Spacecraft strong noise photon point cloud denoising method and high-confidence fast denoising system

Abstract

The present application relates to the technical field of photon detection, and discloses a spacecraft strong noise photon point cloud denoising method and a high-confidence rapid denoising system, which comprises the following steps: acquiring a full-stage photon point cloud data stream of a spacecraft platform; performing the following operations on the photon point cloud data in each stage: rasterizing the photon point cloud data to obtain a pseudo image, and extracting signal photons from the pseudo image using an anisotropic radial basis function to obtain density dimension data; constructing a density threshold for distinguishing signals and noises according to historical noises along the running track direction of the spacecraft platform, and removing noises in the density dimension data according to the density threshold; removing small cluster noises from the density dimension data after removing the noises, and identifying ground surface signals in the density dimension data after removing the small cluster noises; and combining the height of the spacecraft in the last stage, and tracking the ground surface signals using Kalman filtering. The present application can improve the photon point cloud denoising effect and speed in a strong background noise environment, has strong applicability and high confidence.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photon detection, in particular to a spacecraft strong noise photon point cloud denoising method and a high-confidence fast denoising system. BACKGROUND

[0002] The photon counting lidar based on single photon detection technology has the characteristics of long distance, high resolution and high precision, and is widely used in long distance ranging and remote sensing mapping fields. By using high repetition rate, low energy pulsed laser and photon counting technology, the surface information of the target can be accurately described. This technology can effectively reduce the energy consumption of the laser, and has great potential for satellite and other spacecraft platforms to obtain ground elevation information, and has a wide application prospect for earth observation, deep space exploration, spacecraft landing and other applications.

[0003] The single photon detector has high sensitivity and can detect weak photon signals of the order of single photons, but it is affected by the sun background radiation, atmospheric scattering, self-dark counting including after-pulse effect, resulting in a large number of noise of the photon detector. In a strong background noise environment, it is an important prerequisite for subsequent applications to effectively distinguish noise and signal photons. For the terrain remote sensing application of the spacecraft platform, a large laser detection range produces a large amount of echo photon point cloud data; at the same time, in the sunlight background, the strong background noise leads to a low signal-to-noise ratio; in addition, the existence of a large number of high-energy particle radiation in the space environment makes the dark counting of the photon detector increase more significantly, resulting in more serious background noise rate. Therefore, how to quickly and accurately extract the target echo photon signal from the large amount of photon point cloud in the strong background noise condition has become the research focus and difficulty.

[0004] At present, the photon point cloud denoising method mainly includes three types: grid-based point cloud filtering method, local statistical information-based point cloud filtering method and clustering-based point cloud filtering method, wherein the latter two are based on the original point cloud method. The filtering method based on the original point cloud has high recognition rate of signal photons, good extraction effect and more applications. However, the filtering method based on the original point cloud has high time complexity, especially when the data volume is large, the operation time is very long, which reduces the running efficiency. The clustering-based point cloud filtering method has a simpler calculation process than the local statistical information-based method, and runs faster, but the uneven distribution of point clouds will affect the filtering effect.

[0005] Meanwhile, the data volume of the original photon point cloud is usually large, if there is prior geographical information, the target ground elevation can be obtained in advance through the built-in digital elevation model (DEM) information, so as to set a threshold for the detection range, thereby reducing the data volume of the photon point cloud, and subsequent processing is carried out after the data is downloaded. However, if there is no prior geographical information, it is necessary to extract signals from the massive photon point cloud in the entire detection range, and the existing method is not strong in adaptability to high background noise environment light signals, and it is difficult to realize fast extraction of large-scale detection range ground light signals without any prior geographical information, and it is difficult to realize fast denoising and real-time denoising of massive photon point cloud, which is not conducive to the subsequent application of the photon counting laser radar. SUMMARY

[0006] Therefore, the technical problem to be solved by the present application is to overcome the deficiencies in the prior art, and to provide a spacecraft strong noise photon point cloud denoising method and a high-confidence fast denoising system, which can improve the photon point cloud denoising effect and speed in a strong background noise environment, and has high confidence and strong applicability.

[0007] To solve the above technical problems, the present application provides a spacecraft strong noise photon point cloud denoising method, comprising:

[0008] Obtaining the photon point cloud data stream of the spacecraft platform in all stages, and performing the following operations on the photon point cloud data in each stage:

[0009] Griding the photon point cloud data to obtain a pseudo image, and using an anisotropic radial basis function to extract signal photons from the pseudo image to obtain density dimension data;

[0010] According to the historical noise along the running track direction of the spacecraft platform, a density threshold for distinguishing signals and noise is constructed, and the noise in the density dimension data is removed according to the density threshold;

[0011] Removing small cluster noise from the density dimension data after removing the noise, and identifying the ground signal in the density dimension data after removing the small cluster noise;

[0012] Combining the spacecraft height of the previous stage, and using Kalman filtering to track the ground signal.

[0013] Further, the use of an anisotropic radial basis function to extract signal photons from the pseudo image to obtain density dimension data comprises:

[0014] Constructing a density kernel anisotropic radial basis function, and performing grid sampling on the anisotropic radial basis function to generate a density kernel matrix;

[0015] Convolution operation is performed on the sliding window of the pseudo image by taking the density kernel matrix as a convolution kernel to obtain the density value d of the center point c in the θ direction θ (c) is:

[0016]

[0017] wherein, R c represents the neighborhood range of the center point c, W θ (x) is the anisotropic radial basis function of the pixel point x in the θ direction, x is a pixel point in the pseudo image, and z(x) is the pixel value corresponding to the pixel point x;

[0018] The density value d θ (c) is normalized to obtain the normalized d θ (c) is

[0019] A plurality of density kernel matrices under multiple angles are generated, each density kernel matrix is respectively applied to the pseudo image to generate a corresponding density dimension data, and the density value of the corresponding pixel of each density dimension data is taken as the maximum value to obtain the final density dimension data D(c) as:

[0020]

[0021] wherein, θ1, θ2,..., θn are multiple angles, max() represents the maximum value operation, represents the normalized density value of the center point c in the θn direction.

[0022] Further, the anisotropic radial basis function of the pixel point x in the θ direction is:

[0023]

[0024] wherein, A θ is a transformation matrix, a is the horizontal stretching ratio, θ is the clockwise rotation angle of the density kernel, σ is the standard deviation of the Gaussian function, c represents the center point position, R c is the neighborhood range of the center point.

[0025] Further, the density threshold value is:

[0026] th i =q max({d i})+(1-q)mean({d i}),

[0027] wherein, th iis a density threshold value for the ith column along the direction of the running track of the spacecraft platform, q is a threshold factor, max() represents a maximum operation, and mean() represents a mean operation;{d i} is a set of density values for the ith column, i is:

[0028]

[0029] where d i，j represents a density value of the ith column and the jth row, j is a row index, is a predicted value of the spacecraft height at the next stage obtained by Kalman filtering, and r is a signal retrieval window size.

[0030] Further, the density dimension data after noise removal is further removed of small cluster noise, including:

[0031] An area threshold t is set, and the area of each cluster c i is removed, and a cluster set C1 is formed as:

[0032]

[0033] where P represents a cluster set obtained after noise in the density dimension data is removed.

[0034] The area of each cluster in C1 is taken as a weight, and the center height of the cluster is calculated as:

[0035]

[0036] where z p represents a height corresponding to a pixel p in the density dimension data.

[0037] The center height of the cluster is calculated as a weighted mean value and a weighted standard deviation as:

[0038]

[0039]

[0040] where, represents an area of the kth cluster, represents a center height of the kth cluster, and σ min represents a preset minimum value of the weighted standard deviation.

[0041] Clusters with a weighted mean value less than a weighted standard deviation are selected as a final cluster set C2.

[0042]

[0043] Further, the identification of the ground surface signal in the density dimension data after removing small cluster noise comprises:

[0044] The average thickness T and average signal intensity S of the final cluster set C2 are calculated:

[0045]

[0046]

[0047] wherein w i is the lateral width of the i-th cluster, and D(x) is the density dimension data obtained by taking the point x in the cluster set C2 as the center point;

[0048] The signal intensity divergence SID is defined as:

[0049] SID = T / S,

[0050] The signal intensity divergence is used to distinguish the ground surface signal and the atmospheric backscattering signal.

[0051] Further, the combination of the spacecraft height of the previous stage is used to track the ground surface signal using Kalman filtering, comprising:

[0052] The system state model is constructed as:

[0053] x k+1 = Ax k +w k ,

[0054] Z k = Hx k +v k ,

[0055]

[0056] wherein x k represents the system state vector of the k-th stage, A is the system state matrix, w k is the process noise vector; Z k represents the measurement value of the k-th stage, H is the measurement matrix, v k is the measurement noise vector, H k is the density dimension height, V k is the density dimension height rate of change;

[0057] The Kalman filter prediction and system state update model is constructed as:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] wherein, is the updated system state vector at the kth stage, represents the predicted value of the system state vector, represents the prior error estimation covariance matrix, P k represents the posterior error estimation covariance matrix, Q k is the process noise vector v k corresponding covariance matrix, K k represents the Kalman gain matrix, R k is the measurement noise vector v k corresponding covariance matrix, I is the unit matrix;

[0064] According to the formula the updated system state vector at the k+1 stage is obtained is expressed as wherein is the predicted value of the density height at the next stage, and is passed to the operation of constructing the density threshold value distinguishing signals and noises at the next stage, so as to realize the tracking identification of the ground surface signals.

[0065] Further, the measurement value Z k at the kth stage is:

[0066] The measurement noise vector v k corresponding covariance matrix R k is:

[0067] The process noise vector v k corresponding covariance matrix Q k is:

[0068]

[0069] wherein, is the estimated value of the density height obtained by the i-th state update, is the estimated value of the change rate of the density height obtained by the i-th state update, is the average value of the estimated values of the density height in the previous n times of the kth stage, ​The average value of the estimation value of the density dimension height variation rate of k in the previous n times.

[0070] Further, the density dimension height H k is:

[0071]

[0072] The density dimension height variation rate V k is: when the spacecraft vertical velocity is zero, V k is proportional to the rate of change of the ground height, that is, the terrain slope; if the vertical velocity is not zero, V k is proportional to the superposition of the spacecraft vertical velocity and the rate of change of the ground height.

[0073] The application also provides a spacecraft strong noise photon point cloud high-confidence fast denoising system, comprising:

[0074] A data acquisition module is configured to acquire a photon point cloud data stream of the spacecraft platform in all stages.

[0075] A data preprocessing module is configured to rasterize the photon point cloud data to obtain a pseudo image, extract signal photons from the pseudo image using an anisotropic radial basis function to obtain density dimension data, and use FPGA for hardware acceleration.

[0076] A signal and noise separation module is configured to construct a density threshold for distinguishing signal and noise according to historical noise along the running track direction of the spacecraft platform, and remove noise in the density dimension data according to the density threshold.

[0077] A post-processing module is configured to remove small cluster noise from the density dimension data after removing noise, and identify ground signals in the density dimension data after removing small cluster noise.

[0078] A Kalman filtering module is configured to track the ground signals using Kalman filtering in combination with the spacecraft height in the previous stage.

[0079] The post-processing module and the Kalman filtering module are deployed on an ARM platform.

[0080] The above technical solutions of the application have the following beneficial effects compared with the prior art:

[0081] The application rasterizes point clouds and constructs density dimension data by density dimension method, and on this basis, combines Kalman filtering to denoise photon point cloud data of a spacecraft platform ground surface, so that fast extraction of ground echo photon signals in a high background noise environment in a large-scale detection range of photon point clouds can be realized without any prior geographic information; the density threshold denoising and small cluster noise removal method can still achieve effective denoising effect when the point cloud distribution is uneven, improve the photon point cloud denoising effect and speed in a strong background noise environment, and has high confidence and strong applicability. BRIEF DESCRIPTION OF DRAWINGS

[0082] In order to make the content of the application more easily understood, the application will be further described in detail below according to specific embodiments of the application and in conjunction with the drawings, in which:

[0083] Figure 1 is a flowchart of the method of the application.

[0084] Figure 2 is a step diagram in each cycle of the method of the application.

[0085] Figure 3 is a schematic diagram of a multi-directional anisotropic radial basis function.

[0086] Figure 4 is a graph of the change of the height along the orbital distance under different noise count rates in the embodiment of the application.

[0087] Figure 5 is a comparison graph of the processing effect of the application and DBSCAN on relatively flat ground areas under different noise count rates in the embodiment of the application.

[0088] Figure 6 is a comparison graph of the processing effect of the application and DBSCAN on mountainous and steep terrain areas under different noise count rates in the embodiment of the application.

[0089] Figure 7 is a processing time graph of point cloud data of different noise magnitudes and longitudinal window sizes before the Kalman filter initialization in the method of the application in the embodiment of the application.

[0090] Figure 8 is a processing time graph of point cloud data of different noise magnitudes and longitudinal window sizes after the Kalman filter is used in the method of the application in the embodiment of the application. DETAILED DESCRIPTION

[0091] The application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the application and implement it, but the embodiments are not limiting the application.

[0092] Embodiment one

[0093] Referring to Figure 1 As shown in the figure, the application discloses a spacecraft strong noise photon point cloud denoising method, comprising the following steps:

[0094] S1: acquiring the photon point cloud data stream of the spacecraft platform in all stages, and performing data preprocessing operation, signal and noise separation operation, post-processing operation and Kalman filtering operation on the photon point cloud data in each stage.

[0095] S2: in the data preprocessing operation, the original point cloud is rasterized and convolved with a density kernel matrix to generate density dimension data, comprising: acquiring the photon point cloud data of the spacecraft platform in the stage, rasterizing the photon point cloud data to obtain a pseudo image, and using an anisotropic radial basis function to extract signal photons from the pseudo image to obtain density dimension data.

[0096] S2-1: the preprocessing mode of the photon point cloud filtering algorithm determines the processing efficiency of the algorithm. The preprocessing mainly includes three modes of histogram-based, pseudo image-based and original point cloud-based. The filtering algorithm based on the original point cloud has the highest accuracy, but the processing efficiency is the lowest, and it cannot realize real-time extraction of the photon point cloud data stream. The histogram-based filtering algorithm has the highest efficiency, but it is not sensitive to the terrain details and slope, and has low extraction accuracy. The point cloud rasterization converts the original photon point cloud into a pseudo image, and converts the algorithm calculation unit from a point to a pixel, which is a point cloud processing mode capable of realizing high efficiency. In the usual cognition, rasterization will cause loss of point cloud accuracy, but the degree of accuracy loss often depends on the rasterization mode, and the grid size, that is, the pixel resolution, means that smaller grid size means smaller accuracy loss. In addition, the pseudo image after processing will be restored to the original point cloud, and this method will greatly reduce the loss of point cloud accuracy caused by rasterization. Therefore, in the present application, a two-dimensional pseudo image is obtained by rasterizing the photon point cloud data.

[0097] In this embodiment, the photon point cloud data is first segmented along the direction of the running track of the spacecraft, the point cloud is discretized into uniformly spaced grids in the two-dimensional profile, and the number of photon point clouds in each small grid is counted as the pixel value corresponding to the grid. In order to minimize the loss of geometric information between point clouds, the longitudinal size of each grid conforms to the minimum detail feature of the terrain, and the transverse size conforms to the size of the laser spot. The photon point cloud data is rasterized to obtain a two-dimensional pseudo image.

[0098] S2-2: constructing a density kernel anisotropic radial basis function, and rasterizing and sampling the anisotropic radial basis function to generate a density kernel matrix.

[0099] S2-2-1: the process of constructing the density kernel anisotropic radial basis function is:

[0100] Density-dimension Algorithm (DDA) uses anisotropic radial basis function as the kernel function of quantifying photon density, and takes density data as dimension, and enhances the contrast of signal photons and background noise through clustering to extract signal photons.

[0101] Radial basis function (RBF) is a mathematical function used to calculate density in data clustering. The value of radial basis function only depends on the distance between all neighborhood points x in the defined region D and the center point c:

[0102] φ(x,c)=f(||x-c||) (1),

[0103] Where ||·|| is the Euclidean distance, and Gaussian radial basis function is used in the application:

[0104]

[0105] Therefore, the distance between all neighborhood points x in the region D and the center point c can be obtained as:

[0106]

[0107] Where σ is the standard deviation of the Gaussian function, used to control the width of the radial basis function.

[0108] Radial basis function is a weight matrix. For data clustering of photon point cloud, radial basis function assigns high weight to photons close to the center point, and the weight gradually decreases towards the outside of the search window, following the Gaussian distribution, which can highlight the photon aggregation position and realize the conversion of the original point cloud to the local density of the point cloud.

[0109] Anisotropic norm is different from the standard Euclidean norm (L2 norm), which allows different weights to be assigned to the components of vectors or matrices in different directions. Since the surface signal extends more in the horizontal direction than in the vertical direction, the radial basis function is extended in the horizontal direction by anisotropic norm, which transforms the radial basis function into an elliptical function. After anisotropic radial basis function processing, the weight of the point in the horizontal direction is higher than that in the vertical direction.

[0110] In two-dimensional space, the anisotropic norm is defined as:

[0111] ||v|| a =||Av||2 (4),

[0112] Where A is the transformation matrix. For the center point c and its neighborhood point x, the anisotropic norm is:

[0113] ||x-c|| a =||A(x-c)||2 (5),

[0114] For two-dimensional data, the transformation matrix is:

[0115]

[0116] where a is the horizontal stretching ratio.

[0117] The anisotropic direction of the anisotropic radial basis function is closely related to the terrain trend. In order to match the change of the terrain slope, the anisotropic radial basis function needs to be rotated about the center point, at this time the transformation matrix A is changed to A θ :

[0118]

[0119] where θ is the clockwise rotation angle of the density kernel, and a schematic diagram of the multi-directional anisotropic radial basis function is shown in Figure 3 , Figure 3 (a) in (c) is θ = 0°, Figure 3 (b) in (c) is θ = 30°, Figure 3 (c) in (c) is θ = -30°.

[0120] The anisotropic radial basis function is obtained as:

[0121] W θ (x, c) = φ (||A θ (x-c)||2) (8).

[0122] Formula (8) is the anisotropic radial basis function of all neighborhood points x and the center point c in the region D. By transforming formula (8), the anisotropic radial basis function of the neighborhood point x within the neighborhood range R c limited to the single center point c is expressed as:

[0123]

[0124] where A θ is the transformation matrix, a is the horizontal stretching ratio, θ is the clockwise rotation angle of the density kernel, σ is the standard deviation of the Gaussian function, c represents the center point position, and R c is the neighborhood range of the center point.

[0125] S2-2-2: The ratio of the size of the density kernel matrix is determined by the anisotropic norm, and the selection of the matrix size is determined according to the neighborhood size of the actual pseudo image participating in the density calculation. The anisotropic radial basis function is rasterized and sampled to generate a density kernel matrix according to the matrix size.

[0126] S2-3: The density kernel matrix is used as a convolution kernel to perform convolution operation on the sliding window of the pseudo image, to obtain the density value d of the center point c in the θ direction.θ (c) is:

[0127]

[0128] wherein R c represents the rectangular window area where the density kernel matrix centered at c, i.e. the neighborhood of the center point c, x is a pixel point in the pseudo image, z(x) is the pixel value corresponding to the pixel point x, W θ (x) is the anisotropic radial basis function of pixel point x in the direction of θ.

[0129] S2-4: the density value d θ (c) is normalized to ensure the total weight is uniform, and the normalized d θ (c) is:

[0130]

[0131] S2-5: generate a plurality of density kernel matrices at different angles, since the rasterized density kernel matrix is not sensitive to the angles near the stretching direction, only three density kernel matrices at 0°, ±30° are generated in this embodiment. First, each density kernel matrix is respectively applied to the pseudo image to generate three corresponding density dimension data, and the maximum value of the density values of the corresponding pixels of the three density dimension data is taken to obtain the final density dimension data D(c) as:

[0132]

[0133] wherein θ1, θ2, …, θn are a plurality of angles, max() represents the maximum value operation, represents the normalized density value of the center point c in the direction of θn. The final density dimension data in this embodiment is:

[0134]

[0135] S3: signal and noise separation operation, including: constructing a density threshold for distinguishing signals and noises according to the historical noise along the running track direction of the spacecraft platform, and removing the noise in the density dimension data according to the density threshold.

[0136] S3-1: Signal and noise separation is a key step in this invention, determining the completeness of signal photon extraction. Differences in background photon levels between day and night, variations in reflectivity across different surface types, differences in atmospheric aerosol and other molecular densities, and even differences in terrain slope can all alter the level of background noise. The surface detection algorithm needs to automatically determine the noise filtering density threshold along the spacecraft platform's orbit. It is generally believed that the density threshold should match the noise level along the spacecraft platform's orbit. However, in high background noise regions, the low signal-to-noise ratio often makes it difficult to distinguish between noise and signal density. Therefore, the density threshold is matched to both signal and noise intensity (by default, the region with the highest density is the signal region, and the noise intensity is the average density). The density threshold is:

[0137] th i =qmax({d i})+(1-q)mean({d i})(12),

[0138] Among them, th i The density threshold for the i-th column along the orbital direction of the spacecraft platform is given by q, which is a threshold factor typically ranging from 0.6 to 0.8; max() represents the maximum value operation, and mean() represents the mean value operation; {d i Let {d} be the set of density values ​​in the i-th column. Before the Kalman filter is initialized, this set covers the entire detection range. However, after the Kalman filter is initialized, in order to achieve adaptive signal retrieval range, {d}... i The set is:

[0139]

[0140] Where, d i,j This represents the density value in the i-th column and j-th row, where j is the row index. denoted as , where is the predicted spacecraft altitude for the next stage obtained by Kalman filtering, and r is the signal retrieval window size.

[0141] The calculation method is as follows: the system state vector at stage k Among them, H k V represents the density dimension height of stage k, i.e., the spacecraft height. k Let k be the density dimension height change rate at stage k; the next stage is k+1, and the predicted system state vector for stage k+1 is... Calculated using formula (27), It can be broken down into in This is the predicted altitude of the spacecraft in the next stage, obtained through Kalman filtering.

[0142] S3-2: Calculate the density threshold value th of each column in the track direction in the density dimension data i After that, the clusters with density less than th in the ith column are removed from the density dimension data as noise, and the clusters with density greater than th are kept as signal clusters. i i

[0143] S4: After the signal and noise separation operation, the image data still has some small cluster noise left, so a post-processing operation is needed to accurately filter the data and finally restore it to the original point cloud. The post-processing operation includes: removing small cluster noise from the density dimension data after removing noise, and identifying the ground signal in the density dimension data after removing small cluster noise.

[0144] S4-1: Due to uneven background noise distribution, some small cluster noise is still left in some noise-intensive areas after the signal and noise separation operation, so small cluster removal is needed. Generally, the area of each cluster connected region can be detected to remove small area clusters, but if the area threshold is too large, some signal small clusters will be removed as noise, and if it is too small, the noise small clusters cannot be completely removed, so the method in this embodiment is:

[0145] S4-1-1: First, set a small area threshold t and remove the clusters ci with area smaller than the area threshold t to form the cluster set C1 as:

[0146]

[0147] where P represents the cluster set obtained by the signal and noise separation operation.

[0148] S4-1-2: Calculate the weighted average value of the center height z of each cluster in C1 as the weight

[0149]

[0150]

[0151]

[0152] where, represents the area of the kth cluster, represents the center height of the kth cluster, z p ​​​​​​This represents the height of pixel p in the density dimension data; when the surface signal is too flat, the weighted standard deviation will approach 0, therefore a minimum value σ needs to be set for the weighted standard deviation. min To ensure the integrity of the signal clusters.

[0153] S4-1-3: Select clusters whose weighted average is less than their weighted standard deviation as the final cluster set C2:

[0154]

[0155] S4-1-4: Finally, the weighted variance of C2 needs to be calculated again. This is used to update the subsequent Kalman filtering steps.

[0156]

[0157] S4-2: For the rapid extraction of surface elevation signals from spacecraft platforms, since the initial surface elevation is unknown, it is necessary to retrieve surface signals throughout the flight altitude using the density dimension method. Once the surface signal is retrieved, the Kalman filter is initialized. To ensure that the retrieved signal is a surface signal and not a backscattered signal from clouds or aerosols, and to ensure that the Kalman filter can be effectively initialized, it is necessary to identify the signal type. Therefore, it is necessary to distinguish between surface signals and atmospheric backscattered signals in the density dimension data after removing small cluster noise.

[0158] Because the atmospheric backscattered signal has a wider longitudinal distribution and weaker local signal density compared to the surface signal, the average thickness T and average signal intensity S of the final cluster set C2 are calculated as follows:

[0159]

[0160]

[0161] Where wi is the horizontal width of the i-th cluster, and D(x) is the density dimension data obtained by taking point x in the cluster set C2 as the center point. This is the sum of density-dimensional data obtained by taking each point in the cluster set C2 as the center point; the signal intensity divergence SID is defined as:

[0162]

[0163] Signal intensity divergence (SID) reflects the degree of signal divergence and can be used to distinguish between surface signals and atmospheric backscattered signals. A discrimination threshold is set based on the characteristics of the actual point cloud data. If the calculated SID is greater than this threshold, it is considered an atmospheric backscattered signal; if the calculated SID is lower than this threshold, it is considered a surface signal.

[0164] S5: Kalman filtering operation, comprising: in combination with the spacecraft height of the last stage, using Kalman filtering to track the ground surface signal, which can adaptively search the range of photon signals, while reducing the data processing amount, and realizing effective denoising of the photon point cloud.

[0165] In the process of processing the photon point cloud data, if the signal-to-noise ratio of the point cloud signal is low, many noise clusters will be misidentified as signal clusters, causing the loss of signal photons; in addition, if the ground surface is covered by a thin cloud layer and a high-density aerosol molecular layer, the photon echo intensity will be attenuated, the signal-to-noise ratio will be weakened, and the signal and noise separation operation process is easy to be disturbed by the cloud layer to cause signal loss, therefore, the Kalman filtering method is introduced in the present application to track the ground surface target to adaptively search the range of photon signals while reducing the data processing amount. The Kalman filter is an optimal estimation method for linear systems, which has shown the superiority of the method in the fields of control, navigation, etc., and the Kalman filter can also be used to process photon point cloud data, and a processing flow needs to be designed for density dimension data and density dimension method.

[0166] S5-1: constructing a density dimension height H k is:

[0167] The present application adopts a spacecraft dynamics model, a system state vector x k contains a ranging height H k and a longitudinal velocity V k two state quantities, the state quantities are combined with the density dimension method, the final cluster set C2 obtained from formula (18) is substituted into formula (23) to obtain a weighted average value as a density dimension height, that is, the density dimension height is:

[0168]

[0169] A density dimension height rate of change V k is constructed as: when the vertical velocity of the spacecraft is zero, V k is directly proportional to the rate of change of the ground surface height, that is, the terrain slope; if the vertical velocity is not zero, V k is directly proportional to the superposition of the vertical velocity of the spacecraft and the rate of change of the ground surface height.

[0170] S5-2: constructing a system state model in combination with the density dimension height and the rate of change of the density dimension height as:

[0171] x k+1 = Ax k +w k (24),

[0172] Z k = Hx k +vk (25),

[0173]

[0174] where x k denotes the system state vector at the kth stage, is the system state matrix, AT is the laser pulse repetition period, w k is the process noise vector; Z k denotes the measurement value at the kth stage, is the measurement matrix, v k is the measurement noise vector.

[0175] S5-3: Construct the Kalman filter prediction and system state update model as:

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] where, is the updated system state vector at the kth stage, denotes the predicted value of the system state vector, denotes the prior error estimation covariance matrix, P k denotes the posterior error estimation covariance matrix, Q k is the process noise vector w k corresponding covariance matrix, K k denotes the Kalman gain matrix, R k is the measurement noise vector v k corresponding covariance matrix, I is the identity matrix.

[0182] The initial velocity of the default spacecraft is 0, so the initial state of the Kalman filter is where is the density altitude calculated by formula (23), the measurement value Z k is also selected to be updated, so the measurement value Z k at the kth stage is:

[0183]

[0184] The measurement noise covariance matrix R kThe weighted variance of C2 obtained by formula (19) is Therefore, the measurement noise vector v k The corresponding covariance matrix R k is:

[0185]

[0186] The update of the process noise covariance matrix needs to calculate the variance of the state estimation value obtained from the previous n update steps, so the process noise vector v k The corresponding covariance matrix Q k is:

[0187]

[0188]

[0189]

[0190] wherein, is the estimated value of the density dimension height obtained by the i-th state update, is the estimated value of the density dimension height rate of change obtained by the i-th state update, is the average value of the estimated value of the density dimension height of k in the previous n times, is the average value of the estimated value of the density dimension height rate of change of k in the previous n times, denotes the variance of the estimated value of the density dimension height obtained from the previous n update steps of k, denotes the variance of the estimated value of the density dimension height rate of change obtained from the previous n update steps of k.

[0191] According to formula The updated system state vector of k+1 stage is obtained is expressed as is expressed as wherein is the predicted value of the density dimension height of the next stage, that is, the predicted value of the spacecraft height of the next stage, and is transmitted to the signal and noise separation operation of the next stage, so as to realize adaptive signal retrieval range and realize tracking identification of the ground surface signal.

[0192] Embodiment two

[0193] The application further discloses a spacecraft strong noise photon point cloud high-confidence fast denoising system, which comprises a data acquisition module, a data preprocessing module, a signal and noise separation module, a post-processing module and a Kalman filtering module.

[0194] The data acquisition module is used for acquiring photon point cloud data streams of all stages of a spacecraft platform.

[0195] The data preprocessing module is used for rasterizing the photon point cloud data to obtain a pseudo image, and is used for extracting signal photons from the pseudo image to obtain density dimension data by using an anisotropic radial basis function. The convolution operation in the generation of the density dimension data is a step with a large amount of calculation in the algorithm, and it is difficult to realize real-time effect by using a CPU for calculation. Therefore, in the embodiment, the advantage of large-scale parallel processing of the convolution operation is used, and the process of generating the density dimension data from the original point cloud is accelerated by using a field programmable gate array (FPGA) for hardware acceleration.

[0196] The signal and noise separation module is used for constructing a density threshold for distinguishing the signal and the noise according to historical noise along the running track direction of the spacecraft platform, and removing the noise in the density dimension data according to the density threshold.

[0197] The post-processing module is used for removing small cluster noise from the density dimension data after removing the noise, and identifying the ground surface signal in the density dimension data after removing the small cluster noise.

[0198] The Kalman filtering module is used for tracking the ground surface signal by using Kalman filtering in combination with the spacecraft height in the previous stage.

[0199] The post-processing and Kalman filtering parts with complex operation branches are deployed in the CPU, and the algorithm is realized by using the ZYNQUltraScale+MPSoC architecture of Xilinx, which integrates a four-core ARM Cortex-A53 processor and an FPGA programmable logic part, and the two are connected by an AXI bus at a high speed, wherein the frequency of the ARM Cortex-A53 is 1.2 GHz, and the clock frequency of the FPGA is 150 MHz.

[0200] In order to realize on-chip efficient processing of the point cloud data, the FPGA generates the density dimension data synchronously with the original point cloud data stream by the logic structure of the convolution pipeline, and then the original point cloud data and the density dimension data are transmitted to the ARM end DDR through the AXI bus for subsequent processing.

[0201] Embodiment three

[0202] The application further discloses a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the spacecraft strong noise photon point cloud denoising method in the embodiment one.

[0203] Embodiment four

[0204] The application further discloses a device including a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the spacecraft strong noise photon point cloud denoising method in the embodiment one when executing the computer program.

[0205] The application aims to realize fast denoising of ground surface photon signals in a high background noise environment with a large-scale detection range without any prior geographic information, and a new photon point cloud filtering method combining a density dimension method (DDA) and Kalman filtering (KF) is designed for spacecraft platform ground surface photon point cloud extraction application, which is called DDA-KF, wherein the DDA algorithm combines the speed advantage of a grid-based point cloud filtering method and the precision advantage of a filtering method based on local statistical information, and Kalman filtering is introduced in the processing of the photon point cloud stream data to track the ground elevation and adaptively search the signal range.

[0206] The application grids the point cloud and constructs density dimension data by the density dimension method, and on this basis, the photon point cloud data of the spacecraft platform ground surface is denoised in combination with Kalman filtering, so that fast extraction of ground echo photon signals in a high background noise environment with a large-scale detection range of the photon point cloud can be realized without any prior geographic information; according to the density threshold denoising and the small cluster noise removal method, effective denoising effect can still be achieved when the point cloud is unevenly distributed, the denoising speed and effect are improved, the confidence is high, and the applicability is strong. In the future, it can be used in the fields of fast ground elevation acquisition, spacecraft landing and deep space exploration.

[0207] In order to further illustrate the beneficial effects of the application, in this embodiment, the adaptability to low signal-to-noise ratio ground surface photon point cloud signal extraction, the adaptability to terrain slope and the processing efficiency of large-scale spatial photon point cloud are considered, and simulation experiments are performed by using the method of the application and the DBSCAN point cloud clustering algorithm.

[0208] In order to evaluate the algorithm performance, a plurality of point cloud test data sets are simulated and generated by using the original photon point cloud data set of the MABEL photon counting laser radar. The MABEL is an airborne photon counting laser radar system designed by NASA, which is used for simulation and verification of ICESat-2 satellite-borne laser altimetry. The MABEL works at an altitude of 20km, simultaneously carries two kinds of 532 / 1064nm lasers, and the laser repetition frequency is adjustable in the range of 5-25kHz. Only the 1064nm waveband data with a laser repetition frequency of 5kHz is selected for simulation. Table 1 shows the instrument parameters of the MABEL in the 1064nm waveband.

[0209] Table 1 Instrument parameters of the MABEL in the 1064nm waveband

[0210] Parameter Value Wavelength 1064 nm Energy per pulse 5-7 μJ Pulse frequency 5-25 kHz Filter bandwidth 400 pm Divergence angle 100 μrad Field of view angle 210 μrad Aperture 127 mm System detection efficiency 1-2% @ 1064 nm

[0211] The MABEL dataset has separated the signal photons from the noise photons and labeled each type of photon. First, it takes the signal flag photons as the target photons, and then adds different levels of noise to extract the surface signal.

[0212] According to the photon detection model of the photon counting lidar, the number of noise photon events in a unit time interval follows a Poisson distribution, that is:

[0213]

[0214] where k is the number of noise photon events in a unit time interval, N n is the average number of noise photon events in a unit time interval. The probability of a noise photon event occurring in a unit time interval is:

[0215]

[0216] First, according to the average number of noise photons N n , the noise photon event probability P n is obtained, and then a uniformly distributed random number with a value range of [0, 1] is generated to determine the occurrence of noise photon events in each time interval:

[0217]

[0218] MABEL uses a GM-APD detector at 1064nm, and the detection of the signal will be affected by the dead time effect, that is, after detecting a photon signal, it needs to wait for a period of time before detecting the next photon signal, and the influence of the dead time effect increases with the increase of background noise, so it needs to be corrected. According to the size of the dead time, the photons in the dead time are removed from the front to simulate the influence of the dead time. Since the dead time effect will cause the number of signal photons and noise photons to decrease, the noise level needs to be recalculated. The dead time of Si GM-APD is usually within 100ns, and 50ns is used as the detector dead time.

[0219] Recall rate (R), precision (P) and F-Measure (F) are used as quantitative evaluation indicators. Recall rate represents the proportion of correctly identified signal photons to the true signal photon number. Precision represents the proportion of correctly identified signal photons among all identified signal photons. F-Measure (F) is the harmonic mean of precision and recall rate. The calculation formula of the indicators can be referred to as follows:

[0220]

[0221]

[0222]

[0223] Wherein, TP represents the correctly detected signal photons, FP represents the noise photons detected by the algorithm in error, and FN represents the signal photons detected as noise photons.

[0224] When the system parameters are determined, the data signal-to-noise ratio is mainly affected by the background noise rate and the terrain slope. Therefore, two kinds of point cloud data of flat terrain and steep terrain in mountainous areas are selected to simulate the algorithm processing effect under different background noise levels. The original data in this embodiment uses two groups of data in the MABEL flight data on September 27, 2013 as the simulation test original data.

[0225] Figure 4 is a graph of the change of the height along the track distance under different noise count rates, Figure 5 Table 2 is a comparison result of the processing effect of the present application (DDA-KF) and DBSCAN on relatively flat ground areas under different noise count rates.

[0226] Table 2 is a comparison table of the processing effect of the present application and DBSCAN on relatively flat ground areas under different noise count rates.

[0227]

[0228] Figure 6 Table 3 is a comparison result of the processing effect of the present application and DBSCAN on steep terrain areas in mountainous areas under different noise count rates.

[0229] Table 3 is a comparison table of the processing effect of the present application and DBSCAN on steep terrain areas in mountainous areas under different noise count rates.

[0230]

[0231] From Figure 5 , Figure 6 , Table 2, Table 3 can be seen that for flat terrain areas, the F value of the two methods under 1-4MHz background noise is basically the same, and the F value of the present application under 5-6MHz strong background noise is slightly higher than that of DBSCAN. Since the multi-directional density kernel matrix can better match the terrain slope change, under different noise levels, the F value of the present application on steep areas in mountainous areas is higher than that of DBSCAN. With the increase of noise level, the advantage of the present application becomes more obvious. In the 6MHz high background noise environment, the F-measure is about 47% higher than that of DBSCAN, indicating that the present application has strong adaptability and high confidence in strong background noise environment.

[0232] Then, the method of the present application deployed in ZYNQ UltraScale+MPSoC is compared with the processing speed of CPU-side DBSCAN algorithm in this embodiment, and the CPU platform is AMD Ryzen 7 5800H. In order to simulate the large-scale ground signal detection mode under the spacecraft platform, on the basis of the simulated photon point cloud simulation data of different background noise levels in the MABEL data set, simulated point cloud data of different longitudinal window sizes are generated to compare the processing efficiency of the two methods for different noise levels and different window sizes. The horizontal segmentation interval of the point cloud data is fixed at 500 shots to simulate the real-time segmentation processing of the photon point cloud stream data at a processing frequency of 10 Hz under a repetition frequency of 5 kHz.

[0233] The different background noise count rates and longitudinal window sizes before the Kalman filter initialization of the method of the present application are shown in Table 4. The processing time (unit: ms) of the method of the present application for point cloud data of different noise levels and longitudinal window sizes before the Kalman filter initialization is shown in Table 5, and the horizontal segmentation processing interval is 500 shots. Figure 7

[0234] Table 4 Table of background noise count rates and longitudinal window sizes before Kalman filter initialization

[0235]

[0236] The different background noise count rates and longitudinal window sizes after the Kalman filter initialization of the method of the present application are shown in Table 5. The processing time (unit: ms) of the method of the present application for point cloud data of different noise levels and longitudinal window sizes after the Kalman filter initialization is shown in Table 5, and the horizontal segmentation processing interval is 500 shots. Figure 8

[0237] Table 5 Table of background noise count rates and longitudinal window sizes after Kalman filter initialization

[0238]

[0239] From Figure 7 , Figure 8 , Table 4, Table 5, it can be seen that the running time of the present application is 1-4 orders of magnitude lower than that of the DBSCAN algorithm, and the running time of the present application does not decrease with the increase of the background noise density, but only increases slightly with the increase of the longitudinal window size. However, when the Kalman filter is initialized to track and search the ground, the running time of the present application is maintained at about 6 ms and does not change with the increase of the background noise rate and the longitudinal window size. Therefore, the present application has extremely high superiority and stability in processing efficiency.

[0240] ​​Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0241] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0242] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0243] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0244] Obviously, the above-described embodiments are only examples and are not intended to limit the present application. Based on the above description, those skilled in the art can make other variations and modifications of the present application without departing from the present application. Thus, the present application is not limited to the embodiments described above, but rather only by the claims that follow.

Claims

1. A spacecraft strong noise photon point cloud denoising method, characterized in that, The method comprises the following steps: Obtain the photon point cloud data stream of the spacecraft platform in all stages, and perform the following operations on the photon point cloud data in each stage: Grid the photon point cloud data to obtain a pseudo image, and extract signal photons from the pseudo image to obtain density dimension data using anisotropic radial basis functions; Construct a density threshold value for distinguishing signals and noises according to historical noises along the running track direction of the spacecraft platform, remove noises in the density dimension data according to the density threshold value, and the density threshold value is: th i = qmax({d i}) + (1 - q)mean({d i}), where th i is the density threshold of the i-th column along the direction of the spacecraft platform's operational orbit, q is a threshold factor, max() represents a maximum operation, and mean() represents a mean operation;{d i is a set of density values of the i-th column, and{d i is: wherein d i,j denotes the density value of the i-th column, j-th row, j is the row index, is the predicted value of the spacecraft altitude at the next stage obtained by Kalman filtering, and r is the signal retrieval window size. Remove small cluster noises from the density dimension data after removing the noises, and identify the ground surface signals in the density dimension data after removing the small cluster noises; Track the ground surface signals using Kalman filtering in combination with the spacecraft height in the previous stage.

2. The spacecraft strong noise photon point cloud denoising method of claim 1, wherein: The step of extracting signal photons from the pseudo image to obtain density dimension data using anisotropic radial basis functions comprises the following steps: Construct a density kernel anisotropic radial basis function, and perform grid sampling on the anisotropic radial basis function to generate a density kernel matrix; convolve the density kernel matrix as a convolution kernel on the sliding window of the pseudo image to obtain the density value d of the center point c in the θ direction θ (c) is: wherein R c represents the neighborhood range of the center point c, W θ (x) is the anisotropic radial basis function of the pixel point x in the direction of θ, x is a pixel point in the pseudo image, and z(x) is the pixel value corresponding to the pixel point x. for the density value d θ (c) performing a normalization to obtain a normalized d θ (c) is Generate a plurality of density kernel matrices under different angles, apply each density kernel matrix to the pseudo image to generate corresponding density dimension data, and take the maximum value of the density values of the corresponding pixels of each density dimension data to obtain the final density dimension data D(c) as: where θ1, θ2, …, θn are a plurality of angles, and max() represents a maximum value operation, represents the density value of the normalized center point c in the θn direction.

3. The spacecraft strong noise photon point cloud denoising method of claim 2, wherein: The anisotropic radial basis function of the pixel point x in the θ direction is: where A θ is a transformation matrix, a is the horizontal stretching ratio, θ is the clockwise rotation angle of the density kernel, σ is the standard deviation of the Gaussian function, c represents the center point position, R c is the neighborhood range of the center point.

4. The spacecraft strong noise photon point cloud denoising method according to any one of claims 1-3, characterized in that: The step of removing small cluster noises from the density dimension data after removing the noises comprises the following steps: an area threshold t is set and the area clusters c smaller than the area threshold t i removing, forming a cluster set C1 as: Wherein, P represents a cluster set obtained by removing the noises in the density dimension data; The area of each cluster in C1 is calculated As the weight, the center height of the cluster is calculated is: wherein z p represents the height corresponding to the pixel p in the density dimension data; Calculate the center height of the cluster weighted average and weighted standard deviation for: wherein, represents the area of the kth cluster, represents the center height of the kth cluster, σ min represents the minimum value of the preset weighted standard deviation; Select the clusters with a weighted average value less than a weighted standard deviation as the final cluster set C2:

5. The spacecraft strong noise photon point cloud denoising method of claim 4, wherein: The step of identifying the ground surface signals in the density dimension data after removing the small cluster noises comprises the following steps: Calculate the average thickness T and the average signal intensity S of the final cluster set C2: where w i is the lateral width of the ith cluster, D(x) is the density dimension data obtained with the point x in the cluster set C2 as the center point; Define the signal intensity divergence SID as: SID = T / S, Distinguish the ground surface signals and the backscattering signals of the atmosphere according to the signal intensity divergence.

6. The spacecraft strong noise photon point cloud denoising method of claim 4, wherein: The step of tracking the ground surface signals using Kalman filtering in combination with the spacecraft height in the previous stage comprises the following steps: Construct a system state model as: x k+1 = Ax k + w k , Z k = Hx k + v k , where x k represents the system state vector of the kth stage, A is the system state matrix, w k is the process noise vector; Z k represents the measurement value of the kth stage, H is the measurement matrix, v k is the measurement noise vector, H k is the density dimension height, V k is the density dimension height rate of change; Construct a Kalman filter prediction and system state update model as: wherein, is the updated system state vector for the kth stage, denotes the predicted value of the system state vector, denotes the prior error estimate covariance matrix, P k denotes the posterior error estimate covariance matrix, Q k is the process noise vector v k the corresponding covariance matrix, K k denotes the Kalman gain matrix, R k is the measurement noise vector v k the corresponding covariance matrix, I is the identity matrix; According to the formula The updated system state vector of the k+1 stage is obtained The is expressed as Wherein The predicted value of the density dimension height of the next stage is The operation of passing the density threshold value of the construction area signal and noise to the next stage realizes the tracking identification of the ground surface signal.

7. The spacecraft strong noise photon point cloud denoising method of claim 6, wherein: the measured value Z of the kth phase k is: The metrology noise vector v k The corresponding covariance matrix R k is: The process noise vector v k The corresponding covariance matrix Q k is: wherein, is an estimate of the density dimensionality at the i-th state update, is an estimate of the rate of change of the density dimensionality at the i-th state update, is an average of the estimates of the density dimensionality for the previous n state updates of k, is an average of the estimates of the rate of change of the density dimensionality for the previous n state updates of k.

8. The spacecraft strong noise photon point cloud denoising method of claim 7, wherein: The density dimension height H k is: The density dimension height change rate V k For: When the spacecraft's vertical velocity is zero, then V k It is directly proportional to the rate of change of ground elevation, i.e., the terrain slope; if the vertical velocity is not zero, then V k It is directly proportional to the superposition of the spacecraft's vertical velocity and the rate of change of its altitude on the Earth's surface.

9. A spacecraft strong noise photon point cloud high confidence fast denoising system, characterized in that, The method comprises the following steps: A data acquisition module is configured to acquire the photon point cloud data stream of the spacecraft platform in all stages; A data preprocessing module is configured to grid the photon point cloud data to obtain a pseudo image, extract signal photons from the pseudo image to obtain density dimension data using anisotropic radial basis functions, and perform hardware acceleration using an FPGA; A signal and noise separation module is configured to construct a density threshold value for distinguishing signals and noises according to historical noises along the running track direction of the spacecraft platform, remove noises in the density dimension data according to the density threshold value, and the density threshold value is: th i = qmax({d i}) + (1 - q)mean({d i}), where th i is the density threshold value for the ith column along the direction of the spacecraft platform's orbit, q is a threshold factor, max() denotes a max operation, mean() denotes a mean operation; {d i} is a set of density values for the ith column, and {d i} is: wherein d i,j denotes the density value of the i-th column, j-th row, j is the row index, is the predicted value of the spacecraft altitude at the next stage obtained by Kalman filtering, and r is the signal retrieval window size. A post-processing module is configured to remove small cluster noises from the density dimension data after removing the noises, and identify the ground surface signals in the density dimension data after removing the small cluster noises; A Kalman filtering module is configured to track the ground surface signals using Kalman filtering in combination with the spacecraft height in the previous stage; The post-processing module and the Kalman filtering module are deployed on an ARM platform.

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