vertex as a new trial point. The calculation formula is:

[0094]

[0095] If τ x * If the value falls within the current search interval and satisfies the stability condition, then use τ. x * The trial points generated by replacing the golden section continue to iterate; otherwise, the golden section search strategy shown in formula (21) is still used.

[0096] Furthermore, when the first and second derivatives of the objective function are available, Newton's iteration can be used to perform a fine search for the maximum points, and the updated formula can be obtained as follows:

[0097]

[0098] To ensure the solution is within the interval [t] min ,t max Within the specified interval, the updated results need to be projected back to the interval to ensure monotonic improvement of the function value. Finally, when the termination threshold is met, the precise estimate of the maximum point of the objective function and its corresponding objective function value are obtained, expressed as:

[0099]

[0100] To verify the effectiveness of the method of the present invention, a detailed description is provided below with reference to specific embodiments.

[0101] Given that the sound source signal is a chirp signal, the signal's starting frequency f0 = 200 Hz, the signal's time width T = 1 second, the corresponding modulation frequency K = 600 Hz / s, and the sampling frequency f... s =2000Hz, the corresponding time quantization error is Δt = 1 / f s =500μs, which is a relatively large quantization error for signal arrival time estimation and target localization and tracking, and will significantly reduce the localization estimation performance. The received signal is windowed according to ω(t) shown in formula (1), with a window length of 50ms and 50% data overlap between the two windows to reduce spectral leakage caused by the truncation effect and improve the smoothness of the analysis. The 50% overlap will not increase the amount of computation too much and can ensure good time-frequency continuity.

[0102] In this embodiment, a verification experiment was conducted on the proposed continuous estimation method for Chirp signal transmission time to demonstrate that the method can still achieve high-precision transmission time estimation under low sampling rate conditions. Specifically, the experimental setup is as follows: the transmitter generates a Chirp signal with a starting frequency of f0 = 200Hz, a signal duration of 1 second, a sampling frequency of 2000Hz, and a corresponding sampling interval of 0.5 milliseconds, meaning the theoretical time quantization error is 0.5 milliseconds. During the experiment, the receiver gradually moves away from the sound source, with a maximum propagation distance of d. max The speed of sound in the medium is c, therefore the actual transmission time is τ = d / c Under the above conditions, applying the proposed Chirp signal continuity estimation algorithm to the received signal yields the following transmission time estimation result: Figure 2 As shown in the figure, within the quantization error range corresponding to a sampling interval, the estimation result can change synchronously with the actual transmission time, and no step-like or abrupt errors caused by sampling frequency limitations occur. This indicates that the estimation algorithm used in this embodiment can overcome the time quantization error limitation introduced by the sampling frequency and achieve sub-sampling accuracy transmission time estimation. Therefore, this embodiment verifies that the method proposed in this invention has good continuous estimation characteristics, that is, it can maintain high ranging accuracy and stability even in low sampling rate environments.

[0103] In this embodiment, the unique maximum value characteristic of the objective function for estimating the chirp signal transmission time with respect to the value to be estimated is analyzed and explained. The transmission time of the chirp signal is set to 0.695 (a non-integer multiple of the sampling interval), and the objective function value varies with the sample length and the time point of the matching template as follows: Figure 3 As shown. With a fixed sample length, from a horizontal perspective, the objective function gradually increases, then gradually decreases after reaching its maximum value, and has a unique maximum value. With a fixed matching template time point, from a vertical perspective, as the sample length increases, the accumulated energy of the objective function value gradually increases, and the corresponding function value also gradually increases.

[0104] In this embodiment, the necessity of the proposed Chirp signal transmission time stability estimation method is explained. The experimental conditions are set as follows: under the same channel transmission environment, the received signal is noise-added, SNR is set to 5dB, and other experimental parameters remain consistent. Under a fixed sampling length, the two types of received signals are processed separately, and the distribution of the objective function over time is calculated. Figure 4The results show that when the received signal is interfered with by noise, the objective function exhibits multiple spurious peaks in the horizontal direction. These spurious peaks are numerically close to or even partially exceed the true peak value, thus disrupting the "unique maximum value" property of the objective function and potentially leading to deviations or errors in transmission time estimation. Noise interference makes the peak characteristics of the objective function unstable, thereby affecting the reliability of transmission time estimation. This phenomenon fully demonstrates that in real-world channel environments, it is necessary to construct a chirp signal transmission time estimation method with stable characteristics to effectively suppress noise-induced spurious peak interference and maintain the true peak value of the objective function even in noisy environments, thereby achieving more stable and accurate transmission time estimation.

[0105] In this embodiment, the estimation accuracy of the proposed Chirp signal transmission time stability estimation method is analyzed and explained. The time width of the sound source signal is also set to 1 second, and the receiving end uses both the method of this invention and the comparison algorithm to estimate the transmission time under the same channel conditions. Figure 5 The results clearly show that the stable estimation method for Chirp signal transmission time proposed in this invention can achieve continuous transmission time estimation. Its estimated value closely follows the changes in the true transmission time and is not limited by the quantization effect of the sampling frequency. In contrast, the comparative algorithm, because it directly relies on time-domain sampling points, inevitably has its estimation results constrained by the sampling frequency, resulting in a fixed difference between the estimated curve and the actual transmission time, exhibiting a significant quantization ladder effect, and failing to achieve continuous transmission time estimation. Further analysis is conducted using two consecutive signal cycles as an example. Under this condition, the method of this invention can not only detect the signal but also simultaneously output the transmission time estimation result. When the time delay estimation value remains stable, it indicates that the receiver is currently acquiring a valid sound source signal, and the estimation result can be directly used for subsequent target localization and tracking. When the time delay estimation result is unstable or shows irregular changes, it indicates that the sound source is in a silent state or has no valid signal input, thus the stability characteristics of the estimation result can be used to achieve effective target detection.

[0106] In summary, this embodiment verifies that the Chirp signal transmission time stability estimation method proposed in this invention can not only overcome the time quantization error limitation caused by the sampling frequency and achieve continuous transmission time estimation with sub-sampling accuracy, but also determine the existence of the target signal through the stability of the estimation result, thus demonstrating significant technical advantages in target localization, tracking and detection.

[0107] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention without creative effort.

Claims

1. A method of time of flight estimation with chirp signal stabilization, characterized in that, Includes the following steps: Step 1: Establish the Chirp signal model; Step 2: Establish the principle of chirp signal arrival time estimation; Step 3: Construct the cost function for estimating the continuous arrival time of the Chirp signal; Step 4: Construct the objective function for stable arrival time estimation of the Chirp signal; Step 5: Define the estimation interval and calculate the objective function; Step 6: Update the golden ratio iteration interval; Step 7: Convergence Criteria and Stage Switching; Step 8: Refinement and accelerated iteration of parabolic interpolation; In step 3, based on the waveform of the emitted sound source Chirp signal, a corresponding matching template time series is designed, represented as follows: Wherein, the variable corresponding to the matching template time sequence is , is the corresponding time matching amount of the received signal on the matching template time sequence; The received signal is The matching template time sequence After time alignment, the signal at the corresponding time point is multiplied to obtain a matching template time product sequence, denoted as: Integrating the time-product sequence of the matching template over the sampling time interval yields the time-product sequence of the matching template, expressed as: Calculate the average value of the time-multiplied cumulative product sequence of the matched template over the time integration interval, expressed as: The time-multiplied cumulative product sequence of the mean-matched template is calculated as follows: Step 4 involves: multiplying the mean-matched template time product sequence. Accumulation over a time interval is represented as: The corresponding discrete form, at the sampling points At this location, the sampling interval is , represented as Simultaneously, within the time interval, the time-multiplied cumulative product sequence of the mean-matched template is processed. Multiplication by point is represented as Strict continuous-time product is expressed by logarithmic integral, that is: The corresponding discrete-time form is, Calculate the time-multiplied cumulative product sequence of the mean-matched template. The cumulative product-cumulative ratio is expressed as: The contribution factor in solving the objective function is expressed as: Known This represents the energy value. It is used for logarithmic compression or scaling of energy; from the perspective of information entropy... This represents the product of the probability value and its logarithm, reflecting the contribution of the probabilistic event to the overall uncertainty. It is a non-linear weighting, which varies with... Increase Growth slows down, therefore, overall growth is sublinear, used to balance the characteristics of "growth trend" and "logarithmic scale".

2. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 1: Establish the Chirp signal model The sound source emits a chirp signal, and the real passband chirp signal model is as follows: in, For amplitude, This is a time window, which can be a rectangular window or a Hamming window. Baseband phase; After removing the carrier frequency and transferring it to baseband, the corresponding complex baseband Chirp analytic signal is obtained, with the complex envelope being... Set sampling frequency Discrete time ,in ,but 。 3. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 2 establishes the principle of Chirp signal arrival time estimation. The sound source is The baseband model for transmitting Chirp signals at constant intervals is represented as follows: The speed of sound signal propagation in the medium is The distance between the sound source and the receiver is After a period of propagation, the signal reaches the receiver at time t2, and the signal propagation time is... The signal arriving at the receiving end is an attenuated, noise-delayed signal from the sound source, denoted as: in, For propagation attenuation or channel gain factor, This refers to receiver noise. Substitution The received signal is represented in the form of... The received signal is delayed in time from the transmitted signal. It also incorporates noise and channel effects.

4. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 5 involves setting the estimation range for the Chirp signal transmission time estimate. ,in, The minimum value within the time interval. The maximum value of the time interval is defined as the time width of the chirp signal emitted by the sound source; the initial iteration time interval is set. The corresponding objective function interval is In a given interval Within, for the objective function with a unique maximum value Perform iterative solutions and set tolerances. Initialize the endpoints of the time interval, represented as: 。 5. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 6 is as follows: In the current iteration... Next, order For the current interval, take the internal sampling points: in, ; Calculate separately and Corresponding objective function value and ,like The maximum point is located at ,renew Otherwise, the maximum point is located at ,renew Then, the internal points and function values ​​are recalculated according to the above formula, and the iteration continues.

6. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 7 is as follows: when the interval length satisfies This suggests that the golden section phase has converged.

7. The method for estimating the stable transmission time of a Chirp signal according to claim 1, characterized in that, Step 8 involves using parabolic interpolation to accelerate the approximation of the maximum point, at which point... Select three differences within And calculate its corresponding function value. Construct a quadratic interpolation polynomial, and take its vertex as a new trial point. The calculation formula is as follows: like If it falls within the current search interval and satisfies the stability condition, then use... The trial points generated by replacing the golden section continue to iterate; otherwise, the golden section search strategy shown in the formula in step 6 is still used.

8. The method for estimating the stable transmission time of a Chirp signal according to claim 7, characterized in that, In step 8, if the first and second derivatives of the objective function are available, Newton's iteration is used to perform a fine search for the maximum points, and the updated formula is as follows: To ensure the solution is within the interval Within the interval, the update results need to be projected back to ensure monotonic improvement of the function value. When the termination threshold is met, the accurate estimate of the maximum point of the objective function and its corresponding objective function value are obtained, expressed as: .

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