Radar system and method for estimating distance and speed using step frequency waveforms

Abstract

The invention relates to a radar system and a method for estimating distance and speed using step frequency waveforms. A radar system and method is provided and includes transmitting a radar signal within a frame having N radar chirps, the N radar chirps having a step frequency waveform; receiving and sampling radar signals reflected from a target; a distance FFT process including a first domain fast Fourier transform (FFT) and a Doppler FFT process including a second domain FFT are performed on the received value to generate a distance FFT value and a Doppler FFT value. The distance and velocity of the target are estimated based on the distance FFT value and the Doppler FFT value, where the estimated distance r and the estimated velocity v of the target are calculated based on at least one equation comprising: (i) a first term corresponding to the target distance r0 measured by a first radar chirp of the N radar chirps, and (ii) a second term corresponding to the target distance r0 measured by a second radar chirp of the N radar chirps; and (ii) a second term corresponding to a center wavelength [lambda] N / 2 of a plurality of radar chirps of the frame.

Description

Technical Field

[0001] The present disclosure relates to radar systems and methods, and more particularly, to radar systems and methods for estimating range and velocity using a stepped frequency waveform. Background Art

[0002] This section provides background information related to the present disclosure, which is not necessarily prior art.

[0003] Automotive radar sensors are used in vehicle sensing systems to determine information about objects in the vehicle environment, such as the position, size, orientation, velocity, and acceleration of objects in the vehicle environment. The sensed information can be used, for example, by other vehicle systems, such as autonomous driving systems and / or advanced driver assistance systems (ADAS), such as automatic and adaptive cruise control systems, blind spot monitoring systems, etc., to control the steering system, braking system, throttle system, driver alert and warning systems, and / or other vehicle systems.

[0004] A radar system can transmit multiple radar chirps within a particular transmit frame and then receive signals corresponding to the transmitted chirps reflected from objects within the vehicle environment. The frequency of the radar signal can vary during each individual chirp. For example, the frequency during a particular chirp can increase from the initial frequency of the chirp to the higher end frequency of the chirp over the time period of the chirp, resulting in a rising chirp having an increasing frequency over the time period of the chirp. Alternatively, the frequency during a particular chirp can decrease from the initial frequency of the chirp to the lower end frequency of the chirp over the time period of the chirp, resulting in a falling chirp having a decreasing frequency over the time period of the chirp.

[0005] In addition, in the processing of the transmit frame, the initial frequency and the end frequency of each chirp can remain the same for each chirp. However, in other radar systems, a stepped frequency waveform can be used such that the initial frequency and the end frequency of the transmitted signal change chirp by chirp. For example, a radar system can utilize a descending frame or a stepped-down frequency waveform such that the initial frequency and the end frequency of each subsequent chirp are lower than the initial frequency and the end frequency of the previous chirp within the frame. Alternatively, a radar system can utilize an ascending frame or a stepped-up frequency waveform such that the initial frequency and the end frequency of each subsequent chirp are higher than the initial frequency and the end frequency of the previous chirp within the frame.

[0006] However, existing radar systems may suffer from errors due to range migration, Doppler aliasing, etc. Summary of the Invention

[0007] This section provides a general overview of the present disclosure and is not a complete disclosure of its full scope or all of its features.

[0008] A radar system is provided, the radar system including at least one processor and a memory, the radar system being configured to: transmit a radar signal within a frame having N radar chirps, the N radar chirps having a stepped frequency waveform such that an initial transmission frequency and an end transmission frequency are changed for each subsequent chirp within the N radar chirps, and N is greater than 1; receive and sample the radar signal reflected from a target to generate received values from the received and sampled radar signal; perform range FFT processing including a first-domain fast Fourier transform (FFT) and Doppler FFT processing including a second-domain FFT on the received values to generate range FFT values and Doppler FFT values; estimate a range and a velocity of the target based on the range FFT values and the Doppler FFT values, wherein the estimated range r and the estimated velocity v of the target are calculated based on at least one arithmetic expression, the arithmetic expression including: (i) a first term corresponding to a target range r0 measured by a first radar chirp among the N radar chirps, and (ii) a second term corresponding to a center wavelength λ of the plurality of radar chirps of the frame N / 2 corresponding thereto.

[0009] Among other features, the at least one arithmetic expression further includes: a third term corresponding to an average range measurement result from all N radar chirps within the frame wherein, T N corresponds to the transmission time of each chirp.

[0010] Among other features, the at least one arithmetic expression includes the following arithmetic expression:

[0011]

[0012]

[0013] wherein: F1 and F2 respectively represent the frequencies measured after the first-domain FFT and the second-domain FFT; s c and s f respectively represent the direction of the chirp slope and the direction of the frame slope; f r1 represents the first-domain range frequency, defined as wherein, k c is the chirp slope and c is the speed of light; f r2 represents the second-domain range frequency, defined as λ0 is the wavelength of the first chirp in the frame; and n is the chirp index.

[0014] Among other features, the stepped frequency waveform of the radar signal of the N radar chirps is generated to meet the following conditions:

[0015]

[0016] Among other features, the at least one processor and memory are further configured to determine s c s f is greater than 0 and s c is less than 0, and in response to s c s f being greater than 0 and s c being less than 0, expand the index of the second domain FFT.

[0017] Among other features, the at least one processor and memory are further configured to determine s c s f is positive or negative, and based on s c s f being positive or negative, perform a downshift of the Doppler spectrum of the Doppler FFT values.

[0018] Among other features, the at least one processor and memory are further configured to perform the expansion of the Doppler spectrum based on the number K of times the range frequencies of the first domain FFT are folded.

[0019] Among other features, the at least one processor and memory are further configured to calculate K based on the following equation:

[0020]

[0021] where, represents the maximum coverage of the second domain range, r1Bin is the range bin size of the first domain range, and Δf corresponds to the frequency offset between the radar chirps among the N radar chirps.

[0022] Among other features, the at least one processor and memory are configured to generate the stepped frequency waveform of the N radar chirps such that the initial transmit frequency and the end transmit frequency of each radar chirp after the first radar chirp are respectively lower than the initial transmit frequency and the end transmit frequency of the immediately preceding radar chirp.

[0023] Among other features, the radar system is installed in a vehicle having at least one vehicle system, the at least one processor and memory are configured to transmit the estimates of the range and the velocity of the target to the at least one vehicle system, and the at least one vehicle system is configured to control at least one of a steering system, a braking system, a throttle system, or a driver alert and warning system based on the estimates of the range and the velocity of the target.

[0024] A method is also provided, including: transmitting a radar signal within a frame having N radar chirps by using at least one processor and a memory of a radar system, where the N radar chirps have a stepped-frequency waveform such that an initial transmission frequency and an end transmission frequency are changed for each subsequent chirp within the N radar chirps, and N is greater than 1; receiving and sampling, by using an analog-to-digital converter of the radar system, the radar signal reflected from a target to generate received values from the received and sampled radar signal; performing, by using the at least one processor and the memory, range FFT processing including a first-domain fast Fourier transform (FFT) and Doppler FFT processing including a second-domain FFT on the received values to generate range FFT values and Doppler FFT values; estimating, by using the at least one processor and the memory, a range and a velocity of the target based on the range FFT values and the Doppler FFT values, where an estimated range r and an estimated velocity v of the target are calculated based on at least one arithmetic expression, and the arithmetic expression includes: (i) a first term corresponding to a target range r0 measured by a first radar chirp among the N radar chirps, and (ii) a second term corresponding to a center wavelength λ of the plurality of radar chirps of the frame N / 2 corresponding to the second term.

[0025] In other features, the at least one arithmetic expression further includes: a third term corresponding to an average range measurement result from all N radar chirps within the frame where T N corresponds to a transmission time of each chirp.

[0026] In other features, the at least one arithmetic expression includes the following arithmetic expression:

[0027]

[0028]

[0029] where: F1 and F2 respectively represent frequencies measured after the first-domain FFT and the second-domain FFT; s c and s f respectively represent the direction of the chirp slope and the direction of the frame slope; f r1 represents a first-domain range frequency, defined as where k c is the chirp slope and c is the speed of light; f r2 represents a second-domain range frequency, defined as λ0 is the wavelength of the first chirp in the frame; and n is the chirp index.

[0030] In other features, the stepped-frequency waveform of the radar signal of the N radar chirps is generated to meet the following conditions:

[0031]

[0032] Among other features, the method further includes: determining s c s f whether it is greater than 0 and s c whether it is less than 0, and in response to s c s f being greater than 0 and s c being less than 0, expanding the index of the second-domain FFT.

[0033] Among other features, the method further includes: determining s c s f whether it is positive or negative, and based on s c s f whether it is positive or negative, performing a downward shift of the Doppler spectrum of the Doppler FFT values.

[0034] Among other features, the method further includes: performing an expansion of the Doppler spectrum based on the number of times K that the range frequencies of the first-domain FFT are folded.

[0035] Among other features, the method further includes: calculating K based on the following formula:

[0036]

[0037] wherein, represents the maximum coverage of the second-domain range, r1Bin is the range bin size of the first-domain range, and Δf corresponds to the frequency offset between the radar chirps among the N radar chirps.

[0038] Among other features, the method further includes: generating the stepped-frequency waveform of the N radar chirps such that the initial transmit frequency and the end transmit frequency of each radar chirp after the first radar chirp are respectively lower than the initial transmit frequency and the end transmit frequency of the immediately preceding radar chirp.

[0039] Among other features, the radar system is installed in a vehicle having at least one vehicle system, and the method further includes: transmitting the estimates of the range and the velocity of the target to the at least one vehicle system, and the at least one vehicle system is configured to control at least one of a steering system, a braking system, a throttle system, or a driver alert and warning system based on the estimates of the range and the velocity of the target.

[0040] Based on the description provided herein, other application areas will become apparent. The description and specific examples in this summary are intended for illustrative purposes only and are not intended to limit the scope of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings described herein are for illustrative purposes only, are not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0042] Figure 1 is a block diagram of a vehicle having a radar system according to the present disclosure.

[0043] Figure 2 is another block diagram of a vehicle having a radar system according to the present disclosure.

[0044] Figure 3 is a diagram illustrating a chirp of a radar signal with a frequency-modulated continuous waveform (FMCW) transmitted within a frame, where all chirps have the same center frequency.

[0045] Figure 4 is a diagram illustrating a stepped-frequency waveform of a radar signal chirp transmitted within a frame.

[0046] Figure 5 is a diagram illustrating a two-dimensional matrix of return signal samples for a received radar signal, a first-dimensional fast Fourier transform (FFT) bin, and a second-dimensional FFT bin.

[0047] Figure 6 Illustrates the speed estimation error of an existing system.

[0048] Figure 7 Illustrates the distance estimation error of an existing system.

[0049] Figure 8 Illustrates the reduced speed estimation error produced by the system and method of the present invention.

[0050] Figure 9 Illustrates the reduced distance estimation error produced by the system and method of the present disclosure.

[0051] Figure 10 Illustrates the down-chirp waveform of the transmitted radar signal.

[0052] Figure 11 Illustrates the reduced speed estimation error produced using waveform constraints according to the present disclosure.

[0053] Figure 12 Illustrates the reduced distance estimation error produced using waveform constraints according to the present disclosure.

[0054] Figure 13 Illustrates the zero Doppler indices for respective distance bins according to the present disclosure.

[0055] Figure 14 Illustrates the expanded second domain indices according to the present disclosure.

[0056] Figure 15 Illustrates the aliased range frequency that unfolds when the chirp slope multiplied by the frame slope is positive according to the present disclosure.

[0057] Figure 16 Illustrates an example of positive and negative index regions within a single block after Doppler spreading according to the present disclosure.

[0058] Figure 17 Illustrates the shifting technique according to the present disclosure.

[0059] Figure 18 Illustrates a flowchart of an integrated framework for handling waveform variations according to the present disclosure.

[0060] In the various views of the drawings, corresponding reference numerals denote corresponding components. Detailed Description

[0061] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0062] The present disclosure provides methods, processes, and conditions for improving the accuracy of estimating the distance and velocity of an object using a radar system that transmits a radar signal by changing the frequency of a radar chirp within a transmitted frame according to a stepped frequency waveform.

[0063] In a first aspect of the present disclosure, new algorithms for estimating distance and velocity are provided that reduce the distance and velocity estimation errors due to range migration, as discussed further below in detail.

[0064] In a second aspect of the present disclosure, waveform constraints and conditions are provided that reduce the distance and velocity estimation errors due to Doppler aliasing errors, as discussed further below in detail.

[0065] In a third aspect of the present invention, an integrated framework for processing four different combinations of stepped frequency waveforms is provided, namely, rising chirp - rising frame, falling chirp - rising frame, rising chirp - falling frame, and falling chirp - falling frame. As discussed further below in detail, the integrated framework can provide a process and method by which the Doppler index, i.e., the second domain index, is extended based on range information and the Doppler index is unfolded based on positive and negative velocity coverage, as discussed further below in detail.

[0066] Referring to Figure 1 and Figure 2 , a radar system 100 of a vehicle 102 according to the present disclosure is shown. The radar system 100 transmits a signal 104 that is reflected from an object or target 106 in the environment of the vehicle 102. Although in Figure 1For illustrative purposes, a single target 106 is shown, but in reality, target 106 may include multiple objects. The radar system 100 receives the signal 108 reflected from the target 106. Based on the characteristics of the received signal 108, the radar system 100 determines information about the target 106, such as distance and speed, which is then used to determine other information about the target 106, such as the position, size, azimuth, speed, acceleration, etc. of the target.

[0067] The radar system 100 includes a processor 200 and a memory 202. The memory 202 stores code executed by the processor 200 to perform the required functions for transmitting, receiving, and processing signals 104, 108, and determining information about the target 106 (such as distance and speed) based on the characteristics of the received signal 108. Although the exemplary implementation shows a single processor 200, multiple processors and / or modules working together can alternatively be used. The radar system 100 includes a transmitter 204 that transmits the signal 104 and a receiver 206 that receives the signal 108 using an antenna array 207. The antenna array 207 includes one or more transmit (TX) antennas and one or more receive (RX) antennas for transmitting and receiving signals 104, 108. The processor 200, for example, executes the transmit / receive code 208 stored in the memory 202 to control the transmitter 204 and the receiver 206 to transmit and receive signals 104, 108 using the antenna array 207. The memory 202 also stores the code 210 used by the processor 200 to perform a first-domain fast Fourier transform (FFT) on the received radar signals 108, 208 and the code 212 to perform a second-domain Doppler FFT. For example, the processor 200 uses the distance FFT code 210 to perform a distance FFT to generate a first-domain distance index and uses the Doppler FFT code 212 to perform a Doppler FFT to generate a second-domain Doppler index. The processor 200 then uses the distance estimation code 214 and the speed estimation code 216 to process the distance index and the Doppler index according to the present disclosure to determine the distance and speed of the target 106, respectively. The processing and methods utilized by the distance estimation code 214 and the speed estimation code 216 executed by the processor 200 according to the present disclosure are discussed in further detail below.

[0068] The processor 200 may transfer the determined information about the target 106 (such as the position, size, azimuth, speed, and acceleration of the target 106 determined based on the distance and speed information) to other vehicle systems 220, such as an autonomous driving system and / or an advanced driver assistance system (ADAS), such as an adaptive cruise control system, a blind spot monitoring system, etc. The other vehicle systems 220 can then utilize and process the information about the target 106 to appropriately control the steering system, the braking system, the throttle system, the driver alert and warning system, and / or other systems of the vehicle 102 based on the information about the target 106.

[0069] The radar system 100 also includes an analog-to-digital converter (ADC) 205 that samples the received radar signal 108 using a specified sampling rate and converts analog information about the received radar signal (such as the received frequency) into a digital format. The ADC 205 can be implemented using a separate processor, multiple processors, and / or a separate module configured to perform analog-to-digital radar signal processing in accordance with the present disclosure.

[0070] Existing radar systems use frequency-modulated continuous-wave (FMCW) technology to determine the distance, speed, and angle or azimuth of objects in a vehicle environment. For example, Figure 3 An FMCW waveform is illustrated, including multiple chirps 302 within a single frame. Here, f c represents the center frequency for all chirps 302 within the frame. The frequency bandwidth of each chirp is represented by B1, and the pulse repetition time (PRT) or the time period between each chirp is shown as T. The chirp slope is defined as k c = B1 / T. In Figure 3 the example of, the center frequency of each chirp remains constant within the frame.

[0071] Referring to Figure 4 , a stepped-frequency waveform is illustrated, where the initial start frequency and the final end frequency of each chirp 302 change chirp by chirp. As Figure 4 shown, Δf represents the center frequency offset between adjacent chirps 302. Similar to the chirp slope of traditional FMCW, the frame slope of the stepped-frequency waveform can be determined as k f = Δf / T. When Δf is zero, the stepped-frequency waveform returns to the Figure 3 traditional FMCW waveform shown. For clarity and without sacrificing general applicability, the present disclosure discusses and describes the use of the stepped-frequency waveform for radar signal processing.

[0072] After the transmitted signal 104 is reflected from the target, the ADC samples the returned signal 108 at a sampling rate of f s to form Figure 5The two-dimensional matrix 500 shown. Each row in matrix 500 corresponds to the ADC samples collected from the chirps within a frame. In other words, a matrix 500 with x columns and y rows corresponds to the result of the ADC taking x samples for each of the y chirps within the frame. The row index corresponds to the chirp index, indicating the chirp from which the ADC samples of that row are obtained. To determine the distance and velocity of a target using the stepped-frequency FMCW method, the processor 200 executes the distance FFT code 210 to determine the first-dimensional FFT (or 1D FFT), which results in a bin represented at 502. The resulting bin at 502 is indexed by the chirp index and the distance index. Additionally, a specific distance index 504 within each chirp of the frame exemplifies a significant peak at that index within the chirp and corresponds to the estimated distance of the target. The processor 200 also executes the Doppler FFT code 212 to perform a second-dimensional FFT (or 2D FFT) on the ADC data cube, which produces a bin represented at 506. The resulting bin at 506 is indexed by the Doppler index and the distance index. The result of the second-dimensional FFT reveals significant peaks with higher amplitudes at 508, distinguishing them from adjacent low-amplitude noise bins. Then the distance and velocity of the object can be calculated based on the position of the peaks. In existing systems, such as the system described in EP3796038 titled "Object Range and Velocity Detection from Varying Radar Pulse Repetition Times", which is incorporated herein by reference, equations 1 and 2 are used to estimate the distance and velocity of the target:

[0073]

[0074]

[0075] where F1 and F2 respectively represent the frequencies measured after the first-domain FFT and the second-domain FFT, the parameters r and v represent the distance and Doppler velocity of the target, λ0 corresponds to the wavelength of the first chirp in the frame, and s c and s f represent the direction of the chirp slope and the direction of the frame slope. When the chirp slope is positive, s c is assigned 1, otherwise s c is assigned -1. Similarly, when the frame slope is positive, s f is assigned 1, otherwise s f is assigned -1. The term f r1 refers to the first-domain range frequency, defined as where k c is the chirp slope and c represents the speed of light. By utilizing f r1 , the distance r of the target is transformed into a frequency value measured within the first domain. Similarly, fr2 represents the second domain distance frequency, defined as

[0076] Assuming that F1 and F2 from Equation 1 and Equation 2 can be obtained from the positions of the target peaks after 2D FFT, and all other parameters are fixed and determined by the waveform, it becomes straightforward for the processor 200 to calculate the unknown parameters distance r and target velocity v using Equation 1 and Equation 2.

[0077] In the case where the target velocity is relatively low, Equation 1 and Equation 2 both produce satisfactory accuracy for distance and velocity estimation. However, when the target exhibits faster motion as the velocity increases, for each chirp, the measured distance varies significantly, which leads to a considerable error if a constant target distance is assumed. This phenomenon, known as range migration, introduces errors in the distance and velocity estimation of systems and methods using Equation 1 and Equation 2. Figure 6 and Figure 7 illustrate an example of the distance and velocity estimation errors caused by range migration. As Figure 6 and Figure 7 shown, as the target velocity increases, the estimation accuracy in both distance and velocity decreases.

[0078] In addition to the distance and velocity estimation errors caused by range migration, Figure 6 and Figure 7 also respectively illustrate two different discontinuities 600 and 602 present in the estimation results. These "jump" errors occur when the velocity measurement results become aliased. For example, when the Doppler velocity of the target is aliased, the velocity measurement results become wrapped and inaccurate. Although there are various techniques available for unwrapping the aliased Doppler velocity, these methods can only be applied after the initially incorrect wrapped velocity has been calculated. Since Equation 1 and Equation 2 assume that the measurement results are non-aliased, the wrapped velocity introduces an offset in both distance and velocity.

[0079] As described above, the existing systems using Equation 1 and Equation 2 have two main drawbacks. First, as the target velocity increases, the presence of range migration leads to an increase in errors in the distance and velocity measurement results. Second, when the Doppler velocity becomes aliased, using the wrapped velocity introduces an additional offset in both the distance measurement result and the velocity measurement result.

[0080] New distance and velocity equations

[0081] To overcome these limitations and drawbacks of the existing systems, the present disclosure includes using algorithms that address these limitations and drawbacks and minimize the above-mentioned errors for distance and speed calculations. The present disclosure also provides waveform conditions and constraints for the stepped frequency waveform to further reduce and minimize the errors. In particular, instead of Algorithm 1 and Algorithm 2, the systems and methods of the present disclosure utilize Algorithm 3 and Algorithm 4:

[0082]

[0083]

[0084] Where:

[0085] F1 and F2 respectively represent the frequencies measured after the first-domain FFT and the second-domain FFT;

[0086] s c and s f respectively represent the direction of the chirp slope and the direction of the frame slope (as described above);

[0087] f r1 refers to the first-domain range frequency, defined as where k c is the chirp slope, and c represents the speed of light (as described above);

[0088] f r2 represents the second-domain range frequency, defined as (as described above);

[0089] r0 is the target range measured by the first chirp of the frame;

[0090] v is the Doppler velocity of the target;

[0091] λ N / 2 is the center wavelength of the frame;

[0092] λ0 is the wavelength of the first chirp in the frame;

[0093] T n is the transmission time of each chirp; and

[0094] n is the chirp index.

[0095] Algorithm 3 and Algorithm 4 differ from Algorithm 1 and Algorithm 2 in several aspects. For example, in Algorithm 3 and Algorithm 4, the target range measured by the first chirp (denoted as r0) is used to replace the unspecified target range r in Algorithm 1 and Algorithm 2. Additionally, Algorithm 3 and Algorithm 4 utilize and refer to the center wavelength λ N / 2 of the frame, rather than just the wavelength λ0 of the first chirp in the frame as in Algorithm 1 and Algorithm 2.

[0096] When further compared with Equation 1 and Equation 2, Equation 3 and Equation 4 take into account the effects of range migration and wavelength variations between chirps within a stepped frequency waveform. For example, assuming the target moves at a constant velocity within a frame, the range measurements from individual chirps can be expressed as r0 - vT n . Then, the target range measured over the entire frame is the average range value of all chirp measurements, given as follows: Therefore, using the average range measurements from individual chirps provides a more accurate representation of the real-world scenario. The same principle applies to the Doppler frequency in the first domain. Since individual chirps have different wavelengths, the average Doppler frequency is expressed as 2v / λ in Equation 3 and Equation 4 N / 2 , rather than 2v / λ0 as used in Equation 1 and Equation 2.

[0097] Thus, compared with the systems and methods using Equation 1 and Equation 2, the radar systems and methods using Equation 3 and Equation 4 provide more accurate target range and velocity measurements.

[0098] Mathematical Proof of Equation 3 and Equation 4

[0099] This section provides the mathematical proof to support Equation 3 and Equation 4.

[0100] The linear frequency modulation waveform can be defined according to Equation 5:

[0101]

[0102] where t i = i / f s , represents the ADC sampling time; f n = f0 + nΔf, represents the center frequency of each chirp. The received signal reflected from the target is expressed according to Equation 6:

[0103]

[0104] where τ i,n = 2r i,n / c is the time delay for each fast sample t i . The target range is given by r i,n = r0 - vT n - vt i , where, represents the chirp timing, which is described in further detail in EP3796038. In the receiver, the transmitted signal is conjugated and multiplied with the received signal, as in Equation 7:

[0105]

[0106] Through several cancellations, Equation 7 can be expressed as Equation 8:

[0107]

[0108] Considering that the quadratic phase delay is relatively small and can be ignored, Equation 8 can be further simplified to Equation 9:

[0109]

[0110] Substitute r0 - vT n - vt i for τ i,n , and Equation 10 is obtained:

[0111]

[0112] If the quadratic term is ignored and f n = f0 + ns f Δf and are used in Equation 10, then this equation can be expressed as Equation 11:

[0113]

[0114] The term 2r0f0 / c in Equation 11 is a constant term and can be ignored. By using and , Equation 11 can be further simplified to Equation 12:

[0115]

[0116] Since t i is the fast time (referring to the frequency and time scale for each sampling within the chirp), and nT0 is the slow time (referring to the frequency and time scale of the chirp frame as a whole), the first-domain frequency and the second-domain frequency associated with each chirp are respectively represented by Equation 13 and Equation 14.

[0117]

[0118]

[0119] To simplify the equation, the first-domain frequency can be made non-negative by multiplying Equation 12 by -s c , thereby obtaining Equation 15 and Equation 16:

[0120]

[0121]

[0122] After performing a 2D FFT, the first domain frequencies measured by each chirp as defined in Equation 15 are averaged to obtain a final detection result with a frequency given by Equation 17:

[0123]

[0124] Obviously, Equation 16 remains constant and is independent of the chirp index n. Then Equation 16 can be expressed as Equation 18:

[0125]

[0126] Range and velocity error reduction

[0127] Figure 8 and Figure 9 shows the results obtained and the reduced errors when using Equations 3 and 4. Compared with Figure 6 and Figure 7 the errors illustrated, a significant reduction in range and velocity errors can be observed. However, some estimation / jump errors due to aliased Doppler velocities as shown in 600 and 602 persist.

[0128] Mitigation and reduction of "jump" errors

[0129] This section describes waveform constraints and conditions for stepped frequency waveforms that mitigate and reduce the above "jump" errors.

[0130] Equations 3 and 4 can be rewritten as Equations 19 and 20, as follows:

[0131]

[0132]

[0133] When Doppler aliasing occurs, the Doppler velocity becomes folded M times. Therefore, there is a difference given by V un M between the folded velocity and the measured velocity, where V un represents the maximum unambiguous velocity supported by the waveform. Using Equations 19 and 20, the range error can be expressed according to Equation 21:

[0134]

[0135] Similarly, the velocity error can be calculated according to Equation 22:

[0136]

[0137] From Equations 21 and 22, it is clear that if the waveform parameters satisfy the conditions outlined in Equation 23, both the range and velocity errors can be reduced to zero:

[0138]

[0139] The waveform condition of Equation 23 means that a decreasing chirp waveform is required to eliminate the estimation error caused by Doppler aliasing. Figure 10 A decreasing chirp waveform is illustrated, where the frequency of each chirp decreases over the time period of the chirp. Figure 10 The waveform of also illustrates a decreasing frame waveform, where the initial and end frequencies of each subsequent chirp are lower than the initial and end frequencies of the previous chirp within the frame.

[0140] Figure 11 and Figure 12 illustrates the range and velocity estimation errors when the stepped frequency waveform meets the conditions specified in Equation 23 above, compared to waveforms that do not meet the conditions of Equation 23. It is noted that both the velocity error and the range error are significantly reduced compared to the errors shown in Figures 6 to 9 . In addition, the "jump" error illustrated in the previous figures has been eliminated. Thus, compared to waveform design conditions / constraints that use Equations 3 and 4 without applying Equation 23, following the waveform design conditions / constraints of Equation 23 significantly reduces the range and velocity calculation errors.

[0141] Calculate the second domain index

[0142] Another advantage of the method for calculating range and velocity according to the present disclosure is a streamlined and adjustable method for calculating the second domain index.

[0143] In Equations 19 and 20, the unknown values of r0 and v will be determined, while the other parameters are predefined by the waveform or obtained from measurements. After performing the 2D FFT, the quantities F1 and F2 can be derived from the indices (idx1, idx2) of the target. Specifically, F1 corresponds to the first domain index and can be calculated using the following equation:

[0144] F1 = idx1 × f1 Bin Equation 24

[0145] where, f1Bin represents the first domain frequency interval size, defined as f1Bin = f s / N fft1 , where, N fft1 is the first domain FFT size. On the other hand, the calculation of the value of F2 is more complex because it depends on the relationship between the second domain range and Doppler frequency under different conditions. In this section, s c s f >0 examples of stepped frequency waveforms, together with another example, illustrate how to determine F2.

[0146] To determine the value of F2, the pattern of the zero Doppler index must be determined for each range bin. When sc s f When s > 0 and v = 0, a positive value of F2 will be observed, resulting in the formation of multiple diagonals with a positive slope, as Figure 13 illustrated, which depicts the zero Doppler index for each range bin. However, due to the limited frequency range in the second domain, any second domain range frequency exceeding the unambiguous frequency will cause aliasing, resulting in the generation of multiple diagonals instead of a single line. To unfold the aliased range frequencies, the number of times the range is folded must be determined for each range bin. This value of the fold number, denoted as K, can be calculated according to Equation 25:

[0147]

[0148] where represents the maximum coverage of the second domain range, and r1Bin is the range bin size of the first domain range in meters. When the fold number K is determined, the second domain index can be unfolded, as Figure 14 shown. In the case where the value of s c s f results in a negative range frequency, an additional downward shift is required before expanding the spectrum, as Figure 15 depicted. After expanding the spectrum, the zero Doppler index V0 can be calculated using Equation 26:

[0149]

[0150] In addition to the aliased range frequencies in the second domain, the Doppler frequencies can also be subject to aliasing. The maximum index intervals between the positive and negative Doppler frequencies and the zero Doppler index can be represented as pVelCov and nVelCov, respectively. The combined coverage of these two regions should be equal to the size of the second domain FFT, i.e., pVelCov + nVelCov = N fft2 . Figure 16 illustrates an example of the positive and negative index regions within a single block after Doppler expansion as Figure 14 shown. The region denoted by "+" represents the region of positive Doppler frequencies, while the region denoted by "-" represents the region of negative Doppler frequencies. Both the positive and negative Doppler frequency regions exhibit discontinuities and folding. For example, the lower right region denoted by "+" below the zero Doppler index line contains folded positive Doppler frequency indices, while the indices within the upper left triangular region denoted by "-" belong to folded negative Doppler frequencies. Therefore, for the indices located in these two triangular regions, as Figure 17 shown, shift techniques need to be applied to correct their positions.

[0151] Integrated Framework

[0152] The present disclosure provides a comprehensive framework with arithmetic expressions and processing methods for solving waveform variations, such as rising chirp - rising frame, falling chirp - rising frame, rising chirp - falling frame, and falling chirp - falling frame. The comprehensive framework of the present disclosure extends the Doppler index based on distance information and unfolds the Doppler index based on positive velocity coverage and negative velocity coverage.

[0153] For example, Figure 18 A flowchart of a calculation method and algorithm 700 that illustrates the use of a comprehensive framework for calculating a first - domain frequency and a second - domain frequency under all four conditions of a stepped - frequency waveform: rising chirp - rising frame, falling chirp - rising frame, rising chirp - falling frame, and falling chirp - falling frame. Algorithm 700 can be executed by a processor 200 that executes distance - estimation code 214 and velocity - estimation code 216 stored in a memory 202. At 702, target indices (idx1, idx2) are obtained after a 2D FFT. The target indices (idx1, idx2) correspond to the distance index and Doppler index of the first domain and the second domain. At 704, the zero - Doppler index is initially calculated using arithmetic expression 26. At 706, based on arithmetic expression 25, for a distance interval, the number of times the distance has been folded or the block index K is calculated. At 708, the algorithm determines whether a downward shift of the Doppler spectrum is required according to the sign of the parameter s c s f When s c s f is negative, the algorithm proceeds to 710 and performs the downward shift, then proceeds to 712. At 708, when s c s f is not negative, the algorithm proceeds to 711. At 711 and 712, the Doppler spectrum is extended based on the K value, as discussed above with reference to Figures 14 to 17 At 714 and 716, the algorithm determines whether the unfolding of the second - domain index is necessary based on the offset between idx2 and v0, and performs the unfolding of the second domain at 718 and 720 if necessary. At this stage, the correction of the second - domain index is completed, and the algorithm proceeds to 722. At 722, F1 and F2 are determined by the index pair (idx1, idx2) and the waveform parameters f1Bin and f2Bin. And the corresponding target distance r0 and target velocity v can be calculated by using arithmetic expressions 19 and 20.

[0154] Conclusion

[0155] Thus, the present disclosure provides significant progress and technical benefits in the field of using stepped - frequency waveforms in radar systems to estimate target distance and velocity. In particular, the present disclosure addresses key challenges in accurate estimation by considering range migration in the first - domain frequency calculation and eliminating estimation errors caused by Doppler aliasing. Additionally, a comprehensive framework is provided to effectively handle different waveform conditions.

[0156] As discussed above, the first aspect of the present invention addresses range migration during the calculation of the first domain frequency. By addressing the range migration effect, the accuracy of range estimation is significantly improved. This innovation takes into account factors such as target motion and the time delay between fast time and slow time, resulting in more accurate and reliable range and velocity calculations.

[0157] As further discussed above, the second aspect of the present disclosure addresses the problem of estimation errors caused by Doppler aliasing. Doppler aliasing introduces inaccuracies in range and velocity estimation, leading to distorted target trajectories. The systems and methods of the present disclosure minimize and / or eliminate these errors by providing guidelines, techniques, and waveform conditions and constraints to remove the effects of Doppler aliasing. This innovation ensures more accurate velocity estimation and enhances the overall quality of target tracking and fusion processing.

[0158] As further discussed above, the present invention provides a comprehensive framework that considers and processes different waveform conditions. The framework addresses waveform variations such as rising chirp - rising frame, falling chirp - rising frame, rising chirp - falling frame, and falling chirp - falling frame. By considering these different conditions, the framework enables more accurate frequency calculation and index unfolding, thereby improving estimation accuracy in various scenarios.

[0159] Compared with existing methods, the results of the present disclosure provide a significant improvement in the accuracy of target range and velocity estimation. These advancements have a wide range of applications in autonomous systems, where precise target tracking and situation awareness are crucial.

[0160] The foregoing description of the embodiments has been provided for purposes of illustration and description and is not intended to be exhaustive or to limit the present disclosure. The individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in another embodiment, even if not explicitly shown or described. The various embodiments can also vary in many ways. Such variations should not be regarded as a departure from the present disclosure, and all such modifications are intended to be included within the scope of the present disclosure. Although the various embodiments are described above as having certain features, any one or more of those features described with respect to any embodiment of the present disclosure can be implemented in and / or combined with the features of any other embodiment, even if the combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and permutations of one or more embodiments with each other are still within the scope of the present disclosure.

[0161] Exemplary embodiments are provided so that this disclosure will be thorough and will fully convey its scope to those skilled in the art. Specific details are set forth, including examples of specific components, devices, and methods, to provide a thorough understanding of the embodiments of this disclosure. It will be apparent to those skilled in the art that specific details need not be employed, and the exemplary embodiments may be embodied in many different forms and should not be construed as limiting the scope of this disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.

[0162] In the written description and claims, one or more steps within a method may be performed in a different order (or simultaneously) without changing the principles of this disclosure. Similarly, one or more instructions stored in a non-transitory computer-readable medium may be executed in a different order (or simultaneously) without changing the principles of this disclosure. Unless otherwise indicated, numbering or other marking of instructions or method steps is for convenience of reference and does not indicate a fixed order.

[0163] Spatial and functional relationships between elements (e.g., between modules) are described using various terms, including "connected," "engaged," "interface," and "coupled." Unless explicitly described as "direct," when describing the relationship between a first element and a second element in the above disclosure, the relationship includes a direct relationship where no other intermediate elements exist between the first element and the second element, and an indirect relationship where one or more intermediate elements exist between the first element and the second element (spatially or functionally).

[0164] The phrase "at least one of A, B, and C" should be interpreted as representing a logical (A OR B OR C) using non-exclusive logic OR and should not be interpreted as meaning "at least one of A, at least one of B, and at least one of C." The term "set" does not necessarily exclude the empty set. The term "non-empty set" can be used to indicate the exclusion of the empty set. The term "subset" does not necessarily require a proper subset. In other words, a first subset of a first set can be coextensive with (equal to) the first set.

[0165] In the drawings, the direction of the arrows indicated generally represents the information flow of interest (e.g., data or instructions) being illustrated. For example, when element A and element B exchange various information, but the information sent from element A to element B is relevant to the illustration, the arrow can point from element A to element B. This one-way arrow does not mean that no other information is sent from unit B to unit A. Additionally, for the information sent from unit A to unit B, unit B can send a request for that information or receive an acknowledgment of that information from unit A.

[0166] In this application, including the following definitions, the term "module" or the term "controller" may be replaced by the term "circuit". The term "module" may refer to processor hardware (shared, dedicated, or grouped) that executes code and memory hardware (shared, dedicated, or grouped) that stores the code executed by the processor hardware, which is part of or includes the processor hardware.

[0167] The module may include one or more interface circuits. In some examples, the interface circuit may implement a wired or wireless interface connected to a local area network (LAN) or a wireless personal area network (WPAN). Examples of LANs are the Institute of Electrical and Electronics Engineers (IEEE) standards 802.11-2016 (also known as the WIFI wireless networking standard) and IEEE standard 802.3-2015 (also known as the Ethernet wired networking standard). Examples of WPANs are the Bluetooth wireless networking standards from the Bluetooth Special Interest Group (SIG) (including core specification versions 3.0, 4.0, 4.1, 4.2, 5.0, and 5.1 from the Bluetooth SIG).

[0168] The module can communicate with other modules using the interface circuit. Although the module may be described as directly communicating logically with other modules in this disclosure, in various implementations, the module can actually communicate via a communication system. The communication system includes physical and / or virtual networking devices such as hubs, switches, routers, and gateways. In some implementations, the communication system is connected to a wide area network (WAN) such as the Internet or traverses a wide area network such as the Internet. For example, the communication system may include multiple LANs connected to each other via the Internet or point-to-point leased lines using technologies including Multiprotocol Label Switching (MPLS) and Virtual Private Networks (VPNs).

[0169] In various implementations, the functions of the module can be distributed among multiple modules connected via a communication system. For example, multiple modules can implement the same function distributed by a load balancing system. In another example, the functions of the module can be split between a server (also known as a remote or cloud) module and a client (or user) module. For example, the client module may include a native or web application executed on a client device and communicating with the server module over a network.

[0170] As described above, the term code can include software, firmware, and / or microcode, and can refer to programs, routines, functions, classes, data structures, and / or objects. Shared processor hardware includes a single microprocessor that executes some or all of the code from multiple modules. Group processor hardware includes microprocessors that, in combination with additional microprocessors, execute some or all of the code from one or more modules. References to multiple microprocessors include multiple microprocessors on discrete die, multiple microprocessors on a single die, multiple cores of a single microprocessor, multiple threads of a single microprocessor, or combinations of the above.

[0171] Shared memory hardware includes a single memory device that stores some or all of the code from multiple modules. Group memory hardware includes memory devices that, in combination with other memory devices, store some or all of the code from one or more modules.

[0172] The term memory hardware is a subset of the term computer-readable medium. The term computer-readable medium as used herein does not include transitory electrical or electromagnetic signals propagated through a medium (such as on a carrier wave); the term computer-readable medium is thus considered tangible and non-transitory. Non-limiting examples of non-transitory computer-readable media are non-volatile memory devices (such as flash memory devices, erasable programmable read-only memory devices, or mask read-only memory devices), volatile memory devices (such as static random access memory devices or dynamic random access memory devices), magnetic storage media (such as analog or digital magnetic tape or hard disk drives), and optical storage media.

[0173] The devices and methods described in this application can be implemented in part or in whole by a special-purpose computer created by configuring a general-purpose computer to execute one or more specific functions included in a computer program. Such devices and methods can be described as computerized devices and computerized methods. The above functional blocks and flowchart elements serve as software specifications that can be translated into computer programs through the routine work of a skilled technician or programmer.

[0174] The computer program includes processor-executable instructions stored on at least one non-transitory computer-readable medium. The computer program can also include or rely on stored data. The computer program can include a basic input / output system (BIOS) that interacts with the hardware of the special-purpose computer, device drivers that interact with specific devices of the special-purpose computer, one or more operating systems, user applications, background services, background applications, and the like.

[0175] The computer program may include: (i) descriptive text to be parsed, such as HTML (HyperText Markup Language), XML (eXtensible Markup Language), or JSON (JavaScript Object Notation), (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. By way of example only, the source code may be written using the syntax of languages including C, C++, C#, ObjectiveC, Swift, Haskell, Go, SQL, R, Lisp, Fortran, Perl, Pascal, Curl, OCaml, and the languages of HTML5 (the fifth revision of the HyperText Markup Language), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Visual Lua, MATLAB, SIMULINK, and

Claims

1. A radar system, comprising at least one processor and a memory, wherein the radar system is configured to: transmitting a radar signal within a frame having N radar chirps, the N radar chirps having a stepped frequency waveform such that an initial transmission frequency and an ending transmission frequency are changed for each subsequent chirp within the N radar chirps, and N is greater than 1; receiving and sampling a radar signal reflected from a target to generate a reception value from the received and sampled radar signal; Performing a range FFT process including a first domain fast Fourier transform FFT and a Doppler FFT process including a second domain FFT on the received value to generate a range FFT value and a Doppler FFT value; The distance and speed of the target are estimated based on the distance FFT value and the Doppler FFT value, wherein: The estimated range r and the estimated velocity v of the target are calculated based on at least one equation, the equation comprising: (i) a first term corresponding to the target range r0 measured by the first radar chirp of the N radar chirps, and (ii) a central wavelength λ of the plurality of radar chirps of the frame. N / 2 The corresponding second item.

2. The radar system according to claim 1, wherein: The at least one equation also includes a third term corresponding to the average range measurement from all N radar chirps within the frame: Among them, T N Corresponds to the transmission time of each chirp.

3. The radar system according to claim 1, wherein: The at least one equation includes the following equation: Where: F1 and F2 represent the frequencies measured after the first domain FFT and the second domain FFT, respectively; c and f They represent the direction of chirp slope and frame slope respectively; f r1 represents the first domain distance frequency, defined as Among them, k c is the chirp slope and c is the speed of light; f r2 represents the second domain distance frequency, defined as λ0 is the wavelength of the first chirp in the frame; and n is the chirp index.

4. The radar system according to claim 1, wherein: The stepped frequency waveform of the radar signal of the N radar chirps is generated to meet the following conditions:

5. The radar system of claim 1, wherein the at least one processor and memory are further configured to determine s c s f Is it greater than 0 and s c Is it less than 0, and respond to s c s f Greater than 0 and s c Less than 0, expand the index of the second domain FFT.

6. The radar system according to claim 5, wherein: The at least one processor and memory are further configured to determine s c s f is positive or negative, and is based on s c s f is positive or negative to perform a downward shift of the Doppler spectrum of the Doppler FFT values.

7. The radar system according to claim 6, wherein: The at least one processor and memory are further configured to perform expansion of the Doppler spectrum based on a number of times K that the range frequency of the first domain FFT is folded.

8. The radar system according to claim 7, wherein: The at least one processor and memory are further configured to calculate K based on the following formula: in, represents the maximum coverage range of the second domain distance, r1Bin is the interval size of the first domain distance, and Δf corresponds to the frequency offset between the radar chirps in the N radar chirps.

9. The radar system according to claim 1, wherein: The at least one processor and memory are configured to generate the stepped frequency waveform of the N radar chirps such that the initial transmission frequency and the end transmission frequency of each radar chirp after a first radar chirp are respectively lower than the initial transmission frequency and the end transmission frequency of an immediately preceding radar chirp.

10. The radar system according to claim 1, wherein: The radar system is installed in a vehicle having at least one vehicle system, the at least one processor and memory are configured to transmit the estimate of the distance and the speed of the target to the at least one vehicle system, and the at least one vehicle system is configured to control at least one of a steering system, a braking system, a throttle system, or a driver alert and warning system based on the estimate of the distance and the speed of the target.

11. A method comprising: transmitting, with at least one processor and memory of the radar system, a radar signal within a frame having N radar chirps, the N radar chirps having a stepped frequency waveform such that an initial transmit frequency and an ending transmit frequency are changed for each subsequent chirp within the N radar chirps, and N is greater than 1; receiving and sampling a radar signal reflected from a target using an analog-to-digital converter of the radar system to generate a reception value from the received and sampled radar signal; Using the at least one processor and the memory, the received value is subjected to a range FFT process including a first domain fast Fourier transform (FFT) and a Doppler FFT process including a second domain FFT to generate a range FFT value and a Doppler FFT value; The method further comprises estimating the range and speed of the target based on the range FFT value and the Doppler FFT value using the at least one processor and the memory, wherein the estimated range r and the estimated speed v of the target are calculated based on at least one formula, the formula comprising: (i) a first term corresponding to the target range r0 measured by the first radar chirp of the N radar chirps, and (ii) a first term corresponding to the central wavelength λ of the plurality of radar chirps of the frame. N / 2 The corresponding second item.

12. The method according to claim 11, wherein: The at least one equation also includes a third term corresponding to the average range measurement from all N radar chirps within the frame: Among them, T N Corresponds to the transmission time of each chirp.

13. The method according to claim 11, wherein: The at least one equation includes the following equation: Where: F1 and F2 represent the frequencies measured after the first domain FFT and the second domain FFT, respectively; c and f They represent the direction of chirp slope and frame slope respectively; f r1 represents the first domain distance frequency, defined as Among them, k c is the chirp slope and c is the speed of light; f r2 represents the second domain distance frequency, defined as λ0 is the wavelength of the first chirp in the frame; and n is the chirp index.

14. The method according to claim 11, wherein: The stepped frequency waveform of the radar signal of the N radar chirps is generated to meet the following conditions:

15. The method according to claim 11, further comprising: Determine c s f Is it greater than 0 and s c Is it less than 0, and respond to s c s f Greater than 0 and s c Less than 0, expand the index of the second domain FFT.

16. The method according to claim 15, further comprising: Determine c s f is positive or negative, and is based on s c s f is positive or negative to perform a downward shift of the Doppler spectrum of the Doppler FFT values.

17. The method according to claim 16, further comprising: The spreading of the Doppler spectrum is performed based on the number of times K the range frequency of the first domain FFT is folded.

18. The method according to claim 17, further comprising: K is calculated based on the following formula: in, represents the maximum coverage range of the second domain distance, r1Bin is the interval size of the first domain distance, and Δf corresponds to the frequency offset between the radar chirps in the N radar chirps.

19. The method according to claim 11, further comprising: The stepped frequency waveform of the N radar chirps is generated so that the initial transmission frequency and the end transmission frequency of each radar chirp after the first radar chirp are respectively lower than the initial transmission frequency and the end transmission frequency of the immediately preceding radar chirp.

20. The method according to claim 11, wherein: The radar system is installed in a vehicle having at least one vehicle system, and the method also includes: transmitting the estimate of the distance and the speed of the target to the at least one vehicle system, and the at least one vehicle system is configured to control at least one of a steering system, a braking system, a throttle system, or a driver alert and warning system based on the estimate of the distance and the speed of the target.

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