Frequency estimation system and method for coherence range estimation

Abstract

A distance estimation method comprising: transmitting, by a transmitter, a radiation wave modulated in a frequency domain to a scene; receiving a reflection of the transmission wave from the scene; and causing a copy of the transmission wave to interfere with the received reflections to generate a sequence of samples of beat signals having wrapped phases in the time domain. The method further includes iteratively estimating the frequency of the beat signal in the time domain until a termination condition is satisfied. The frequency of the beat signal is iteratively estimated based on a phase unwrapping of the beat signal samples affected by a correlated phase error derived from a phase noise statistical characteristic of the transmitter and a linear regression that fits the frequency of the beat signal into the unwrapped phase of the beat signal.

Description

Technical Field

[0001] This disclosure generally relates to object detection in a scene using frequency modulated continuous wave (FMCW) technology, and more specifically, to FMCW-based apparatus and methods for coherent range estimation of objects in a scene. Background Technology

[0002] Many applications, such as autonomous vehicles, industrial robots, navigation, aerospace, meteorological element measurement, and atmospheric environmental monitoring, require accurate object detection to perform critical functions. Reliable object detection is typically performed using long-range sensing technologies, such as light detection and ranging (LIDAR), which uses pulsed laser light to measure the range (variable distance) of objects in a scene. Several types of LiDAR are currently available for range estimation of such objects in a scene of interest. Traditional pulsed LiDAR emits short pulses of light towards an object and calculates the distance based on the time it takes for the reflected light to return to the LiDAR system. Because pulsed LiDAR is incoherent, it only measures the light intensity at the detector, making it susceptible to errors caused by ambient light or interference from other LiDAR systems.

[0003] Another method for distance estimation via laser is frequency-modulated continuous wave (FMCW) lidar. Unlike pulsed lidar, FMCW lidar has a constant illumination power, making it compatible with integrated photonics technologies. FMCW lidar is a coherent ranging technique that measures distance by mixing a local copy of the emitted laser beam with the light reflected back to the receiver. The beat frequency of the resulting interferometric signal is proportional to the reflector range, thus distance measurement can be transformed into a frequency estimation problem.

[0004] Despite these advantages, the accuracy of FMCW lidar is typically limited by the phase noise of the laser source. Due to fundamental oscillations, lasers cannot generate light of a single, pure frequency. Instead, thermal variations, mechanical vibrations, and even the quantum properties of photons contribute to the randomness of the oscillation phase, corresponding to deviations in the emission frequency. In applications using noisy lasers in FMCW lidar, laser phase noise similarly causes the interference signal to deviate from the true beat frequency. These deviations increase with the range relative to the object, thus there is usually a maximum range (coherence range) within which measurements can be performed without excessive error. This understanding is based on classical frequency estimation techniques, which assume a sine wave in additive noise, where the maximum likelihood estimate of the sine wave frequency in additive noise is the peak of the periodogram. However, peak-finding methods perform poorly when the phase noise distributes signal power over a certain frequency range.

[0005] Traditional techniques perform frequency estimation in the frequency domain. However, a drawback of these methods is that the statistical properties of phase noise are not fully understood in the frequency domain. Attempting to interpret these phase noise statistics increases the complexity of the measurement system and / or requires more hardware and computational resources. Therefore, better methods are needed to estimate the frequency of beat signals. Summary of the Invention

[0006] Some implementations aim to provide an improved frequency estimation technique for determining the extent of objects in a scene of interest. In this regard, some implementations also aim to provide systems and methods for performing frequency estimation in the time domain, wherein phase noise statistics can be better described and understood through explicit modeling. Some example implementations aim to perform frequency estimation in the time domain and utilize known phase noise statistics. Some example implementations specifically provide frequency estimation techniques for scenes where the maximum distance to be measured is greater than the coherence length of the light source.

[0007] Some example implementations are based on the understanding that, for coherent ranging techniques, the distance to an object in the scene is a beat frequency function of the interferometric signal, generated by mixing a local copy of the transmitted beam with light reflected back to the receiver, thus transforming the object distance measurement task into a frequency estimation problem. In coherent ranging techniques (such as FMCW), depth measurement is affected by associated noise. Therefore, some example implementations are based on the understanding that, for FMCW lidar, laser phase noise causes the interferometric signal to deviate from the true beat frequency; therefore, beat frequency estimation is highly susceptible to error if the statistical characteristics of phase noise are not considered. In this regard, some example implementations are based on the understanding that, since the statistical characteristics of phase noise are difficult to fully understand in the frequency domain, they can be explicitly modeled in the time domain.

[0008] Some example implementations also recognize that frequency estimation in the time domain can be performed through a two-stage process including phase unrolling and linear regression. In this regard, some example implementations consider prior information about the linear characteristics of the underlying unrolled phase. Some example implementations recognize that FMCW depth measurements are affected by correlated noise, and therefore incorporate phase error estimation into the alternating optimization. To this end, example implementations perform frequency estimation from the perspective of phase unrolling, explicitly considering the correlation in the phase noise.

[0009] Some example implementations also aim to determine the maximum likelihood expansion sequence of the wrapped phase using a linear minimum mean square error estimate of the phase error. Some example implementations recognize that the statistical properties of the phase error are easier to derive than the power spectral density (PSD) obtained from noisy sinusoidal measurements. Therefore, example implementations of this disclosure are able to incorporate the frequency noise distribution of non-white lasers into the frequency estimation task.

[0010] Various example implementations treat the laser-based light source used for frequency estimation as part of a larger-scale estimation problem. In this field, FMCW lidar shows promise for applications such as autonomous navigation due to its greater robustness to ambient light and interference from other lidar systems compared to pulsed lidar. However, as mentioned above, phase noise in FMCW lidar causes instantaneous frequencies to deviate from the desired frequency modulation and reduces the temporal coherence in the interferometric beam. Some example implementations are based on the understanding that the loss of temporal coherence becomes more severe with increasing distance from the target. The coherence range (determined by the amount of phase noise) is considered to be a distance beyond which ranging cannot be reliably performed. Some example implementations also recognize that, for long distances (e.g., required for navigation), the hardware solution is to use lasers with low linewidth (i.e., low phase noise). However, such low linewidth lasers tend to be expensive and increase the overall hardware complexity of the system.

[0011] Several example implementations recognize that the range can be increased by taking into account the effects of phase noise. For example, some example implementations assume a frequency-based white noise laser model where the power spectral density (PSD) asymptotically follows a Lorentz distribution as a function of range, thus allowing the Lorentz distribution to be fitted to the measured PSD of the interferometric signal. Other example implementations also recognize that, to address the problem of phase noise affecting lidar measurements, one solution is to perform frequency domain estimation by fitting a Lorentz curve to the measured PSD. However, the Lorentz curve is an approximate representation of the interfering PSD, and fitting methods based on Gaussian statistical assumptions are not optimal.

[0012] Some other example implementations also recognize that, to address the issue of phase noise affecting lidar measurements, another solution is to use an additional reference arm and a fixed depth to measure the characteristics of phase impairment (including phase noise and nonlinearity). Specifically, impairment correction can be achieved (so peak finding can be used in the standard frequency domain) instead of incorporating impairment modeling into the estimation process. However, these solutions require additional hardware and calibration.

[0013] Given the above implementations, various example implementations are based on the understanding that attempting to correct phase errors or fitting the PSD to a curve with simple assumptions about the distribution leads to suboptimal or infeasible solutions. Some example implementations also recognize that these methods cannot achieve acceptable levels of accuracy, especially under high signal-to-noise ratio (SNR) conditions. For these purposes, several example implementations propose using accurate phase noise statistics in the time domain to achieve better performance, particularly at high SNR. Furthermore, some example implementations provide time-domain methods that use the statistical properties of realistic laser models, rather than simple frequency white noise models.

[0014] Thus, a major problem in some exemplary implementations is how best to handle the effects of phase noise during ranging. In this regard, some exemplary implementations recognize that the statistical properties of phase noise are most easily described in the time domain (i.e., directly in the phase of the interferometric signal) rather than in the frequency domain after the Fourier transform. Specifically, some exemplary implementations describe the phase error of the interferometric signal under frequency white noise versus frequency colored noise in closed-form, compared to the PSD of frequency white noise, which is known only in closed-form. Some exemplary implementations achieve this by considering the phase error as a stationary Gaussian process, thus fully described by its autocorrelation function. Some exemplary implementations are based on the understanding that, using a quadrature demodulator, the phase of the interferometric signal can be extracted to perform phase-based frequency estimation. While FMCW lidar systems typically use a single balanced detector, a quadrature demodulator contains two balanced detectors for direct in-phase and quadrature measurements.

[0015] Some example implementations provide solutions for frequency estimation via phase expansion. Some example implementations leverage the advantages of phase error correlation to expand the measured phase, and then again use phase error correlation for linear regression of the expanded phase. In this regard, some example implementations provide iterative algorithms based on the above principles, and these iterative algorithms can be initialized and improved using less precise methods (e.g., Lorentz fitting) to exhibit better accuracy at high SNR.

[0016] To achieve the aforementioned goals and advantages, some exemplary implementations provide systems, methods, and procedures for estimating the coherence range of objects in a scene.

[0017] For example, some exemplary embodiments provide an FMCW device including a transmitter configured to transmit at least one radiated wave into a scene, wherein the transmitted wave is linearly modulated in the frequency domain, the linear modulation being impaired, resulting in nonlinearity of the transmitted wave in the frequency domain. A receiver receives a reflection of the transmitted wave from the scene, and a mixer interferes a copy of the transmitted wave with the received reflection to generate a beat signal. A pair of analog-to-digital converters generate a sample sequence of the beat signal with a wrapped phase in the time domain. A processor is configured to iteratively estimate the frequency of the beat signal until a termination condition is met. The frequency of the beat signal is iteratively estimated based on the phase unwrapping of the beat signal samples affected by correlated phase errors derived from the phase noise statistics of the unwrapped phase of the beat signal and a linear regression fitting the frequency of the beat signal to the unwrapped phase of the beat signal. The circuitry can use the estimated frequency of the beat signal to estimate the distance to an object in the scene.

[0018] Some example implementations also provide a frequency estimation method using an FMCW device, comprising transmitting at least one radiated wave to a scene, wherein the transmitted wave is linearly modulated in the frequency domain, the linear modulation being impaired, resulting in nonlinearity of the transmitted wave in the frequency domain. The method further comprises receiving a reflection of the transmitted wave from the scene and interfering a copy of the transmitted wave with the received reflection to generate a beat signal and a sample sequence of beat signals with a wrap-around phase in the time domain. The method further comprises iteratively estimating the frequency of the beat signal in the time domain until a termination condition is met. The frequency of the beat signal is iteratively estimated based on the phase unwrapping of beat signal samples affected by correlated phase errors derived from the phase noise statistics of the unwrapped phase of the beat signal and a linear regression fitting the frequency of the beat signal to the unwrapped phase of the beat signal.

[0019] Some example implementations also provide a non-transitory computer-readable medium storing instructions executable by a computer to perform a frequency estimation method using an FMCW device. The frequency estimation method includes transmitting at least one radiated wave to a scene, wherein the transmitted wave is linearly modulated in the frequency domain, the linear modulation being impaired, resulting in nonlinearity of the transmitted wave in the frequency domain. The method also includes receiving a reflection of the transmitted wave from the scene and interfering a copy of the transmitted wave with the received reflection to generate a beat signal and a sample sequence of beat signals with a wrap-around phase in the time domain. The method further includes iteratively estimating the frequency of the beat signal in the time domain until a termination condition is met. The frequency of the beat signal is iteratively estimated based on the phase unwrapping of beat signal samples affected by correlated phase errors derived from the phase noise statistics of the unwrapped phase of the beat signal and a linear regression fitting the frequency of the beat signal to the unwrapped phase of the beat signal.

[0020] According to some example implementations, the generated beat signal is distorted due to nonlinearity in the linear modulation caused by the impairment. In some example implementations, the current iteration of the iterative estimation includes, for each sample in the sample sequence of the beat signal, determining the current phase error and phase spread number of fitting the previous frequency and previous phase shift of the beat signal determined during previous iterations. The current phase error of the current sample in the beat signal sequence is correlated with the previous phase error of the previous samples in the beat signal sequence via predetermined phase noise statistics. The current iteration of the iterative estimation also includes updating the current frequency and current phase shift of the beat signal used for the current iteration based on the determined current phase error and the determined phase spread number.

[0021] According to some example implementations, the iterative estimation of frequency is based on an alternative optimization method, which includes the Viterbi algorithm. This algorithm probabilistically determines the current phase error and phase unwrapping number to maximize the likelihood of fitting the current phase error and phase unwrapping number across the entire sample sequence of the beat signal. For each current sample in the sample sequence of the beat signal, the Viterbi algorithm performs a causal estimate of the current phase error and current phase unwrapping number using the previous phase error and previous phase unwrapping number determined for previous samples. The causal estimate of the current phase error and current phase unwrapping number is determined via linear least mean square error estimation.

[0022] The currently disclosed embodiments will be further explained with reference to the following figures. The figures shown are not necessarily drawn to scale, but generally focus on illustrating the principles of the currently disclosed embodiments. Attached Figure Description

[0023] Figure 1A The workflow for depth estimation in a scene using the principles of a frequency-modulated continuous wave device, based on some example implementations, is shown.

[0024] Figure 1B A schematic diagram of an FMCW lidar system for estimating the distance to an object, according to some example embodiments, is shown.

[0025] Figure 2A Detailed schematic diagrams of an FMCW lidar system according to some embodiments of the present disclosure are shown.

[0026] Figure 2B The diagram shows a swept signal emitted from a tunable laser and a delayed copy captured at the receiver of an FMCW lidar system, according to some example implementations.

[0027] Figure 2C An exemplary method for distance estimation using an FMCW lidar system is shown according to some example implementations.

[0028] Figure 3 An iterative frequency estimation method based on the principles of an FMCW lidar system is shown according to some example implementations.

[0029] Figure 4 Descriptions based on some example implementations are shown. Figure 3 The iterative frequency estimation method is a one-iteration method.

[0030] Figure 5 An algorithm for Viterbi phase expansion for frequency estimation, according to some example implementations, is shown.

[0031] Figure 6A schematic diagram of a frequency estimation process based on signal phase, according to some example implementations, is shown.

[0032] Figure 7A A detailed schematic diagram of the phase expansion steps of a frequency estimation algorithm according to some example implementations is shown.

[0033] Figure 7B A detailed schematic diagram of the phase expansion steps of a frequency estimation algorithm according to some example implementations is shown.

[0034] Figure 7C The process of frequency refinement via linear regression in a frequency estimation algorithm according to some example implementations is illustrated.

[0035] Figure 8 The illustration depicts a scenario of an example use case for an FMCW lidar system, based on some example implementations.

[0036] Figure 9 A system block diagram for implementing an FMCW lidar system is shown according to some example implementations.

[0037] While the foregoing figures illustrate embodiments disclosed in this disclosure, other embodiments are also covered as mentioned in the discussion. This disclosure presents illustrative embodiments by way of representation and not limitation. Those skilled in the art can devise various other modifications and embodiments falling within the scope and spirit of the principles of the embodiments disclosed herein. Detailed Implementation

[0038] The following specification provides exemplary embodiments only and is not intended to limit the scope, applicability, or configuration of this disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with a feasible description of implementing one or more exemplary embodiments. Various changes to the function and arrangement of the elements are contemplated without departing from the spirit and scope of the subject matter disclosed in the appended claims.

[0039] Specific details are set forth in the following description to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the embodiments with unnecessary details. In other instances, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, the same reference numerals and names in the various figures denote the same elements.

[0040] Furthermore, various implementations can be described as processes drawn as flowcharts, flow diagrams, data flow diagrams, structure diagrams, or block diagrams. Although flowcharts can describe operations as sequential processes, many operations can be performed in parallel or simultaneously. Moreover, the order of operations can be rearranged. A process may terminate upon completion of its operations, but may have additional steps not discussed or included in the diagrams. Furthermore, not all operations in any particular described process may occur in all implementations. A process may correspond to a method, function, program, subroutine, subroutine, etc. When a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or the main function.

[0041] Furthermore, implementations of the disclosed subject matter can be carried out, at least partially, manually or automatically. They can be performed, or at least assisted by, using machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof, for manual or automatic implementation. When implemented in software, firmware, middleware, or microcode, program code or code segments for performing the necessary tasks can be stored in a machine-readable medium. The processor can then perform the necessary tasks.

[0042] Imaging technology has been widely adopted in numerous application areas due to the need to understand the environment surrounding an object in order to make informed decisions. For example, in remote sensing applications, it is often desirable to describe the physical characteristics of an area as clearly as possible. In other applications, such as autonomous and semi-autonomous vehicles, making time-sensitive decisions is crucial for the operation of these vehicles. For all such applications, accurate depth estimation of objects in the scene of interest is essential. Accurate depth estimation can be achieved by taking into account errors that occur during scene measurement. In most such scenarios, illumination sources typically introduce these errors into the measurement.

[0043] LiDAR is an increasingly popular sensing mode suitable for a wide range of applications, from autonomous driving to industrial robotics and lunar navigation. Traditional pulsed lidar emits short pulses of light at an object and calculates the distance based on the time it takes for the reflected light to return to the lidar system. Because pulsed lidar is incoherent, measuring only the light intensity at the detector, it is susceptible to errors caused by ambient light or other lidar interference. Another method for distance estimation via laser is frequency-modulated continuous wave (FMCW) lidar. Unlike pulsed lidar, FMCW lidar has a constant illumination power, making it compatible with integrated photonics technology. FMCW lidar is a coherent ranging technique that measures distance by mixing a local copy of the emitted laser beam with the light reflected back to the receiver. The beat frequency of the resulting interference signal is proportional to the reflector range, thus transforming distance measurement into a frequency estimation problem.

[0044] However, like any oscillator, a laser cannot produce light of a single, pure frequency. Instead, thermal variations, mechanical vibrations, and even the quantum properties of photons contribute to the randomness of the oscillation phase, corresponding to deviations in the emission frequency. When lasers are used in FMCW lidar, laser phase noise similarly causes the interference signal to deviate from the true beat frequency. It is typically assumed that a sine wave in additive noise has a maximum range that can be measured without significant error. The maximum likelihood estimate of the frequency of a sine wave in additive noise is the peak value of the periodogram, but peak-finding methods perform poorly when the phase noise distributes signal power over a certain frequency range.

[0045] Even when the distance to the object is greater than the coherence length of the laser, FMCW lidar measurements will still include information about the distance. However, a newer technique is needed that takes into account the statistical properties of phase noise when performing frequency estimation. Typically, the statistical properties of phase noise can be explicitly modeled in the time domain. However, frequency estimation is usually performed in the frequency domain, and the statistical properties of phase noise are not easily understood in the frequency domain. Conversely, when the maximum distance to be measured is greater than the coherence length of the laser, performing frequency estimation in the time domain and utilizing known phase noise statistics is more practical.

[0046] Some solutions aim to perform frequency estimation in the time domain via phase unrolling and linear regression. Many such algorithms perform a naive phase unrolling process without taking into account the linearity of the underlying signal. More sophisticated methods utilize prior information that the underlying unrolled phase is linear in the algorithm, alternating between: phase unrolling using estimates of frequency and phase shift, and updating estimates of frequency and phase shift given the unrolled values. However, none of these methods account for the associated noise setting. Since FMCW depth measurements are affected by associated noise, the example implementations disclosed herein incorporate phase error estimation into the alternating optimization.

[0047] Given candidate frequencies, the proposed solution uses the Viterbi algorithm and phase noise statistics to approximately recover the maximum likelihood expansion sequence. The algorithm then alternates between expansion and frequency estimation refinement until convergence. When the signal-to-noise ratio is sufficiently high, the proposed solution consistently achieves superior performance over long distances or using large-linewidth lasers. These and several other advantages are evident from the disclosed systems, methods, and procedures provided in the exemplary embodiments.

[0048] Frequency-modulated continuous wave (FMCW) lidar systems are a special type of lidar system used to measure both the distance and velocity of a moving object. This is achieved by continuously changing the frequency of the transmitted signal at a known rate within a fixed time period using a modulation signal. This modulation is typically used for very precise distance measurement at close range by comparing the phase of the frequencies of two echo signals. Figure 1A A workflow 100A for depth estimation in a scene using the principles of a frequency modulated continuous wave (FMCW) device, based on some example implementations, is shown.

[0049] The transmission wave, used to propagate into the scene, is generated by one or more lasers of a lidar system and emitted toward the scene via a suitable transmitter of the FMCW lidar system. A copy 10 of the transmission wave is also stored locally for further processing. The transmission wave is reflected from the scene, and the reflected wave 20 is collected by a suitable receiver of the FMCW lidar system. The copy 10 of the transmission wave and the reflected wave 20 are fed into a mixer for signal mixing 30, which outputs measurements related to the resulting interference signal. As part of the mixing process, the optical signal can be converted into an analog electronic signal, which is then digitized to produce samples of the interference signal.

[0050] Let T be the scan duration, φ0 be the initial phase, ω0 be the initial angular frequency, and γ be the chirp rate, and φ n The source phase noise. Within one chirped period, the 10 channels of the transmitted wave replica have a normalized electric field expressed by the following equation:

[0051]

[0052] The signal received from reflected wave 20 has an electric field. The signal is scaled and delayed by τ = 2d / c according to the target reflectivity R, where d is the target distance and c is the speed of light. The electric field (E) of the transmitted wave replica 10... LO ) and the electric field (E) of the reflected wave 20 RX The signals are superimposed at the coherent receiver for signal mixing 30, and the intensity after low-pass filtering is measured by the detector, where the measurement window T meas Ensure overlap of mixed chirps.

[0053] The in-phase interferometry 40 and quadrature measurement 50 are obtained as the output of the signal mixing process 30. In some example embodiments, the FMCW receiver can use a single balanced detector to capture the in-phase interferometry 40, and the quadrature measurement 50 is calculated from the in-phase interferometry 40 via a Hilbert transform. In some example embodiments, a quadrature demodulator with two pairs of balanced detectors can capture both the in-phase measurement 40 and the quadrature measurement 50. The in-phase measurement 40 is given by the following equation:

[0054]

[0055] Where, Δφ n (t)=φ n (t)-φ n (t-τ) is the phase change (also known as phase noise), and w I Approximate as having variance Additive white Gaussian noise (AWGN).

[0056] Orthogonal measurement 50 is given by the following formula:

[0057]

[0058] Among them, w I and w I They are independent of each other and have the same distribution.

[0059] The observed interference signal is represented as a complex sine wave of in-phase measurement 40 and orthogonal measurement 50.

[0060] r(t) = i I (t)+ji Q (t)

[0061] =a exp{j2π[ft+θ+η(t)]}+w(r), (4)

[0062] in, It is the signal amplitude, f = γτ is the beat frequency. It is a phase shift, η(t)=Δφ n w(t) represents a stationary random process with phase change, and w(t) = w I (t)+jw Q (t) is the autocorrelation function. A cyclic symmetric complex AWGN. The signal-to-noise ratio (SNR) caused by the AWGN is: Time t n The samples at location (where n = 0, 1, ..., N-1) are provided as follows:

[0063] r n =a exp{j2π[ft n +θ+η n ]}+w n (5) r n The independent variable is extracted as atan2(i Q (t n ),i I (t n )):

[0064] ∠rn =2π[ft] n +θ+η n +∈ n ],(mod 2π) (6)

[0065] Where, ∈ n This describes the effective phase error caused by AWGN and is referred to as Additive Observation Phase Noise (AOPN). The expanded phase is represented in two different ways:

[0066] x n =ft n +θ+ξ n (7)

[0067] Where, ξ n =η n +∈ n It is the total phase error, or equivalently...

[0068] x n =y n +u n (8)

[0069] Among them, y n =∠r n / (2π) is the extracted wrapper phase (modulo 1). It is an unknown integer number of cycles that must be added to the wrap phase to perform phase unrolling.

[0070] The resulting expression represents the interference signal in terms of its amplitude, beat frequency, phase shift, stationary random process representing phase change, and cyclic symmetric complex AWGN with autocorrelation function. Subsequently, the unfolded phase is defined as a function of beat frequency, phase shift, and total phase error. The unfolded phase is the sum of the extracted wrapped phase and the unknown integer number of periods that must be added to the wrapped phase to perform phase unfolding.

[0071] Depth estimation 70 requires using known phase change statistics 60 to estimate the frequency of the beat signal based on the package phase vector. Then, the final depth estimate is recalibrated using the chirp rate γ and the speed of light c, as follows:

[0072]

[0073] However, directly maximizing the likelihood p(y|f,θ) of the wrapped phase is difficult because the locations of discontinuities in the wrapped phase y are unknown. If we recover the unwrap number u, we obtain the complete data x = y + u, then maximizing the likelihood p(x|f,θ) of the unwrap phase becomes straightforward, since x is an affine function in the correlated Gaussian noise. Regarding this, given the observed data y and the frequency... and phase shift Given the initial estimate, the objective becomes the maximum likelihood estimation of a sequence of integer values ​​expanded u. The Viterbi algorithm works by defining the transitions between possible states (expanded values ​​u). n Assign lengths and then recursively find the state sequence with the shortest path length to estimate the maximum likelihood sequence. The most likely sequence has the shortest path. The expanded phase estimate is based on the phase expansion calculated using Viterbi phase expansion. Frequency can be refined by fitting an affine function. and phase shift The estimate.

[0074] Workflow 100A at M initial frequencies and phase shift The estimation procedure is initialized at the discrete set. From the initial pair... and Initially, we only need to expand the path length L of the sequence. V As the frequency decreases, the workflow iteratively performs Viterbi phase expansion and frequency reduction. and phase shift The estimate is refined. Then, the frequency... and phase shift The final estimate is to generate the shortest path length L at all M grid points. V Frequency / offset pairs.

[0075] After obtaining the frequency of the beat signal, the distance estimate to the object from which the reflected wave 20 is reflected can be determined as the output of the depth estimate 70. Thus, by taking into account relevant noise, the example workflow 100A can provide an accurate estimate of the beat frequency even in the case of significant phase errors.

[0076] Example workflow 100A can be compiled into a machine-executable procedure or method and can be executed using an FMCW device or a LiDAR system. See below for further details. Figure 1B A detailed description of the components and operating principles of this FMCW lidar system. Figure 1B A schematic diagram of an FMCW lidar system 100B for estimating the distance from 118 to object 106 is shown. The FMCW lidar system 100B includes a transmitter 102, a transmitter 104, a receiver 108, a mixer 110, an analog-to-digital converter (ADC) 112, a processor 114, and a memory 116.

[0077] In some example embodiments, transmitter 102 includes a suitable light source such as a laser and frequency modulation electronics. In some embodiments, the laser may be a tunable laser, and the frequency is modulated by directly controlling the laser oscillation. In some example embodiments, the laser may be a fixed-frequency laser, and the frequency may be modulated externally, for example, using an electro-optic modulator. In some example embodiments, transmitter 102 emits a radiated wave (such as a laser) into the scene. Before transmission, the radiated wave is linearly modulated in the frequency domain. Linear modulation can be affected by impairments such as source phase noise, resulting in nonlinearity of the radiated wave in the frequency domain.

[0078] In some example embodiments, transmitter 104 includes optics for redirecting and focusing a laser beam onto object 106. Focusing can be achieved via lenses or combinations of lenses. Beam redirection techniques used in some example embodiments include, but are not limited to, mechanical scanning mirrors, optical phased arrays, microelectromechanical systems (MEMS) mirrors, and liquid crystal metasurfaces.

[0079] Receiver 108 includes focusing optics to collect light reflected from an object. The receiver may include one or more lenses for focusing the reflected light and a free-space to fiber optic coupler for coupling the received light into an optical fiber cable.

[0080] Mixer 110 optically combines a copy of the light from transmitter 102 (local oscillator) with the light captured by receiver to generate a beat signal. The beat signal is distorted due to nonlinearity in the linear modulation caused by damage from laser phase noise. In some embodiments, mixing is performed using a beam splitter. In other embodiments, mixing is performed by an optical fiber coupler. The detector of mixer 110 then converts the optical signal into an analog electrical signal (e.g., voltage or current). Such a detector may be a single photodiode or a combination of photodiodes, as in a balanced detector. The detector may also include amplification circuitry to increase the level of the electrical signal.

[0081] The ADC 112 converts an analog electrical signal into a digital signal at a predetermined sampling time. The ADC 112 includes sampling and quantization electronics for outputting the digital signal. In some embodiments, the ADC 112 has samples spaced evenly in time. In other embodiments, the ADC 112 uses an external reference, such as a k-clock, to determine the sampling time corresponding to a linear frequency scan of the laser.

[0082] Processor 114 uses digitized samples of mixed signals to estimate the distance to an object. In some embodiments, processor 114 is an onboard device such as a field-programmable gate array (FPGA). In other embodiments, processor 114 is an external computer. Memory 116 contains, among other things, calibration data and parameters required by the processor to perform accurate distance estimation 118.

[0083] Figure 2A Detailed schematic diagrams of an FMCW lidar system 200 according to some embodiments are shown. In some example embodiments, the FMCW lidar system 200 may be embodied as a device. In some example embodiments, the FMCW lidar system 200 may be a distributed system including electrical and optical devices. For example, the FMCW lidar system 200 may be implemented using a controller and optoelectronic devices. The controller may include data processing components of the FMCW lidar system 200, such as a processor and its associated circuitry. The optoelectronic components may include other electrical and optical components of the FMCW lidar system 200.

[0084] The FMCW lidar system 200 includes a transmitter 202, a receiver 208, a mixer 210, a pair of analog-to-digital converters (ADCs) 212A and 212B, and a processor 214. The transmitter 202 includes a tunable laser 222 and its modulation controller 220. The tunable laser 222 is coupled and connected to an optical fiber via a beam splitter 224 that generates two copies of the laser beam. The first copy is sent to the transmitter 204, where a collimator 226 focuses the light from the optical fiber into a parallel beam. Beam-directing optics (such as a pair of galvanometers 228) are used to guide the emitted beam to an object 206.

[0085] The wavelength of the tunable laser 222 is scanned by the modulation controller 220, such that the optical frequency of the laser beam becomes a linear function of time (i.e., linearly modulated in the frequency domain). Figure 2B As shown, according to some example embodiments, the tunable laser 222 emits a swept-frequency signal, and a delayed copy of the swept-frequency signal is captured at the receiver 208 of the FMCW lidar system 200. Light reflected by the object 206 is captured by the receiver 208, which focuses the light from free space into an optical fiber.

[0086] Assuming T is the scanning duration of the tunable laser 222, then the scanning frequency is the starting frequency f. min and termination frequency f max Linear chirp between them. Phase noise. This causes the emitted light frequency to randomly deviate from the desired linear scan. Subsequently, an initial phase is defined. Initial angular frequency ω0 and chirp rate γ. Within one chirp period, the local oscillator (LO) channel has a normalized electric field, given by the following equation:

[0087]

[0088] Electric field of the received signal of the received light (RX) The distance has been scaled according to the object's reflectivity R and delayed by τ = 2d / c, where d is the distance from transmitter 204 to object 206 and c is the speed of light. For the static lidar system 200 and object 206, the delay τ is constant. However, when E... LO and E RX During optical assembly in mixer 210, due to phase noise, the frequency of the obtained interference signal differs from the expected beat frequency f. beat Different. Depth estimation only uses the measurement window T. meas Interference signals within the signal ensure the overlap of mixed chirps.

[0089] Reference Figure 2A The mixer 210 includes a 90-degree optical mixer 232 and a pair of balanced detectors 230A and 230B. The mixer 210 receives received light (RX) through one input port and local oscillator (LO) light, i.e., a second copy of the laser beam, through another input port. The LO and RX fields are combined in the optical mixer 232 to produce two pairs of mixed outputs. Each output is connected to a balanced detector (230A or 230B), which uses a pair of photodiodes and an amplifier to convert the optical signal into an electrical signal. In this respect, the mixer 210 has one branch for the in-phase component (I) and one branch for the quadrature component (Q). In the I branch, the LO and RX optical signals are combined to obtain the following photocurrent at each photodiode of the balanced detector 230A:

[0090]

[0091] as well as

[0092]

[0093] in, This refers to "phase variation," specifically, phase error in interferometry caused by phase noise in the oscillator of a laser. The balanced detector 230A filters out the DC term and common-mode noise by considering the difference between the two photocurrents.

[0094]

[0095] Considering only the duration within the rectangular function, the in-phase interferometry is

[0096]

[0097] Among them, w I Approximately has variance σ w 2 / 2 additive white Gaussian noise (AWGN).

[0098] In the Q branch, the LO signal is first phase-shifted by π / 2 radians (90°) to obtain

[0099]

[0100] Then, the LO and RX optical signals are combined to obtain the photocurrent at each photodiode of the balanced detector 230B:

[0101]

[0102] as well as

[0103]

[0104] The balanced detector 230B filters out DC terms and common-mode noise by considering the difference between two photocurrents.

[0105]

[0106] Orthogonal measurements take the following forms:

[0107]

[0108] Among them, w Q and w I They are independent of each other and have the same distribution.

[0109] In some example implementations, mixer 210 may use a single coupler instead of an optical mixer to mix the LO and RX electric fields, and a single balanced detector to capture in-phase measurements. The quadrature components are then approximated by the Hilbert transform of the in-phase measurements.

[0110] Each ADC (212A or 212B) includes circuitry for low-pass filtering, sampling, and quantization of the electrical signal to produce in-phase (I) and quadrature (Q) digital measurements. Processor 214 extracts the phase from the I / Q components to perform depth estimation.

[0111] In some example implementations, the FMCW lidar system and the FMCW device can be the same. In some alternative implementations, the lidar system can be external to the FMCW device, wherein the FMCW device can control one or more operations of the lidar. Regardless of the implementation, the FMCW lidar system 200 can execute workflow 100A as a process or method. Figure 2CAn exemplary method 250 for distance estimation using an FMCW lidar system (such as FMCW lidar system 200) is shown according to some example implementations.

[0112] Method 250 includes splitting the incident light into a local beam and a transmitted beam. The splitting operation can be performed by the transmitter 202 of the FMCW lidar system 200. The transmitted beam is transmitted by the transmitter 204 of the FMCW lidar system 200 toward the scene of interest. Reflections of the transmitted beam from the scene are received by the receiver 208 of the FMCW lidar system as a reflected beam. One or more objects can reflect the transmitted beam from the scene toward the FMCW lidar system. A mixer 210 interferes the received beam reflected from the scene with the local beam to produce an interference pattern. In this respect, the mixer 210 can perform the interference according to the principle of the signal mixing process of workflow 100A.

[0113] One or more analog-to-digital converters (ADCs) 112 sample the interference pattern 11 at linearly spaced frequencies for reference. Figure 1A Samples of the interference signal are generated in the manner described in workflow 100A. One or more processors 114 may interface with memory 116 storing executable programs, data, and instructions to determine the distance 13 to an object in the scene by joint phase unrolling and linear regression of the phase extracted from the interference samples. Phase unrolling and refinement by linear regression can be performed as described in reference workflow 100A. The estimated beat frequency is readjusted based on the chirp rate and the speed of light to determine the distance. One or more processors 114 may control interface 120 (such as an output device) to output the determined distance to the object 15 in any suitable manner.

[0114] Figure 3 An iterative frequency estimation method 300 utilizing components of an FMCW device is illustrated according to some example embodiments. The frequency estimation method 300 can be compiled and executed as a control process of an FMCW lidar system. In some example embodiments, method 300 may include actions performed by one or more components of the FMCW lidar system 200. Method 300 includes transmitting 301 at least one radiation wave to a scene. Preprocessing, such as generating and guiding at least one radiation wave, may be performed prior to transmission 301 by any suitable radiation source (e.g., laser, UV lamp, IR lamp). Furthermore, preprocessing may include obtaining a local copy of the transmitted wave. Transmission 301 may include guiding at least one radiation wave to the scene using suitable optics and associated electronics.

[0115] The scene may contain one or more objects, and upon illumination, one or more objects may transmit reflections of the transmitted radiated waves. The reflections of the transmitted waves may be received from the scene by one or more receivers 303. Method 300 further includes interfering 305 with a copy of the transmitted wave and the received reflections of the transmitted wave to generate a beat signal. The interference may be performed as previously described. Figure 1A and Figure 2A The process is described in the following manner. Interference generates a 307 beat signal, which is generated in the time domain as a sequence of samples with a wrapped phase. Subsequently, phase unrolling and linear regression are performed iteratively to estimate the frequency of the 309 beat signal in the time domain until a termination condition is met.

[0116] Figure 4 Descriptions based on some example implementations are shown. Figure 3 The iterative frequency estimation method 300 is used in the current iteration of method 400. For the current iteration, method 400 is initialized using the frequency and phase offset estimates of the iterations immediately preceding the current iteration. For the first iteration, the frequency is used... and phase shift The initial estimates are used to initialize method 400. Therefore, for the first iteration, initial estimates of the frequency and phase shift are obtained as the previous frequency and previous phase shift of the beat signal. Method 400 also includes determining the current phase error and phase unwrapping number (unwrapping number u) of the fitted beat signal's previous frequency and previous phase shift. Figure 1A The basic principle of workflow 100A shown is to determine the phase error and the number of phase unfoldings. Then, a maximum likelihood unfolding sequence of the wrapped phase is determined using the linear minimum mean square error estimate of the phase error. Subsequently, the Viterbi phase unfolding algorithm is used to assign lengths to possible states (unfolded values ​​u). n The conversion between () and (). Method 400 continues to update the current phase offset and the current frequency estimate of the beat signal in the current iteration in 405.

[0117] Figure 5 An algorithm 500 for Viterbi phase expansion for frequency estimation, according to some example implementations, is shown. Algorithm 500 wraps the phase y with M initial frequencies. and phase shift The discrete set is used as input. From the initial pair and Initially, where m = 0, 1, ..., M-1, we only need to expand the path length L of the sequence. V As the frequency decreases, Algorithm 500 iteratively performs phase expansion and frequency... and phase shift The estimate is refined. Then, the frequency... and phase shift The final estimate is to generate the shortest path length L at all M grid points. V Frequency / offset pairs.

[0118] Figure 6 A schematic diagram of a signal phase-based frequency estimation process according to some example implementations is shown. The measured in-phase and quadrature components are combined to obtain a single complex-valued sine wave 602r(t)=i I (t)+ji Q (t).

[0119] The package phase 604 is extracted from the measurement signal 602. However, due to a lack of information about the location and frequency of package occurrences, the package phase may be insufficient to estimate the frequency in the time domain. Predicting the location and amplitude of the phase packages becomes more complex due to biases caused by phase noise. To perform robust frequency estimation, the frequency estimation algorithm 612 therefore jointly expands the phase and estimates the frequency in an alternating manner. In addition to the package phase 604, the estimation algorithm 612 also requires knowledge of the phase noise statistics 606 and the initial frequency estimate 610. The phase noise statistics 606 can be obtained from previous calibrations or manufacturer specifications such as linewidth. The initial frequency estimate 610 is obtained by calculating the power spectral density of the measurement signal 602 via Fourier transform.

[0120] Given these inputs, the frequency estimation algorithm 612 proceeds in two alternating steps: phase unrolling 614, which predicts the position and amplitude of the phase wrapper; and linear regression 616, which updates the frequency estimate. After a sufficient number of iterations, the latest result of the linear regression is taken as the final frequency estimate 618.

[0121] For simplicity, additional symbols are introduced to extend the definition of the sine wave 602 to:

[0122] r(t)=aexp(j2π[ft+θ+η(t)])+w(t),

[0123] Where a=√R is the signal amplitude, f=γτ is the beat frequency, and θ=ω0τ-γτ 2 / 2 is the phase shift, η(t) = Δφ n w(t) represents a stationary random process with phase change, and w(t) = w I (t)+jw Q (t) is the autocorrelation function. =σ w 2 A cyclic symmetric complex AWGN of δ(t). The signal-to-noise ratio (SNR) caused by the AWGN is a 2 / σ w 2 .

[0124] Time t n The samples at point (where n = 0, 1, ..., N-1) are represented as:

[0125] r n =aexp{j2π[ft n +θ+η n ]}+w n .

[0126] r n The main variable is extracted as atan2(i Q (t n ), i I (t n )), and draw the conclusion

[0127] ∠r n =2π[ft] n +θ+η n +∈ n ],(mod 2π)

[0128] Where, ∈ n The effective phase error caused by AWGN is described and is referred to as Additive Observation Phase Noise (AOPN). The expanded phase is further defined as:

[0129] x n =ft n +θ+ξ n

[0130] =y n +un ，

[0131] Where, ξ n =η n +∈ n It is the total phase error, y n =∠r n / (2π) is the extracted wrapper phase (modulo 1). It is an unknown integer number of cycles that must be added to the wrap phase to perform phase unrolling.

[0132] The two equivalent definitions of phase expansion highlight the reason for the two-step estimation process. In the first definition, the phase x is expanded... n =ft n +θ+ξ n It is additive noise ξ n Broken linear function ft n +θ. From the sample x of the noisy linear function nThere are many existing techniques for estimating the slope f, including ordinary least squares (OLS) and generalized least squares (GLS) if the noise is Gaussian. However, for sample x... n Not available. Instead, only the wrapper phase y is available. n It is known. Therefore, the problem becomes how to determine the expansion number u. n This is a challenge in the presence of noise. Nevertheless, preliminary estimates of the frequency f and phase shift θ can guide the expansion process, and the remaining uncertainties can be attributed to the phase error ξ. n Therefore, the cycle is estimated by expanding the phase x. n We use the two definitions to recover the true frequency f. Next, refer to... Figure 7A and Figure 7B Details of the phase expansion step 614 of the frequency estimation algorithm 612 are described. Specifically, according to some example implementations, Figure 7A The calculation of the path length of the expanded sequence is shown, while Figure 7B The shortest path estimate is shown.

[0133] The goal is to find an approximate maximum likelihood estimate, expressed as:

[0134]

[0135] Assuming the expansion process is causal and using a finite memory of length C, the phase expansion is performed sample-by-sample. First, the specific expansion number u at sample n is estimated. n The likelihood of the expansion is then calculated. Then, the Viterbi algorithm is used to determine the most likely sequence of expansions. The Viterbi algorithm calculates the likelihood of possible expansion values ​​u. n The transitions between them are assigned a length (negative log-likelihood function), and then the state sequence with the shortest path length is recursively searched to estimate the maximum likelihood sequence. Since the number of possible unfoldings within each time step is large, a surviving path processing algorithm is used to maintain only a fixed number of K surviving paths.

[0136] The inputs to phase unrolling step 614 are the wrapped phase vector y and the initial frequency estimate. and phase offset estimation Phase noise statistical characteristics, time sample t=[t0,t1,…,t N-1 ] T And the number of surviving paths K. The phase noise statistics are contained in two components: the cross-covariance vector p. C Autocovariance matrix Q C Cross-covariance vector p C It has the following elements:

[0137]

[0138] And the autocovariance matrix Q C It has the following elements:

[0139]

[0140] Where i,j∈(0,…,C-1). These two components are completely determined by the autocorrelation function of the laser source phase noise and additive noise of the receiver. Since f and the statistical characteristics of the phase noise both depend on τ in the FMCW lidar setup, they can be determined according to... Calculate the covariance matrix Q C and related vector p C .

[0141] Phase expansion is performed as follows. For each sampling time t... n There exist K existing possible paths for phase expansion. It is based on the known package phase y and the number of candidate unfoldings Confirmed. Symbol z n-C:n-1 Indicator element [z n-c ,…,z n-1 ] T , which is a subset of vector z. Each existing surviving path k has a length For any sample n = C+1,…,N, and for each surviving path k = 1,…,K, the first C expanded estimates of the path are From the initial frequency estimation and phase offset estimation A defined straight line is The deviation from the line is predicted by estimating the phase error at sample n using the previous expansion estimate.

[0142] In some implementations, the phase error estimate is a linear minimum mean square error (LMMSE) estimate, expressed as:

[0143]

[0144] The LMMSE phase error estimate has a prediction error variance. In other implementations, phase error can be predicted faster using nearest neighbor estimation, but with lower accuracy.

[0145]

[0146] The predicted unfolding phase is

[0147] Given a predicted phase error, each The likelihood function of the value is:

[0148]

[0149] The variance of the prediction error of the LMMSE estimator is:

[0150]

[0151] closest K Value (denoted as) The one with the highest likelihood is considered a candidate for path continuation. Each candidate... The total expansion path length (negative log-likelihood function) is

[0152]

[0153] Repeat the same process for all K surviving paths to obtain the candidate path lengths. Each of the K existing surviving paths has K possible expansion values. At most K 2 There are several possible paths. Among these K... 2 Of the possible paths, only the K most likely (i.e., shortest) paths are preserved. The K new surviving paths extend part or all of their preceding paths, expanding the historical update to... For samples n = 1, ..., C, this procedure is also applicable except that only the first n-1 samples are used for phase error estimation.

[0154] After the last sample n=N, the most likely unfolded sequence It has the shortest path length The surviving path k. The maximum likelihood expansion phase is

[0155] After estimating the maximum likelihood expansion phase, the remaining objective is to refine the frequency. Figure 7C The process of frequency refinement via linear regression 616 in a frequency estimation algorithm 612 according to some example implementations is illustrated. In a given... Given the statistical characteristics of phase noise, the objective is to estimate the best interpretation. The slope f of the straight line.

[0156] Order 1 N =[1,…,1] T Let t represent a vector of length N consisting entirely of 1s, where t = [t1, ..., t2]. N ] T Let A represent a time sample vector of length N, where A = [t, 1]. N ] represents the concatenated vectors t and 1 N The matrix β = [f, θ] represents the vector of parameters to be estimated, and Q... NThis represents the phase error autocovariance matrix of a sequence of length N. In some implementations, the matrix inverse is... It can be calculated directly numerically. In other implementations, it can be done by first calculating the Topulitz matrix Q. N The matrix is ​​approximated as a cyclic matrix, and then the inverse of the cyclic approximation is obtained by using the Fast Fourier Transform algorithm to approximate the matrix inverse. Linear regression is used to estimate the slope (frequency f) and intercept (phase offset θ) of a straight line. In some implementations, linear regression can be performed using generalized least squares estimation (GLS):

[0157]

[0158] The advantage of using GLS is that it can update the frequency and phase shift of the beat signal more accurately. In other implementations, for faster updates, linear regression can be performed using ordinary least squares, ignoring the statistical characteristics of the phase error to avoid Q-factor errors. N The reversal, that is,

[0159]

[0160] The estimate is then used for phase expansion in subsequent iterations.

[0161] Figure 6 The frequency estimation algorithm 612 continues to alternate between Viterbi phase expansion 614 and linear regression 616 until a stopping criterion or termination condition is met. In some implementations, the stopping criterion may be when the path length increases from iteration b-1 to b, i.e., L(b) > L(b-1). In other implementations, the stopping criterion may be when the number of iterations b reaches the maximum number of iterations B (i.e., b = B). The final frequency estimate 618 is the value of f used in the last iteration.

[0162] The following description Figure 6 Some other key aspects of the frequency estimation algorithm 612.

[0163] Initialization: In some implementations, initial frequency estimation can be performed on a single pair. and initial phase offset estimation Execute iterative algorithm 612. In some implementations, initial frequency estimation... This corresponds to the frequency of the peak value in the periodogram of the interference signal. In other implementations, the initial frequency is estimated... This is the frequency corresponding to the center frequency of the Lorentz function fitted to the power spectral density of the interference signal. In some implementations, the algorithm can estimate using M initial frequencies. and M initial phase offset estimates To execute. Then, the final frequency estimation... It is the estimate with the shortest unfolding path among all initializations. In some implementations, there are M initial frequency estimates. These can be linearly spaced frequencies on a grid. In other implementations, M initial frequency estimates... The frequencies can be randomly and uniformly distributed. In other implementations, M initial frequency estimates... The results include alternative frequency estimation techniques, such as the peak value of the periodogram of the interfering signal or the center frequency of the Lorentz function fitted to the power spectral density of the interfering signal.

[0164] Noise statistics: In some implementations, the laser phase noise φ n It is likely dominated by spontaneous emission, therefore the frequency noise ω n =dφ n / dt can be assumed to be white noise and Gaussian. The frequency noise may have a constant frequency. =Δω, where Δν = Δω / (2π) is the full width at half maximum (FWHM) laser linewidth in Hz, and is assumed to be known. In this scenario, the phase noise is a Wiener process. For a fixed delay τ, the resulting phase change Δφ n (t; τ) is a zero-mean stationary Gaussian process with a triangular autocorrelation function.

[0165]

[0166] In other embodiments, the laser phase noise φ n The frequency noise may be affected by the wavelength scanning of the laser emitter. Therefore, it may be colored noise rather than white noise. In some implementations, the frequency noise may have a first-order low-pass transfer function, with its power spectral density expressed as:

[0167]

[0168] Where, α ω These are scaling parameters, and ω1 is the cutoff frequency. The phase change PSD is...

[0169]

[0170] In some implementations, the PSD may have a second-order low-pass transfer function, the expression of which is:

[0171]

[0172] Where, α ω ω2 is the scaling parameter, ω2 is the cutoff frequency, and q is the quality factor. In other implementations, frequency noise has multiple sources, including white noise and flicker (1 / f) noise.

[0173] Additive observation phase noise

[0174] Given the amplitude of the measured signal |r n Under the premise that |, the scaled AOPN term 2π∈ n It has a zero-mean von Mises distribution, and for a, |r n | and σ w 2 It exhibits complex dependencies. The variance of AOPN can be approximated as...

[0175]

[0176] Figure 8 The illustration depicts a scenario illustrating an example use case of an FMCW lidar system according to some exemplary implementations. A vehicle 802 moving on a road link 804 can be connected to a base station 806. The road link may have one or more obstacles 808, and the target may be to cross the road link 804 without colliding with the obstacles 808. For this purpose, it is necessary to accurately estimate the depth / range of the obstacles 808 to be identified, so that a route can be planned for the vehicle 802 to avoid the obstacles 808.

[0177] Vehicle 802 can be a manually driven vehicle, a semi-autonomous vehicle, or a fully autonomous vehicle, and can be configured to communicate with base station 806. In this regard, vehicle 802 can be equipped with suitable components to perform remote sensing, data communication, and data processing. For this purpose, it is conceivable that the vehicle could be equipped with an onboard FMCW lidar system, such as the system described above. The lidar system's transmitter emits radiation waves or beams (shown by solid lines) towards obstacle 808 and receives the emitted waves / beams reflected from the scene ahead (shown by dashed lines). Because vehicle 802 may be moving and / or due to errors in the source laser, conventional techniques may not be able to accurately infer the depth estimate of obstacle 808.

[0178] Vehicle 802 can invoke an FMCW LiDAR system to perform accurate depth estimation of obstacle 808. The FMCW LiDAR system can be fully or partially mounted on vehicle 802. In embodiments where the FMCW LiDAR system is partially mounted on vehicle 802, the relevant calculation steps for frequency estimation can be performed via edge computing with respect to base station 806. In some example embodiments, vehicle 802 can determine the precise extent of obstacle 808 using the FMCW LiDAR system, thereby determining the geographical location of obstacle 808. Therefore, the onboard controller of vehicle 808 can replan the route of vehicle 808 to avoid collisions with obstacle 808. In some example embodiments, vehicle 802 can additionally or alternatively transmit at least the geographical location of obstacle 808 to base station 806 to update the map of the area where road link 804 is located.

[0179] Although the example use cases are described with reference to road vehicles, the example implementations described herein can be applied to any type of vehicle, such as aircraft, water vehicles, spacecraft, etc. Other example uses of some implementations include industrial robots, computer vision systems, and autonomous driving.

[0180] Figure 9 A system block diagram for implementing an FMCW lidar system is shown according to some example embodiments. The controller 911 includes a processor 940, a computer-readable storage device 912, a storage device 958, and a user interface 949 connected via a bus 956, and having an optional display 952 and a keyboard 951. For example, the user interface 964, which communicates with the processor 940 and the computer-readable storage device 912, acquires image data and stores it in the computer-readable storage device 912 upon receiving input from the user on the surface of the user interface 957 (keyboard 953).

[0181] Computer 911 may include a power supply 954, which may optionally be located externally to computer 911, depending on the application. A user input interface 957 adapted for connection to a display device 948 may be connected via bus 956, wherein display device 948 may include a computer monitor, camera, television, projector, or mobile device, etc. Network interface controller (NIC) 934 is adapted for connection to network 936 via bus 956, wherein image data or other data may be presented on a third-party display device, third-party imaging device, and / or third-party printing device external to computer 911.

[0182] Still refer to Figure 9Image data or other electronic data can be transmitted through the communication channel of network 936 and / or stored in storage system 958 for storage and / or further processing. Furthermore, time-series data or other data can be received wirelessly or wiredly from receiver 946 (or external receiver 938), or transmitted wirelessly or wiredly by transmitter 947 (or external transmitter 939), both receiver 946 and transmitter 947 being connected via bus 956. Computer 911 can be connected to external sensing device 944 and external input / output device 941 via input interface 908. For example, external sensing device 904 may include sensors that collect data before, during, and after the machine's time-series data acquisition. Computer 911 can be connected to other external computers 942. Output interface 909 can be used to output processed data from processor 940. Additionally, the user interface 949, which communicates with the processor 940 and the non-transitory computer-readable storage medium 912, acquires area data and stores it in the non-transitory computer-readable storage medium 912 when it receives input from the user on the surface of the user interface 949.

[0183] The above description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of this disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with a feasible description of implementing one or more exemplary embodiments. Various changes to the function and arrangement of the elements are contemplated without departing from the spirit and scope of the subject matter disclosed in the appended claims.

[0184] Specific details are set forth in the following description to provide a comprehensive understanding of the implementation. However, those skilled in the art will understand that implementations can be carried out without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the implementation with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the implementation. Furthermore, the same reference numerals and names in the various figures denote the same elements. Additionally, the various implementations may be described as processes shown in flowcharts, flow diagrams, data flow diagrams, structural diagrams, or block diagrams. Although flowcharts may describe operations as sequential processes, many operations may be performed in parallel or simultaneously. Furthermore, the order of operations may be rearranged. A process may terminate upon completion of its operations, but may have additional steps not discussed or included in the figures. Furthermore, not all operations in any particular described process may occur in all implementations. A process may correspond to a method, function, program, subroutine, subroutines, etc. When a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or the main function.

[0185] Furthermore, implementations of the disclosed subject matter can be carried out, at least partially, manually or automatically. They can be performed, or at least assisted by, using machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof, for manual or automatic implementation. When implemented in software, firmware, middleware, or microcode, program code or code segments for performing the necessary tasks can be stored in a machine-readable medium. A processor can perform the necessary tasks. The various methods or processes outlined herein can be encoded as software executable on one or more processors employing any of various operating systems or platforms. Additionally, such software can be written using a variety of suitable programming languages ​​and / or programming or scripting tools, and can also be compiled into executable machine language code or intermediate code that executes on a framework or virtual machine. Typically, in various implementations, the functionality of program modules can be combined or distributed as needed.

[0186] Embodiments of this disclosure can be embodied as a method, examples of which have been provided. Actions performed as part of this method can be ordered in any suitable manner. Thus, embodiments can be constructed in which actions are performed in a different order than those shown, which may include performing some actions simultaneously, even if the actions are shown as sequential in the illustrative embodiments. Furthermore, ordinal terms such as “first,” “second,” etc., used in the claims to modify claim elements do not themselves indicate any priority, procedure, or order of one claim element over another, or the temporal order of the actions of the method, but are merely labels to distinguish one claim element having a certain name from another element having the same name (except for the use of ordinal terms). Although this disclosure has been described with reference to certain preferred embodiments, it should be understood that various other modifications and variations can be made within the spirit and scope of this disclosure. Therefore, the appended claims cover all such changes and variations within the true spirit and scope of this disclosure.

Claims

1. A frequency modulated continuous wave (FMCW) device, the FMCW device comprising: A transmitter configured to transmit at least one radiated wave to a scene, wherein the transmitted wave is modulated in the frequency domain using linear modulation, the linear modulation being impaired, resulting in nonlinearity of the transmitted wave in the frequency domain; A receiver configured to receive the reflection of the transmitted wave from the scene; A mixer operatively connected to the transmitter and the receiver and configured to interfere a copy of the transmitted wave with a reflection of the received transmitted wave to generate a beat signal. An analog-to-digital converter (ADC) operatively connected to the mixer and configured to generate a sample sequence of the beat signal having a wrap-around phase in the time domain; and A processor configured to iteratively estimate the frequency of the beat signal in the time domain based on 1) a phase expansion of a sample of the beat signal affected by a correlated phase error derived from the phase noise statistics of the transmitter and 2) a linear regression that fits the frequency of the beat signal to the expanded phase of the beat signal, until a termination condition is met.

2. The FMCW device according to claim 1, wherein, In order to execute the current iteration of the estimation, the processor is configured to: For each sample in the sample sequence of the beat signal, determine the current phase error and phase expansion number of fitting the previous frequency and previous phase shift of the beat signal determined during previous iterations, wherein the current phase error of the current sample in the sequence of the beat signal is associated with the previous phase error of the previous sample in the sequence of the beat signal through predetermined phase noise statistics; and The current frequency and current phase offset of the beat signal used in the current iteration are updated based on the determined current phase error and the determined phase expansion number.

3. The FMCW device according to claim 2, wherein, The processor is configured to iteratively estimate the frequency of the beat signal in the time domain using an alternative optimization method, the alternative optimization method including a Viterbi algorithm that probabilistically determines the current phase error and the phase unrolling number such that the current phase error and the phase unrolling number fit the likelihood of the entire sample sequence of the beat signal.

4. The FMCW device according to claim 3, wherein, The alternative optimization method uses generalized least squares (GLS) regression to update the frequency and phase shift of the beat signal.

5. The FMCW device according to claim 3, wherein, The alternative optimization method uses least squares regression to update the frequency and phase shift of the beat signal.

6. The FMCW device according to claim 3, wherein, The termination condition compares the likelihood given by the Viterbi algorithm with a threshold.

7. The FMCW device according to claim 3, wherein, For each current sample in the sample sequence of the beat signal, the Viterbi algorithm uses the previous phase error and the previous phase unrolling number determined for the previous samples to perform a causal estimate of the current phase error and the current phase unrolling number.

8. The FMCW device according to claim 7, wherein, The causal estimates of the current phase error and the current phase expansion number are determined by linear minimum mean square error estimation.

9. The FMCW device according to claim 1, wherein, The phase noise statistical characteristics include the autocorrelation function of the phase noise of the transmitter and the autocorrelation function of the additive noise of the receiver.

10. The FMCW device according to claim 1, wherein, The termination condition is the number of iterations.

11. A lidar comprising the FMCW device according to claim 1.

12. The FMCW device according to claim 1, wherein, The processor is also configured to estimate the distance to objects in the scene based on the estimated frequency of the beat signal.

13. A lidar comprising the FMCW device according to claim 12, wherein, The transmitter includes a laser source whose coherence length is shorter than the distance to the object.

14. A frequency estimation method using a frequency-modulated continuous wave (FMCW) device, the frequency estimation method comprising the following steps: At least one radiated wave is transmitted to a scene, wherein the transmitted wave is modulated by a transmitter in the frequency domain using linear modulation, and the linear modulation is impaired, resulting in nonlinearity of the transmitted wave in the frequency domain. Receive the reflection of the transmitted wave from the scene; The copy of the transmitted wave is interfered with the reflection of the received transmitted wave to generate a beat signal; Generate a sample sequence of the beat signal with enclosing phase in the time domain; and Based on 1) the phase expansion of a sample of the beat signal affected by a related phase error derived from the phase noise statistical characteristics of the transmitter and 2) a linear regression that fits the frequency of the beat signal to the expanded phase of the beat signal, the frequency of the beat signal in the time domain is iteratively estimated until a termination condition is met.

15. The frequency estimation method according to claim 14, wherein, The current iteration of the frequency estimation includes: For each sample in the sample sequence of the beat signal, determine the current phase error and phase spread number of fitting the previous frequency and previous phase shift of the beat signal determined during previous iterations, wherein the current phase error of the current sample in the sequence of the beat signal is associated with the previous phase error of the previous sample in the sequence of the beat signal through predetermined phase noise statistics; and The current frequency and current phase offset of the beat signal used in the current iteration are updated based on the determined current phase error and the determined phase expansion number.

16. The frequency estimation method according to claim 15, wherein, The iterative estimation of the frequency of the beat signal in the time domain is based on an alternative optimization method, which includes a Viterbi algorithm that probabilistically determines the current phase error and the phase unrolling number to maximize the likelihood of fitting the current phase error and the phase unrolling number across the entire sample sequence of the beat signal.

17. The frequency estimation method according to claim 16, wherein, For each current sample in the sample sequence of the beat signal, the Viterbi algorithm uses the previous phase error and the previous phase unrolling number determined for the previous samples to perform a causal estimate of the current phase error and the current phase unrolling number.

18. The frequency estimation method according to claim 17, wherein, The alternative optimization method uses generalized least squares (GLS) regression to update the frequency and phase shift of the beat signal.

19. The frequency estimation method according to claim 15, wherein, The alternative optimization method uses least squares regression to update the frequency and phase shift of the beat signal.

20. A non-transitory computer-readable medium storing instructions executable by a computer to control a frequency-modulated continuous wave (FMCW) device to perform a frequency estimation method, the frequency estimation method comprising the following steps: At least one radiated wave is transmitted to a scene, wherein the transmitted wave is modulated by a transmitter in the frequency domain using linear modulation, and the linear modulation is impaired, resulting in nonlinearity of the transmitted wave in the frequency domain. Receive the reflection of the transmitted wave from the scene; The copy of the transmitted wave is interfered with the reflection of the received transmitted wave to generate a beat signal; Generate a sample sequence of the beat signal with enclosing phase in the time domain; and Based on 1) the phase expansion of a sample of the beat signal affected by a related phase error derived from the phase noise statistical characteristics of the transmitter and 2) a linear regression that fits the frequency of the beat signal to the expanded phase of the beat signal, the frequency of the beat signal in the time domain is iteratively estimated until a termination condition is met.

Images