Method and system for measuring and drawing continuous irregular curve in real time

Abstract

The invention relates to the technical field of surveying and mapping, in particular to a method and system for measuring and drawing continuous irregular curves in real time. The method comprises the following steps: calculating an Euclidean distance and an accumulated distance between adjacent control points, and normalizing chord length parameters; respectively extracting x-axis, y-axis and z-axis information of all control points, and respectively constructing a segmented cubic spline interpolation function and a linear interpolation function; dividing the chord length parameter interval into a plurality of sampling points, calculating an accumulated arc length between the sampling points, and establishing a mapping relation between the sampling points and the arc length; the number of interpolation points inserted between the two control points is stipulated, the step length of the interpolation points is calculated, the left index of the arc length interval where the step length of the interpolation points is located is searched and calculated according to the dichotomy, the real arc length sampling value of the interval is calculated, and then the coordinates of the interpolation points are calculated; and when each new feature point is added, the interpolation calculation is executed again, and only the curve segment of the affected interval is updated. According to the technical scheme, the efficiency and accuracy of curve measurement can be improved.

Description

Technical Field

[0001] The present invention relates to the field of surveying and mapping technology, and in particular to a method and system for real-time measurement and drawing of continuous irregular curves. Background Art

[0002] There are various curved shapes on the surface of the earth, such as curved roads, curved flower beds, etc. A common task in the field of surveying and mapping is to reduce the shapes of various buildings and facilities to a certain scale and draw them on the map. The traditional method of measuring curves is to use a total station to measure, evenly collect a series of points on the curve to be measured, and then obtain the shape and length of the curve. Compared with the method of measuring only the two end points of a straight line, measuring a curve is undoubtedly much more troublesome, and the use of a total station involves a series of centering and leveling operations, which is relatively time-consuming. In addition, the traditional method also requires internal processing of the data measured by the total station to obtain a visual representation of the true curve shape. The whole process usually takes several hours. Summary of the Invention

[0003] The purpose of the present invention is to provide a method and system for real-time measurement and drawing of continuous irregular curves, which can improve the efficiency and accuracy of curve measurement.

[0004] To achieve the above objectives, in a first aspect, the present invention provides a method for real-time measurement and drawing of a continuous irregular curve, comprising: Calculate the Euclidean distance and cumulative distance between adjacent control points and normalize the chord length parameter; Extract the x-axis, y-axis, and z-axis information of all control points respectively, and construct piecewise cubic spline interpolation functions with the chord length parameter as the independent variable and the x-axis and y-axis information as the dependent variable; construct a linear interpolation function with the chord length parameter as the independent variable and the z-axis information as the dependent variable; The chord length parameter interval is divided into several sampling points, the cumulative arc length between the sampling points is calculated, and a mapping relationship between the sampling points and the arc length is established; Specify the number of interpolation points to be inserted between two control points, calculate the interpolation point step size, find the left index of the arc length interval where the interpolation point step size is calculated using the bisection method, calculate the actual arc length sampling value of the interval, and then calculate the coordinates of the interpolation point to obtain the three-dimensional coordinates; Every time a feature point is added, the interpolation calculation is re-executed and only the curve segments in the affected interval are updated.

[0005] Beneficial Effects of the Basic Solution: This application utilizes continuity constraints in cubic spline interpolation to more closely approximate the true curve shape, making it particularly suitable for fitting irregular curves. It enforces normalization of chord length parameters to ensure that the interpolation parameters strictly correspond to the curve geometry, avoiding uneven interpolation density (local stretching or compression of the curve) caused by path length variations. The number of interpolation points is fixed or adjustable between two control points, ensuring curve uniformity. Linear interpolation is used for the z-axis (height or depth information), prioritizing the continuity of elevation data over smoothness, avoiding curve distortion caused by sudden terrain changes, and reducing the computational complexity of high-order interpolation, thus balancing accuracy and real-time performance. Existing technologies assume that the geometric characteristics of each dimension (x / y / z) of the curve are completely consistent and adopt a unified interpolation strategy. Using high-order interpolation for the z-axis can lead to a surge in computational complexity due to the coupling of three-dimensional data. This can make real-time performance difficult due to the hardware limitations of mobile devices, which conflicts with the portability and lightweight requirements of this system.

[0006] This technical solution only recalculates the cubic spline coefficients for the affected intervals (near the newly added points), and the original parameters are retained for the remaining intervals. No global recalculation is required after the new points are added. By precalculating the cumulative arc length and establishing a mapping relationship, the position calculation of the subsequent interpolation points is based on the actual arc length distribution, rather than a simple parameter division. The left index of the arc length interval corresponding to the interpolation point step is found by bisection, avoiding the linear search of all sampling points, reducing the search time complexity, reducing the amount of calculation, and improving real-time performance. This technical solution is suitable for lightweight deployment, supports real-time reception of new feature points and incremental curve updates on mobile devices, and is suitable for dynamic scenarios such as field mapping and navigation.

[0007] As an implementable preferred solution, the Euclidean distance and cumulative distance between adjacent control points are calculated, and the chord length parameter is normalized, including the following: When the cumulative number of feature points collected is n≥3, a series of three-dimensional control point coordinates are obtained. , Calculate adjacent control points and Euclidean distance for:

[0008] Calculate the cumulative distance using the following formula:

[0009] Normalized chord length parameter , the formula is as follows:

[0010] in, represents the i-th control point; the total number of control points is n; represents the Euclidean distance of the i-th segment; represents the cumulative distance of the i-th segment; for point The corresponding normalized chord length parameter.

[0011] As an implementable preferred solution, the x, y and z axis information of all control points are extracted as follows:

[0012] in, 、 and Represents a list of x, y, and z axis coordinate values extracted from the control points; and are the three-axis coordinate values of the control points; Chord length parameter is the independent variable, x-axis information , y-axis information As the dependent variable, piecewise cubic spline interpolation functions are constructed respectively, and the formula is as follows:

[0013]

[0014] Chord length parameter is the independent variable and z-axis information Construct a linear interpolation function for the dependent variable, the formula is as follows:

[0015] in, represents the analytical expression of the cubic spline interpolation function, Represents the analytical expression of the linear interpolation function.

[0016] As an implementable preferred solution, the chord length parameter interval is divided into several sampling points, the cumulative arc length between the sampling points is calculated, and a mapping relationship between the sampling points and the arc length is established, including the following: Calculate the interpolation points, then the interpolation functions of the x, y, and z axes corresponding to the independent variables are:

[0017] in, For sampling points The corresponding independent variable; The sampling point coordinates are:

[0018] Calculate sampling points The cumulative arc length between:

[0019] in, For sampling points The corresponding cumulative arc length is used to establish a mapping relationship between sampling points and arc lengths.

[0020] As an implementable preferred solution, the number of interpolation points inserted between two control points is specified, the interpolation point step size is calculated, the left index of the arc length interval where the interpolation point step size is calculated is found according to the bisection method, and the actual arc length sampling value of the interval is calculated, and then the coordinates of the interpolation point are calculated to obtain the three-dimensional coordinates, which specifically includes the following: It is specified that a interpolation points are inserted between two control points; the proportional coefficient of the total cumulative arc length of the entire curve and the sum of the distances between the control points is calculated as follows:

[0021] in, is the proportionality factor between the arc length of the curve and the straight line distance; is the total arc length of the curve; is the Euclidean cumulative distance of the control points; According to the Euclidean distance between two control points And the number of interpolation points, calculate the interpolation point step size:

[0022] in, is the step size between interpolation points; is the Euclidean distance between two adjacent control points; is the number of interpolation points between two adjacent control points; Find and calculate the interpolation point step size based on the bisection method The left index of the arc length interval , and calculate the actual arc length sampling value of the interval in which it is located. The formula is as follows:

[0023] in, is the independent variable value of the interpolation point; is the left index of the closest arc length that is smaller than the interpolated point; is the step size of the i-th interpolation point; For the The cumulative arc length of the sampling points; For the The independent variable of each sampling point; Calculate the interpolation point coordinates using the following formula:

[0024] Get the three-dimensional coordinates.

[0025] As an implementable preferred solution, a portable inertial navigation device is used to collect feature points. The portable inertial navigation device includes a three-axis accelerometer and a three-axis gyroscope; and data processing and curve display are performed through software installed on a mobile hardware device.

[0026] As an implementable preferred solution, perform system initialization preparation, including the following: Check whether the portable inertial navigation device has sufficient power to ensure that the device is working properly; initialize the inertial navigation device, including setting the data sampling frequency and coordinate system; Record the initial attitude angle of the inertial navigation device, collect data for a period of time in a stationary state, and calculate the average value as the initial attitude angle; Turn on the mobile hardware device, ensure that the device's network connection is normal, and open the software used to receive and process inertial navigation data; in the software, select the data receiving method, set the color and line type of the curve display; Initialize the parameters of the zero-speed correction algorithm in the software of the mobile hardware device, including the time constant of the zero-bias estimation and the noise variance of the accelerometer and gyroscope; initialize the parameters of the cubic spline interpolation algorithm, including the number of interpolation points and boundary conditions.

[0027] As an implementable and optimal solution, the inertial navigation device is moved along the curve to be measured, and briefly stops at a characteristic point of the curve. The software automatically marks and saves the coordinates of the point. During the movement, the inertial navigation device is kept level, and the spacing between characteristic points meets the set requirements. The inertial navigation device collects raw acceleration and angular velocity data at a set sampling frequency and transmits the data to the mobile hardware device in real time via wired or wireless means.

[0028] In a second aspect, the present invention further provides a system for real-time measurement and drawing of continuous irregular curves, which utilizes the above-mentioned method for real-time measurement and drawing of continuous irregular curves. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of a system for drawing continuous irregular curves for real-time measurements.

[0030] Figure 2 FIG. 1 is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention.

[0031] Reference numerals: electronic device 500 , processor 501 , communication interface 502 , memory 503 , bus 504 . DETAILED DESCRIPTION

[0032] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. It will be understood that the specific embodiments described herein are only partial embodiments of the present invention, which are only used to explain the present application, rather than to limit the present application. It should be noted that the technical features or combinations of technical features described in the following embodiments should not be considered to be isolated, and they can be combined with each other to achieve better technical effects. The same reference numerals appearing in the drawings of the following embodiments represent the same features or components, which can be applied to different embodiments.

[0033] In addition, unless otherwise defined, technical or scientific terms used in the description of the present invention should have the common meanings understood by those skilled in the art in the art to which the present invention belongs.

[0034] The present invention will be further described in detail below with reference to the accompanying drawings: A system for real-time measurement and plotting of continuous irregular curves consists of a portable inertial navigation device, a mobile hardware device (such as a mobile phone, laptop, or tablet), and software (installed on the mobile hardware device). The portable inertial navigation device contains a three-axis accelerometer and a three-axis gyroscope. Its internal inertial measurement unit (IMU) is specially arranged on a printed circuit board (PCB) to obtain high-precision data with minimal bias. The mobile hardware device receives the raw data from the inertial navigation device and runs the software for data processing and curve display.

[0035] Reference Figure 1 , a method for real-time measurement and drawing of continuous irregular curves, comprising: Step S100, system initialization preparation, includes: Step S101: Check whether the portable inertial navigation device has sufficient power to ensure normal operation of the device. Initialize the inertial navigation device, including setting parameters such as the data sampling frequency (such as 100 Hz) and the coordinate system (such as the local horizontal coordinate system).

[0036] Record the initial attitude angles of the inertial navigation device (pitch angle θ0, roll angle φ0, yaw angle ψ0). The data can be collected for a period of time (such as 10 seconds) in a static state and the average value can be calculated as the initial attitude angle.

[0037] Step S102: Turn on the mobile hardware device, ensure the device's network connection is normal, and then open the software used to receive and process inertial navigation data. Make relevant settings in the software, such as selecting the data reception method (wired or wireless) and setting parameters such as the curve display color and line type.

[0038] Initialize the parameters of the zero-velocity correction algorithm in the mobile hardware software, such as the time constant for bias estimation (e.g., set to 5 seconds) and the noise variance of the accelerometer and gyroscope. Initialize the parameters of the cubic spline interpolation algorithm, such as the number of interpolation points and boundary conditions.

[0039] Step S200, data collection and transmission, includes: In step S201, the surveyor holds the inertial navigation device and moves along the curve to be measured. The surveyor briefly stops (≥1 second) at a characteristic point of the curve (such as an inflection point or a curvature change point). The software automatically marks and saves the coordinates of the point.

[0040] Keep the inertial navigation device level during movement (this can be monitored in real time using the software's built-in inclinometer, with a tilt angle ≤ 5°). The recommended spacing between feature points is ≤ 5 meters (complex curves require increased spacing, such as points every 0.5 meters for arcs with a radius less than 2 meters).

[0041] In step S202 , the inertial navigation device collects raw acceleration and angular velocity data according to a set sampling frequency, and transmits the data to the mobile hardware device in real time via a wired or wireless manner.

[0042] Step S300: curve fitting is generated. When the cumulative number of feature points collected is n≥3, a series of three-dimensional control point coordinates are obtained. , , triggering the curve generation process. Every time a feature point is added, the curve is immediately recalculated and the display is updated, including: Step S301: Chord length parameterization, calculation of adjacent control points and Euclidean distance for:

[0043] Calculate the cumulative distance using the following formula:

[0044] Normalized chord length parameter , the formula is as follows:

[0045] in, represents the i-th control point, ;The total number of control points is n; Represents the Euclidean distance of the i-th segment, and the previous point Calculated; Represents the cumulative distance of the i-th segment, Accumulate and obtain; for point The corresponding normalized chord length parameter.

[0046] Step S302: To avoid the oscillation distortion caused by traditional cubic spline interpolation, the cubic spline method is improved without relying on additional information, while taking into account the elevation information of the interpolated points. The x, y, and z axis information of all control points are extracted as follows:

[0047] in, 、 and Represents a list of x, y, and z axis coordinate values extracted from the control points; and , They are the three-axis coordinate values of the control point.

[0048] Chord length parameter is the independent variable, x-axis information , y-axis information As the dependent variable, piecewise cubic spline interpolation functions are constructed respectively, and the formula is as follows:

[0049]

[0050] Chord length parameter is the independent variable and z-axis information Construct a linear interpolation function for the dependent variable, the formula is as follows:

[0051] in, 、 and Represents a list of x, y, and z axis coordinate values extracted from the control points; For control points The corresponding chord length parameter; represents the analytical expression of the cubic spline interpolation function, Represents the analytical expression of the linear interpolation function, which is calculated by the above formula.

[0052] Constructing cubic spline functions for the x and y axes respectively can effectively avoid the defects of the traditional cubic spline function. At the same time, constructing an interpolation function for the z-axis information in a linear interpolation manner can generate the z-axis information without affecting the curvature information of the curve.

[0053] Step S303: Set the chord length parameter interval Divided into 1000 sampling points (taking into account computational efficiency), according to the idea of integration, enough sampling points can be approximated as a curve, and the arc length of the curve can be approximately replaced by the Euclidean distance between adjacent sampling points.

[0054] Assume that the calculation The coordinates of the sampling points, since the above-mentioned independent variable variation range is , then the interpolation functions of the x, y, and z axes corresponding to the independent variables can be calculated by the following formulas:

[0055] In this embodiment, N=1000. For sampling points The corresponding independent variable.

[0056] The sampling point coordinates are:

[0057] The x-axis interpolation function, y-axis interpolation function, and z-axis interpolation function calculated in step S302 are used to calculate: By sampling point The coordinates and the Euclidean distance formula in S301 can be used to calculate the cumulative arc length between sampling points:

[0058] in, For sampling points The corresponding cumulative arc length is used to establish a mapping relationship between sampling points and arc lengths for quick query and calculation.

[0059] Step S304: To ensure that the interpolation points of the curve are generated evenly between the control points, it is specified that the interpolation points between the two control points interpolation points; calculate the proportional coefficient of the total cumulative arc length of the entire curve and the sum of the distances between the control points. The formula is as follows:

[0060] in, is the proportionality factor between the arc length of the curve and the straight line distance; is the total arc length of the curve; is the Euclidean cumulative distance of the control points.

[0061] According to the Euclidean distance between two control points And the number of interpolation points, calculate the interpolation point step size:

[0062] in, is the step size between interpolation points; is the Euclidean distance between two adjacent control points; is the number of interpolation points between two adjacent control points.

[0063] Find and calculate the interpolation point step size based on the bisection method The left index of the arc length interval , and calculate the actual arc length sampling value of the interval in which it is located. The formula is as follows:

[0064] in, is the independent variable value of the interpolation point; is the left index of the closest arc length that is smaller than the interpolated point; is the step size of the i-th interpolation point; For the The cumulative arc length of the sampling points; For the The independent variable of each sampling point.

[0065] Use the calculated t i As an independent variable, the formula for calculating the coordinates of the interpolation point is as follows:

[0066] Get the three-dimensional coordinates.

[0067] In step S400, each time a feature point is added, the interpolation calculation is re-performed, updating only the curve segments in the affected interval to avoid full redrawing. The curve is efficiently drawn using the graphics rendering engine of the mobile hardware device (such as OpenGL ES), supporting real-time zooming and panning.

[0068] Those skilled in the art will appreciate that all or part of the process steps in a method for real-time measurement and drawing of a continuous irregular curve can be implemented by instructing related hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the process steps of various embodiments of a method for real-time measurement and drawing of a continuous irregular curve. Among them, any reference to memory, storage, database, or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0069] The present application also provides an electronic device 500 that utilizes the aforementioned method for real-time measurement and drawing of a continuous irregular curve. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the aforementioned method for real-time measurement and drawing of a continuous irregular curve are implemented. In the present application, the processor serves as the control center of the computer method and can be a processor of a physical machine or a processor of a virtual machine.

[0070] Reference Figure 2 The electronic device 500 includes at least one processor 501, at least one communication interface 502, at least one memory 503, and at least one bus 504. Bus 504 is used to enable communication between these components, communication interface 502 is used to communicate signaling or data with other node devices, and memory 503 stores machine-readable instructions executable by processor 501. When the electronic device 500 is in operation, processor 501 communicates with memory 503 via bus 504. When the machine-readable instructions are invoked by processor 501, the steps of the above-described method for real-time measurement and drawing of a continuous irregular curve are executed.

[0071] The above contents are merely embodiments of the present invention. Common knowledge such as the known specific structures and characteristics in the scheme is not described in detail here. A person of ordinary skill in the art is aware of all common technical knowledge in the technical field to which the invention belongs before the filing date or priority date, is able to obtain all existing technologies in the field, and has the ability to apply conventional experimental means before that date. A person of ordinary skill in the art can, under the guidance of this application, improve and implement this scheme in combination with his or her own abilities. Some typical known structures or known methods should not become an obstacle for a person of ordinary skill in the art to implement this application. It should be pointed out that for a person of ordinary skill in the art, several variations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection claimed in this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for real-time measurement and drawing of continuous irregular curves, characterized in that: include: Calculate the Euclidean distance and cumulative distance between adjacent control points and normalize the chord length parameter; Extract the x-axis, y-axis, and z-axis information of all control points respectively, and construct piecewise cubic spline interpolation functions with the chord length parameter as the independent variable and the x-axis and y-axis information as the dependent variable; construct a linear interpolation function with the chord length parameter as the independent variable and the z-axis information as the dependent variable; The chord length parameter interval is divided into several sampling points, the cumulative arc length between the sampling points is calculated, and a mapping relationship between the sampling points and the arc length is established; Specify the number of interpolation points to be inserted between two control points, calculate the interpolation point step size, find the left index of the arc length interval where the interpolation point step size is calculated using the binary search method, calculate the actual arc length sampling value of the interval, and then calculate the coordinates of the interpolation point; Every time a feature point is added, the interpolation calculation is re-executed and only the curve segments in the affected interval are updated.

2. The method for real-time measurement and drawing of a continuous irregular curve according to claim 1, characterized in that: Calculate the Euclidean distance and cumulative distance between adjacent control points and normalize the chord length parameters, including the following: When the cumulative number of feature points collected is n≥3, a series of three-dimensional control point coordinates are obtained. , Calculate adjacent control points and Euclidean distance for: Calculate the cumulative distance using the following formula: Normalized chord length parameter , the formula is as follows: in, represents the i-th control point; the total number of control points is n; represents the Euclidean distance of the i-th segment; represents the cumulative distance of the i-th segment; for point The corresponding normalized chord length parameter.

3. The method for real-time measurement and drawing of a continuous irregular curve according to claim 2, characterized in that: Extract the x, y and z axis information of all control points respectively: in, 、 and Represents a list of x, y, and z axis coordinate values extracted from the control points; and are the three-axis coordinate values of the control points; Chord length parameter is the independent variable, x-axis information , y-axis information As the dependent variable, piecewise cubic spline interpolation functions are constructed respectively, and the formula is as follows: Chord length parameter is the independent variable and z-axis information Construct a linear interpolation function for the dependent variable, the formula is as follows: in, represents the analytical expression of the cubic spline interpolation function, Represents the analytical expression of the linear interpolation function.

4. The method for real-time measurement and drawing of a continuous irregular curve according to claim 3, characterized in that: The chord length parameter interval is divided into several sampling points, the cumulative arc length between the sampling points is calculated, and the mapping relationship between the sampling points and the arc length is established, including the following: Calculate the interpolation points, then the interpolation functions of the x, y, and z axes corresponding to the independent variables are: in, For sampling points The corresponding independent variable; The sampling point coordinates are: Calculate sampling points The cumulative arc length between: in, For sampling points The corresponding cumulative arc length is used to establish a mapping relationship between sampling points and arc lengths.

5. The method for real-time measurement and drawing of a continuous irregular curve according to claim 1, characterized in that: Specify the number of interpolation points to be inserted between two control points, calculate the interpolation point step size, find the left index of the arc length interval where the interpolation point step size is calculated using the bisection method, calculate the actual arc length sampling value of the interval, and then calculate the coordinates of the interpolation point to obtain the three-dimensional coordinates. Specifically, it includes the following: It is specified that a interpolation points are inserted between two control points; the proportional coefficient of the total cumulative arc length of the entire curve and the sum of the distances between the control points is calculated as follows: in, is the proportionality coefficient between the arc length of the curve and the straight line distance; is the total arc length of the curve; is the Euclidean cumulative distance of the control points; According to the Euclidean distance between two control points And the number of interpolation points, calculate the interpolation point step size: in, is the step size between interpolation points; is the Euclidean distance between two adjacent control points; is the number of interpolation points between two adjacent control points; Find and calculate the interpolation point step size based on the bisection method The left index of the arc length interval , and calculate the actual arc length sampling value of the interval in which it is located. The formula is as follows: in, is the independent variable value of the interpolation point; is the left index of the closest arc length that is smaller than the interpolated point; is the step size of the i-th interpolation point; For the The cumulative arc length of the sampling points; For the The independent variable of each sampling point; Calculate the interpolation point coordinates using the following formula: Get the three-dimensional coordinates.

6. The method for real-time measurement and drawing of a continuous irregular curve according to claim 1, characterized in that: Feature points are collected using a portable inertial navigation device that includes a three-axis accelerometer and a three-axis gyroscope. Data processing and curve display are performed using software installed on a mobile hardware device.

7. The method for real-time measurement and drawing of a continuous irregular curve according to claim 6, characterized in that: Perform system initialization preparations, including the following: Check whether the portable inertial navigation device has sufficient power to ensure that the device is working properly; initialize the inertial navigation device, including setting the data sampling frequency and coordinate system; Record the initial attitude angle of the inertial navigation device, collect data for a period of time in a stationary state, and calculate the average value as the initial attitude angle; Turn on the mobile hardware device, ensure that the device's network connection is normal, and open the software used to receive and process inertial navigation data; in the software, select the data receiving method, set the color and line type of the curve display; Initialize the parameters of the zero-speed correction algorithm in the software of the mobile hardware device, including the time constant of the zero-bias estimation and the noise variance of the accelerometer and gyroscope; initialize the parameters of the cubic spline interpolation algorithm, including the number of interpolation points and boundary conditions.

8. The method for real-time measurement and drawing of a continuous irregular curve according to claim 7, characterized in that: Move the inertial navigation device along the curve to be measured and briefly stop at a characteristic point on the curve. The software will automatically mark and save the coordinates of the point. Keep the inertial navigation device level during the movement and ensure that the spacing between characteristic points meets the set requirements. The inertial navigation device collects raw acceleration and angular velocity data at a set sampling frequency, and transmits the data to the mobile hardware device in real time via wired or wireless means.

9. A system for real-time measurement and drawing of continuous irregular curves, characterized in that: The method for real-time measurement and drawing of a continuous irregular curve as described in any one of claims 1 to 8 is used.

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