HIGH-PRECISION RANGING BASED ON MULTISPECTRAL FULL-WAVEFORM LIDAR

Full-waveform light detection and ranging (LiDAR) has become a well-established technique for remote sensing of surface topography and target characterization, offering numerous opportunities in investigation and interpretation of the structural diversity of surface coverage. However, most prevailing waveform decomposition methods employ the Gaussian function or some other probability distributions to model LiDAR waveforms of specific shapes, which cannot be universally used. Moreover, most of these waveform decomposition methods operate at a single laser wavelength and cannot be applied well to multispectral LiDAR (MSL) or hyperspectral LiDAR (HSL), which can simultaneously collect the spectral and geometric attributes with multiple transmitting laser wavelengths. In this paper, we propose a new multispectral B-spline waveform decomposition model to achieve high precision multi-target ranging. Considering both the spatial consistency of each channel and the irregular shape of the received waveform, LiDAR waveforms are modelled by B-splines rather than any other specific probability distribution. Thus, the proposed method can be extended to other FWMSL data benefiting from the flexibility of B-splines on fitting arbitrary curves. Both simulated MSL echoes and a measured dataset from a FWMSL system with three wavelengths of 556, 670, and 780 nm were used in this study. Compared with two single wavelength waveform decomposition models and a multispectral waveform decomposition model based on Gaussian function, the proposed method has excellent robustness for processing different shapes of waveforms and can improve ranging accuracy significantly for irregular waveforms. * Corresponding author


INTRODUCTION
Full-waveform light detection and ranging (LiDAR) has become a well-established technique for remote sensing of surface topography and target characterization (Sumnall, Hill andHinsley 2016, Li et al. 2016), offering numerous opportunities in investigation and interpretation of the structural diversity of surface coverage. In particular, multiple targets along the laser path can be detected through the waveform decomposition of the full waveform data, thereby obtaining ranging information by calculating the time of flight between the transmitted pulse and each waveform component.
However, most prevailing waveform decomposition methods employ the Gaussian function (Hofton, Minster andBlair 2000, Wagner et al. 2006) or some other probability distributions such as lognormal distribution, generalized normal distribution, and Burr distribution to model LiDAR waveforms of specific shapes (Chauve et al. 2009), which cannot be universally used. Moreover, most of these waveform decomposition methods operate at a single laser wavelength and cannot be applied well to multispectral LiDAR (MSL) or hyperspectral LiDAR (HSL). MSL and HSL have been proposed to simultaneously collect the spectral and geometric attributes with multiple transmitting laser wavelengths in recent years, widely adopted in vegetation detection and land cover mapping (Wei et al. 2012, Guerrero-Rascado et al. 2014, Song et al. 2019, Hakala et al. 2012, Scaioni et al. 2018. In this paper, we propose a new multispectral B-spline waveform decomposition model to achieve high precision multi-target ranging. The proposed method takes into account the spatial consistency of each channel in order to explore the potential advantages of the full waveform multispectral LiDAR (FWMSL) system. This is beneficial to improve the multitarget detection performance of channels with lower signal-tonoise ratios (SNR) with the help of channels with high SNR. Moreover, LiDAR waveforms are modelled by B-splines rather than any other specific probability distribution, and the shape of the received waveform is considered as a mixture of finite transmit pulses after translation and scaling transformations. Thus, the proposed model can be extended to other FWMSL data benefiting from the flexibility of B-splines on fitting arbitrary curves.

FWMSL system
The FWMSL system can record both the transmitted pulse and receiving echo with wavelengths of 556, 670, and 780 nm. The waveforms of the three receiving channels are digitized at a sampling rate of 1.8 GHz in a 12-bit analog-to-digital converter (SP Devices, ADQ412). The solid-state lasers at these three wavelengths are synthesized into a beam at a repetition rate of 20 kHz with average power of 100mW for each laser. The divergence angle of each beam is approximately 0.6 mrad, providing a laser footprint of approximately 3 cm in diameter at a detection distance of 50 m. The pulse widths of these lasers were 2 ns.

B-spline-based modelling
On the basis of prevailing methods, the received LiDAR waveform echo can be regarded as the superposition of finite echo components and background noise (Mallet and Bretar 2009).
where M is the number of the components of the echo waveform, θm represents the descriptive parameters of the mth components, and noise refers to the mean noise level, which is usually estimated by averaging the amplitudes of the first or the last few waveform samples and is then removed from the raw waveform signals (Hofton et al. 2000). Generally, assuming that the laser pulses are all Gaussian, several symmetric Gaussian functions are used to fit the full waveform echo, each function corresponding to an echo component (Hofton et al. 2000, Wagner et al. 2006, Chauve et al. 2008, Lin, Mills and Smith-Voysey 2010. Since the assumption of the Gaussian shape is sometimes oversimplified, especially for trailing waveforms, the Gaussian decomposition method cannot always perform well on real LiDAR waveforms. Therefore, the B-spline technique can be used to fit pulses of any shape and simplify the calculation of echo parameters, including echo width, amplitude, and center position, where the center position is a key parameter for ranging. The B-spline method has been widely used in curve fitting applications (Gruen and Akca 2005, Guan et al. 2014, Shen et al. 2017). Its formula is given by where i b is the control point, P is the degree of the spline, and Bx is the basis function of the B-spline and is given by a recursion formula (Roncat, Bergauer and Pfeifer 2011). The Assuming that the echo shape of the received waveform can be approximated by the corresponding transmit pulse through linear translation and scaling, the knots and control points of the corresponding two B-spline curves should actually meet where m u and m b are the knots and control points of mth Bspline component, respectively. tw u and tw b are the knots and control points of the transmit pulse, respectively. m  and m  are the scale and translation coefficients in the range direction, respectively, and m  refers to the scale factor in the amplitudes, corresponding to mth B-spline component.

Multispectral waveform decomposition
Similar to the Gaussian decomposition method, the peak and inflection points can be combined in the preprocessing stage to estimate the number of echo components and their initial parameters (Song et al. 2019, Wang et al. 2015. The pulse width of the mth echo is initialized by that of the transmitted waveform assuming that the echo is not widened due to the tilt or roughness of the target. Therefore, the initial scale factor 0 m  in the range is given by 1. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B3-2020, 2020 XXIV ISPRS Congress (2020 edition) At this point, the waveform component of each receiving channel can be obtained. However, the waveform component decomposition results of the three receiving channels may not be uniform, which is inconsistent with the real scene. In theory, the echo components of each channel should have the same position distribution. Therefore, the waveform components of each channel need to be further judged whether they correspond to the same target, so as to obtain more accurate waveform parameters.
The components at different wavelengths correspond to the same target if the difference between the position of these components is smaller than one sixth of the width of the transmitted pulse. In this way, the position average and width average of these Gaussian components are taken as the initial parameters of the target. Otherwise, these components at multiple wavelengths are from two or three different targets.

Data description
To evaluate the efficiency and feasibility of the proposed method, two datasets were utilised: a synthetic dataset and a measured dataset from the FWMSL system. The simulated waveforms were designed to mimic the real echo waveforms with different levels of skewness and kurtosis. Noise was introduced with an absolute standard deviation value of 0.5. The sampling rate was set to 1.8G samples per second.
As for the measured dataset, two standard white boards with 99% reflectivity at wavelengths between 200 and 2500 nm were detected. In the experiment, the laser spot partially hit both two white boards. We collected the superposition of the laser pulses scattered from these two planes. The distance between the two targets was changed by moving the second plane away from the first plane from 5 m to 20 m in steps of 1 m.

Validation
The proposed model, referred to as MB, was compared with two single wavelength waveform decomposition models, i.e. Gaussian function (SG) (Hofton et al. 2000) and B-splinebased model (SB) (Shen et al. 2017), and the multispectral waveform decomposition model based on Gaussian function (MG) (Song et al. 2019). Two statistical estimators have been commonly employed to evaluate the ranging performance, namely precision and accuracy. The former represents systematic random errors, while the latter represents systematic errors.
where pre E is the ranging precision measured in a certain ranging position, N is the sampled number.
i R denotes the ith measured data and R is the average of the measured data.
where acu E is the ranging accuracy measured in a certain ranging position, the actual value true R is obtained from the reference ranging finder.

RESULTS AND DISCUSSION
In order to evaluate the running efficiency of the four methods, i.e. MB, SG, SB, and MG, the execution time of ranging based on each method is calculated based on CPU processing. All the programs are running on a computer with 4 GB (gigabyte) of RAM (random-access memory), and an Intel(R) Core(TM) i5-6500U CPU @ 3.20 GHz. The average execution time of the MB, SG, SB, and MG are calculated to be 316.2, 621.4, 567.4, and 632.3 ns for each laser shot with three receiving channels, respectively. This result indicates that the proposed method runs more efficiently than the other three methods because of simpler mathematic expression and less iterations.
Moreover, in order to demonstrate the influence of different waveform decomposition, the results of MB, SG, SB, and MG are compared with each other given the same input signal. The ranging precision and accuracy estimated with the four methods for the simulated and measured waveforms are shown in Figure 1. Firstly, the ranging precision of all waveform decomposition methods decrease with the increase of the distance, among the four methods the proposed method has the best precision. Secondly, the ranging accuracy tends to be stable with increasing distance.
The simulated waveforms contain echoes with different shape characteristics, including symmetrical waveforms similar to Gaussian, trailing echoes, and other arbitrary shape echoes. Figure 1 (a) and (b) demonstrate the results of simulated data. The results show that the proposed method based on the multispectral B-spline model has better ranging performance than the other three methods. The ranging accuracy of the Gaussian based method (SG and MG) is not satisfied and much worse than that of SB and MB when the waveform is sharply-peaked or heavy-tailed. Benefiting from the abundant spectral information with multiple wavelengths, the waveform components decomposed based on the MB model exhibit high consistency at each wavelength and high ranging precision, which is more reliable and offers considerable improvement over the SB model. Additionally, Figure 1 (c) and (d) displays the comparison results for the measured data. From the definition in Section 2.5, two indicators including bias and nonlinearity are calculated to evaluate the ranging accuracy. The results show that the bias and nonlinearity of the proposed method is less than the other three methods. In order to give a specification of the four methods, their precision is given the maximum precision value over the entire measurement range. The specification is present in Since the waveform measured by the FWMSL system is slightly tailed, the B-spline model seems to be more suitable to fitting the transmitted pulse than Gaussian function. Moreover, the multi-target ranging information retrieved based on SG varied at each wavelength, inconsistent with the actual position distribution of targets while the waveform components exhibit a high consistency at each wavelength when using MG (Song et al. 2019). Similarly, the proposed method makes full use of the advantages of FWMSL, with the help of the component position distribution of multiple channels to obtain more accurate waveform information. This study aims to achieve multi-target high-precision ranging using FWMSL data by improving the waveform decomposition method. The accuracy of the proposed method may be further improved by calibration or improving the detection and data acquisition modules.

CONCLUSIONS
In conclusion, this paper proposed a new multispectral Bspline waveform decomposition model to achieve high precision multi-target ranging. The ranging performance of the proposed method was evaluated using both simulated and measured data, compared with the typical Gaussian function involving single/multiple wavelengths and the basic B-spline model based on a single wavelength. The results show that the proposed method has excellent robustness for processing different shapes of waveforms, due to the flexibility of B-spline fitting arbitrary curves. The proposed method takes advantage of multispectral full-waveform data to improve ranging accuracy significantly. Furthermore, the proposed method can be extended to other full waveform MSL or HSL systems of arbitrary waveforms.