Study and design of an online calibrated CAN-bus depth sensor

Abstract

Graphical abstract

As the strategic position of the oceans in the political, military, and economic fields is increasing and the mankind’s use of ocean space is constantly being strengthened, underwater unmanned equipment is of vital importance and embraces a wide range of prospects for application, which plays a vital role in modern maritime military strategy, and is a key factor in ensuring that an advantage is gained in the field of underwater warfare in the new era. Underwater unmanned equipment can perform tasks such as environmental monitoring, target detection, anti-submarine, and anti-mine warfare, and can also be used as a weapon platform and a support platform, with the characteristics of strong concealment and low cost, and can be fitted with an optional payload according to the type of mission. As an essential part of underwater unmanned equipment, depth sensor is responsible for completing the deployment depth of the equipment in the seawater or sailing depth measurement, and the seawater pressure signal is converted into an electrical signal sent to the fuzzing device or control system and other electrical components for decoding and calculation, in order to control the sailing depth, thus completing the measurement of the automatic adaptation range in different depths, so as to ensure that the accuracy and the effectiveness of the target to be measured, which performs a crucial function in the process of equipment action. Meanwhile, for some underwater equipment, especially weaponry, the internal space is compact, the structure is complex, and the integration is high, making disassembly extremely difficult. Long-term use and storage, for sensors, cause time drift, which requires recalibrating. However, when sensors undergo time drift during long-term use or storage and require recalibration, they can only be removed and sent back to the manufacturer for maintenance during major overhauls. This process is time-consuming, and the secondary assembly after disassembly poses safety risks, significantly impacting the equipment’s performance. This paper introduces a CAN bus depth sensor with the capability of online calibration without disassembly, enabling the product to be quickly calibrated online without returning to the factory. This enhances the equipment’s supportability and ensures its long-term stable operation.

Keywords

underwater unmanned equipment depth sensor online calibration

Introduction

With the development of science and technology, the strategic position of the ocean in the political, military, economy, and other fields is increasing, and the degree of human use of ocean space continues to increase, the observation, and operation of traditional means of artificial diving and manned submersible are difficult to meet the needs of modern marine science and technology applications.^1–3 Underwater unmanned equipment is a key factor to ensure the advantage in the field of underwater warfare in the new era and faces a wide range of application prospects, playing a vital role in modern maritime military strategy.^4–6 Underwater unmanned equipment cannot only performs tasks such as environmental monitoring, target detection, anti-submarine, and anti-mine, but also be used as a weapon platform and support platform, which has the characteristics of strong concealment, low cost, and can be equipped with an optional workload according to the type of mission.^7,8

Depth acquisition for direct measurement sensors is predominantly achieved by quantifying physical parameters inherently correlated with water depth. Specifically, pressure sensors, acoustic sensors, optical sensors, and mechanical (contact-based) sensors have been widely adopted as core sensing modalities in this context, as validated by extensive experimental studies and theoretical analyses.^9–11 Based on the principle of hydrostatics, pressure sensors achieve depth quantification by sensing the inherent mapping relationship between hydrostatic pressure and water depth. Their passive measurement mechanism eliminates the need for active signal transmission modules and mechanical contact structures, granting them inherent stability, and potential for interference resistance at the operational principle level. In contrast, acoustic depth sensing technologies—including single-beam echo sounders, multi-beam bathymetric systems, and side-scan sonars—rely on acoustic wave propagation characteristics. These systems emit acoustic signals, capture seafloor reflections, and calculate target distance based on propagation delay and sound velocity calibration models.^12,13 Optical bathymetric techniques comprise multiple branches: airborne dual-wavelength LiDAR systems, which utilize the time difference between surface and seabed laser echoes, and underwater structured-light/laser scanning imaging technologies, which achieve high-precision measurement through spot deformation analysis and 3D point cloud reconstruction.^14–17 However, such active sensing approaches commonly suffer from structural limitations: sensitivity to vibration and shock due to moving components, performance degradation of transducer probes, or optical windows caused by fouling and medium corrosion, significantly undermining reliability in long-term continuous operation scenarios. Mechanical contact-based depth measurement devices, such as encoder-winch sounding systems, rely on physical contact for measurement, permitting only intermittent point sampling. This approach is inadequate for capturing high-frequency fluctuations in dynamic aquatic environments, exhibiting insufficient temporal resolution, and measurement continuity. Indirect positioning-derived bathymetric techniques—typically involving the fusion of real-time kinematic (RTK) or post-processed kinematic (PPK) positioning with acoustic/optical ranging data—derive seabed elevation through multi-source fusion of high-precision positioning information and range measurements, combined with geoid models.^18–22 Nonetheless, these systems are constrained by complex hardware architecture, significant data transmission and processing latency, and susceptibility to cumulative drift errors over prolonged operation, limiting their applicability in real-time measurement scenarios. For specialized platforms with stringent spatial constraints and limited power budgets, such as autonomous underwater vehicles (AUVs), traditional acoustic, and optical depth sensors face pronounced application bottlenecks. Their substantial volume and weight, stringent installation and pointing requirements, and high power consumption conflict with the demands of integrated design and real-time control. In comparison, pressure sensors—featuring all-solid-state packaging, no moving mechanical parts, and advantages such as zero active energy emission, fast response, and continuous measurement—demonstrate marked technical superiority in long-term reliability, dynamic parameter capture capability, and system integration compatibility. Consequently, they provide a high-performance solution for critical applications including long-term unattended observation and real-time closed-loop depth control, establishing themselves as the preferred technological pathway for depth measurement modules in specialized underwater equipment.

As a core sensing component of underwater unmanned platforms, depth sensors are responsible for the critical function of real-time monitoring of deployment or navigation depth. By converting seawater pressure signals into electrical signals and transmitting them to fuzzing devices or control systems for processing, they enable precise control of navigation depth and adaptive range adjustment. This ensures the effective execution of detection tasks and the accuracy and reliability of platform operations, playing an irreplaceable role within the overall system.^23–26 Currently, commonly used depth sensors are primarily based on several working principles, including bellows-spring combinations, electromagnetic relays, capacitance, piezoelectricity, and silicon piezoresistive technology. Bellows-spring combination sensors suffer from low accuracy, susceptibility to wear, and insufficient reliability. Electromagnetic relay-type sensors are constrained by short lifespans, vulnerable contacts, and sensitivity to electromagnetic interference. Capacitive sensors face challenges such as complex manufacturing processes and significant parasitic parameter effects. Piezoelectric sensors, while suitable for dynamic measurements, involve relatively complex signal processing. In contrast, silicon piezoresistive sensors have become the mainstream solution in current depth measurement applications due to their compact size, high accuracy, strong output signals, and excellent dynamic response characteristics.^27–29 It is noteworthy that underwater equipment, particularly weapon platforms, typically features highly integrated structures, limited internal space, and difficulties in disassembly and maintenance. Sensors are prone to time drift during long-term use or storage, necessitating periodic recalibration. Traditional calibration methods rely on disassembly during major overhauls and factory returns, which are not only time-consuming and costly but also risk introducing installation errors and safety hazards during reassembly, thereby affecting the overall performance and operational reliability of the equipment. Addressing the specific requirements of underwater unmanned platforms for long-term deployment and autonomous support capabilities, this paper proposes an innovatively designed CAN bus depth sensor. This sensor integrates an in-situ, disassembly-free intelligent calibration system, enabling automatic calibration during mission intervals or routine inspections without the need for factory returns. This feature significantly enhances the sustained operational capability and lifecycle reliability of underwater unmanned platforms.

Working principles

The sensor is based on the principle of piezoresistive effect, the use of semiconductor technology, and micro-machining technology to produce its core components—pressure sensitive components. Pressure sensitive components will be converted into voltage signals, and then through the conditioning circuit will be conditioned into a pressure signal to meet the requirements of the protocol of the standard CAN bus output.^30–32 The CAN bus, as a cost-effective, high-speed, and reliable fieldbus standard, is capable of fully meeting the requirements of real-time control and distributed control, demonstrating exceptional real-time performance and anti-interference capabilities.^33–36 This bus system encompasses multiple critical components, including circuit input–output protection, constant current supply, signal amplification, and comparison circuits. Each part fulfills specific functions, such as internal and external circuit protection, providing a constant current supply for pressure-sensitive elements, and signal amplification. The principle block diagram of the sensor, as shown in Figure 1, clearly illustrates the collaborative operation of these functional modules.

Figure 1.

Block diagram of sensor principle.

The sensing element operates on the principle of silicon piezoresistive technology. It involves the localized diffusion of P-type impurities on an N-type single-crystal silicon wafer to form resistive strips, which are then connected to form a Wheatstone bridge, thereby creating a pressure sensor chip. The back of the chip is sealed to enable the measurement of pressure signals. In the design of pressure sensors, to enhance the full-scale output, reduce zero-point temperature drift, and improve linearity, the force-sensitive resistors are typically connected in a full-bridge configuration. The bridge is usually powered by either a constant voltage source or a constant current source. When pressure is applied, the resistance of the force-sensitive resistors changes, causing an imbalance in the bridge’s output and generating an output signal proportional to the pressure signal. However, when powered by a constant voltage source, the sensitivity decreases as the temperature rises, making it difficult to compensate for the temperature drift of sensitivity. Therefore, we adopt a constant current source for power supply. The specific connection method of the bridge when powered by a constant current source is illustrated in Figure 2.

Figure 2.

Schematic diagram of constant current power supply circuit.

In the figure, R₁, R₂, R₃, and R₄ are four bridge arm resistors formed by the diffusion method, which are sensitive to pressure, and a change in pressure will cause a change in their resistance values.

At zero voltage, the output of the bridge is:

V_{0} = \frac{R_{1} R_{3} - R_{2} R_{4}}{R_{1} + R_{2} + R_{3} + R_{4}} • I_{0}

(1)

Where I₀ is the supply current; V₀ is the zero output voltage, also known as the zero misalignment voltage. From the above equation, in order to maintain the bridge zero output is zero, generally in the force-sensitive resistor design, should make R₁ = R₂ = R₃ = R₄ = R, to keep the bridge in the zero-voltage state is in equilibrium.

When there is a pressure difference between the two sides of the silicon diaphragm, the diaphragm undergoes deformation, causing the resistance values of the four bridge arms on the silicon diaphragm to change. The piezoresistive effect of semiconductors has an anisotropic characteristic, and through appropriate design, it makes R₁ and R₃ have positive increments and R₂ and R₄ have negative increments when the silicon diaphragm is subjected to pressure, that is, the:

\begin{matrix} R_{1} \to R_{1} + Δ R_{1}, R_{2} \to R_{2} - Δ R_{2}, \\ R_{3} \to R_{3} + Δ R_{3}, R_{4} \to R_{4} - Δ R_{4} \end{matrix}

The bridge is then unbalanced under pressure, producing a voltage output:

V_{P} = \frac{(R_{1} + Δ R_{1}) (R_{3} + Δ R_{3}) - (R_{2} - Δ R_{2}) (R_{4} - Δ R_{4})}{R_{1} + Δ R_{1} + R_{2} - Δ R_{2} + R_{3} + Δ R_{3} + R_{4} - Δ R_{4}} \cdot I_{0}

(2)

If it is guaranteed that R₁ = R₂ = R₃ = R₄ = R, then ΔR₁ = ΔR₂ = ΔR₃ = ΔR₄ = ΔR and equation (2) can be simplified to:

V_{P} = Δ R I_{0}

(3)

Equation (3) shows that the output voltage of the bridge is proportional to ΔR and the supply current I₀ when the silicon diaphragm is under pressure when supplied by the constant current source method. Since the bridge arm resistance R is temperature sensitive and increases with temperature, and the sensitivity decreases with temperature, the constant current source supply has a compensating effect on temperature drift.

Sensor design and realization

Overall sensor design

Figure 3 shows the internal structure diagram of the sensor. The sensor is paired with a signal conditioning circuit board, which is encapsulated in a housing along with its pressure-sensitive element to reduce electromagnetic interference entering through the cable. The functions of the signal conditioning circuit mainly include power supply, signal amplification, filtering, signal acquisition, and protection. It directly determines whether the overall performance of the sensor meets various specifications. When the sensitive element detects a signal, the signal is amplified by the amplification circuit and then processed by the filtering circuit. Subsequently, the signal is acquired and converted by a microcontroller, and finally, the corresponding standard signal is output.

Figure 3.

Schematic diagram of the internal structure of the sensor.

Figure 4 shows the exploded view of the internal components of the sensor. This design uses a constant current source to power the sensor probe; an operational amplifier is employed for differential amplification of the signal; the temperature is measured indirectly by measuring the bridge voltage of the sensor, and the temperature signal is acquired by the internal ADC of the microcontroller. The power supply circuit primarily provides power isolation and supplies power to all circuits within the sensor. The data acquisition circuit consists of four parts: analog signal conditioning and amplification, a microcontroller, A/D conversion, and CAN bus isolation and communication.

Figure 4.

Exploded view of the internal parts of the sensor.

Circuit design

The sensor utilizes a reference source and operational amplifiers to form a constant current source, which supplies power to the pressure-sensitive element. Subsequently, a differential amplification circuit composed of operational amplifiers converts the small electrical signals into standard output signals. The output from the temperature and pressure-sensitive devices, after conditioning, is directly acquired by the analog-to-digital converter (ADC) unit. The microcontroller unit (MCU) then processes and analyzes the acquired data, and the results are transmitted via the CAN bus.

AD sampling circuit design and calculation

This sensor is a digital sensor, and one of its core components is the analog-to-digital converter (ADC). The conversion accuracy of transforming analog signals (output signals from the pressure core) into digital signals (signals that can be processed by a computer) directly determines the performance metrics of the sensor.

Project requirements for the sensor output minimum 0–6.1 MPa, the output value of the minimum right bit for 1 hPa, so the sensor needs to quantify the output digital volume of 0–60,000, the project requires the sensor output resolution of 0.0001 MPa, that is, 1 hPa. that is, each numerical value of the output of the sensor need to represent the pressure value, that is, the minimum quantization capacity of the AD converter must be more than 60,000. Existing general-purpose AD converter conversion for the number of bits is generally divided into 8-, 10-, 12-, 16-, 24-bit, etc., corresponding to the data quantization capacity of 2⁸ = 256, 2¹⁰ = 1024, 2¹² = 4096, 2¹⁶ = 65,536, 2²⁴ = 16,777,216. From the above calculations, it can be seen that the theoretically required minimum AD sampling resolution for this project is 16 bits. However, in practical applications, the following factors will lead to a “reduction” in the effective AD resolution:

The input signal range cannot be completely overlapped with the voltage reference voltage; zero and full scale on the loss of a certain system resolution.

AD converter peripheral devices affect the sampling accuracy, and the design of the device temperature, time drift issues need to be considered.

Sixteen-bit resolution of the AD converter, according to different conditions of use, its effective resolution may be reduced to 15 bits or even lower.

Because of the above reasons the AD converter required for the design of this project was determined to be 24 bits.

After determining the resolution of AD conversion, the conversion speed of AD needs to be determined. This project requires every 5 ms to upload a valid data, digital filtering time shall not be longer than 20 ms, that is, the minimum sampling rate of the selected AD shall not be <1/5 ms = 200 Hz, and in order to ensure the effect of digital filtering, 20 ms digital filtering within the theory of the minimum number of samples should be >10 times, so it is necessary to sample a valid data every 2 ms, that is, the sampling rate of the AD converter shall not be <500 Hz. That is, the sampling rate of the AD converter should not be lower than 500 Hz.

Based on the above calculations, the 24-bit high-precision AD converter HWD7734 was selected for this project, which can accurately obtain 16-bit peak-to-peak resolution at a total conversion time of 500 µs (2 kHz channel switching), with a maximum data throughput up to 15.4 kHz, and operates from a single +5 V analog power supply, and withstands an analog range of inputs up to ±16.5 V over-voltage as shown in Figure 5.

Figure 5.

ADC schematic.

Analog conditioning circuit design and calculation

A constant current source is constructed using a reference source and an operational amplifier to provide a stable power input to the pressure-sensitive element. A differential amplification circuit is then formed using operational amplifiers. The SOI-type pressure sensor outputs a voltage difference in the form of a Wheatstone bridge, with a full-scale voltage of ∼90 mV. Given the relatively small magnitude of this potential difference, it is challenging for subsequent circuits to directly acquire the signal. Therefore, the output signal from the pressure sensor must be amplified using an operational amplifier circuit.

This project uses a stable CW580UT as the voltage reference source for the pressure core. The voltage reference source is 2.5 V, and it is more suitable for this project to amplify the signal from the pressure core to about 4.4 V. An amplification voltage too low would waste the resolution of the AD converter, and an amplification voltage too close to 4.5 V could result in the sensor’s full-scale signal not being accurately captured. Because the AD converter used in the project does not support two-way differential signal amplification, only a single-ended signal input to ground, in order to ensure that the core zero output can be accurately captured in the amplification, you need to pull up the zero level to about 200 mV so that the sensor’s internal amplification circuit full scale for 4.4 V–200 mV = 4.38 V.

The project utilizes an integrated quad operational amplifier, with one of its channels employed in conjunction with a voltage reference source to generate a 1 mA constant current supply, which serves as the excitation current for the sensor core. The remaining three channels are configured to form a two-stage amplification circuit, amplifying the 90 mV differential signal to 4.38 V. The overall amplification factor of the circuit can be calculated as 1800/90 mV = 20×. During production, each sensor may require a different amplification factor due to individual variations in the sensor core, power supply, and passive components such as resistors and capacitors. To address this, the second-stage amplification is fixed at 2×, while the first-stage amplification circuit is designed with additional resistor positions and test points. This design allows the gain of the first-stage amplification circuit to be flexibly adjusted without being constrained by the availability of specific resistor values in standard series. As a result, the sensor can be easily calibrated and optimized during both debugging and production processes, ensuring consistent performance across individual units.

The schematic diagram of the signal amplification circuit is shown in Figure 6, and the schematic diagram of the constant current source circuit is shown in Figure 7.

Figure 6.

Schematic diagram of sensor conditioning circuit.

Figure 7.

Constant current source power supply schematic.

Microcontroller selection

The other is a processor with an integrated CAN bus controller. The latter is used in this project for the following reasons:

As the two devices are integrated together, this can improve the chip integration per unit area, provide convenience in circuit layout and wiring, and can make the circuit board of the splitter smaller.

By integrating the processor and CAN bus control, there is no need to consider excessive timing and control logic in the design, so the processor does not require additional I₀ ports for operation, reducing system complexity and improving system reliability.

This project uses the LC8051F500 microcontroller. The LC8051F500 device is a fully integrated mixed-signal system-on-a-chip MCU. the LC8051F500-A device with on-chip voltage regulator, power-on reset, VDD monitor, watchdog timer, and clock oscillator is a true stand-alone system-on-a-chip.

The main reasons for using this microcontroller are as follows:

First, the product supports 5 V power supply, while other microcontrollers are mostly 3.3 V power supply, and 3.3 V power supply is difficult to achieve a large enough power supply current when powering the pressure core, which will seriously affect the output signal-to-noise ratio of the pressure core. If a 3.3 V-powered microcontroller (e.g. STM32F103C8) is used, more than 3.3 V must be supplied to the pressure core for proper operation. This will increase the complexity of the sensor’s power supply design, while the product structure is already very compact, and the replacement of the national production device volume is significantly larger than the original imported devices.

Second, the volume problem. Existing domestic controller products are generally divided into MCU, DSP, ARM, FPGA, POWERPC, and other categories, DSP and ARM, and other high-bit, high-performance products, although the computing power control capability is higher than the general MCU products, but its package can easily be more than 100 pins, and it is difficult to install the use of this product.

The microcontroller circuit schematic is shown in Figure 8.

Figure 8.

Microcontroller schematic.

Fully isolated power supply design

Sensor power supply is +28 ± 5 VDC. The user requires to achieve double isolation of the power supply and bus, so the project uses two independent switching power supply module to generate two isolated power supply, one of which is 12 V voltage, for the analog signal acquisition part of the power supply, and then in the use of linear power supply chip (non-isolated) output all the way to 5 V power supply for the use of the microcontroller; the other way for the CAN bus power supply. Thus, the power supply, acquisition circuit, and signal bus are all isolated.

In addition to implementing a fully isolated power supply design in the circuit scheme, this design increases the distance between all outer edges of the circuit board and the housing to more than 1 mm in the internal structural design of the sensor (detailed calculations are provided in the subsequent section on dimensional chain calibration).

The sensor employs two isolated switching power supplies operating in parallel. The conversion efficiency of each channel is no <70%, and the maximum no-load current of the power module is 30 mA. However, it should be noted that due to the use of switching power supplies and power conversion components, the inrush current of the sensor at power-on may be relatively high, estimated between 1 and 2 A, with a duration of <1 ms. Based on feedback from the performance of similar products, this transient high current is not expected to adversely affect the system. The schematic diagram of the sensor power supply design is shown in Figure 9.

Figure 9.

Power supply design schematic.

In-line calibration design

In the main program, the sensor cyclically performs AD acquisition, digital filtering, temperature acquisition, and pressure calculation. Through CAN reception interrupts, it receives commands from the main controller to enter the corresponding working modes. Figure 10 shows the sensor control flowchart. In the respective working modes, the corresponding time base interrupt is used to synchronously send data as directed by the main controller.

Figure 10.

Sensor control flowchart.

In the sensor pressure measurement mode, the data communication between the microprocessor LC8051F500 and the analog-to-digital converter chip HWD7734 is carried out through the SPI bus, and the digital signals of pressure and temperature are read at regular intervals, and the CAN bus digital communication is carried out after range division and temperature compensation.

In the sensor online calibration mode, the sensor and the host computer communicate via CAN bus, and upload, download, and store pressure data in response to different commands from the host computer.

In order to reduce the nonlinear error and zero position, sensitivity temperature drift, improve the accuracy of the sensor, use software compensation method is needed. This design adopts the method of segment fitting, the processor reads the pressure A/D value and the temperature A/D value, and uses the least squares curve to fit the pressure output curve under a specific temperature interval, and uses the temperature A/D value to obtain a specific temperature interval, so as to obtain the pressure output value after temperature compensation.

In this design, the “recursive average filtering method” is selected for software filtering, and this software filtering method is that the MCU will be collected by the ADC N data queue. The length of the queue is always N. Each time a new data is sampled, it will be placed in the end of the queue, and the data of the original head queue is thrown away (FIFO principle). The queue of N data in the arithmetic average operation can be obtained new filtering. N data in the queue is for the arithmetic average operation, a new filter can be obtained.

Experimental analysis

Experimental platform

Based on the previous design, the basic functionality of the sensor has been achieved. To achieve optimal software fitting and temperature compensation through online correction, it is first necessary to obtain accurate depth data at different temperature points. The output characteristics of the sensor are measured under standard temperature and pressure conditions for sensor calibration. Based on the experimental data from the calibration, data analysis is performed, and software algorithm compensation for the sensor is realized through algorithm simulation and experimental verification. The schematic diagram of the sensor calibration experiment is shown in Figure 11. The main equipment includes a computer, a CAN communication module, a high-precision pressure control instrument (accuracy 0.01%), a high-pressure gas cylinder, a low-ripple linear power supply, and a high-stability incubator. Figure 12 shows the physical setup of the sensor calibration platform. The sensor to be calibrated is placed inside a constant temperature chamber, with test cables and air guide tubes extending out from the chamber. The sensor is powered by an external DC power supply, and the sensor data is transmitted to a computer via a CAN communication module. Nitrogen is used as the gas source and is connected to a high-precision measurement and control instrument, providing the sensor with highly accurate and stable pressure input.

Figure 11.

Schematic diagram of the calibration test of the sensor.

Figure 12.

Physical diagram of the calibration of the sensor.

Temperature compensation design and analysis

A linear fit to the depth sensor is usually performed while taking temperature drift into account, using a temperature-composite pressure surface fit. The basic principle of surface fitting is as follows.

The output of the known depth transducer is a digital pressure value U with a certain zero and sensitivity temperature drift. If only one-dimensional pressure calibration experiments are performed and then the measured pressure value is solved from the input (P)–output (U) characteristic curve, large errors will occur due to temperature differences. This is due to the fact that the measured pressure P is not a unitary function of the output digital signal U. Surface fitting, on the other hand, introduces an output digital AD value $U_{t}$ that describes the temperature quantity to represent the sensor temperature, and the actual pressure input P can be represented as a binary function of the output digital pressure values U, that is:

P = f (U, U_{t})

(4)

By the same token, we can describe the digital pressure value U of a pressure signal as a binary function of the input pressure P and temperature information, that is:

U = g (P, U_{t})

(5)

The pressure determined by the coordinates can be expressed as a quadratic equation:

P = α_{0} + α_{1} U + α_{2} U_{t} + α_{3} U^{2} + α_{4} U U_{t} + α_{5} {U_{t}}^{2} + ε_{p}

(6)

Ditto:

U = α'_{0} + α'_{1} P + α'_{2} U_{t} + α'_{3} P^{2} + α'_{4} P U_{t} + α'_{5} {U_{t}}^{2} + ε'_{p}

(7)

Where: $α_{0} ~ α_{5}$ , $α_{0}^{'} ~ α_{5}^{'}$ —are constant coefficients;

$ε_{p}$ and $ε'_{p}$ —is an infinitesimal term of higher order.

By determining the polynomial coefficients of the above two equations, the surface fitting equations for detecting the binary input–output characteristics of the input pressure P and the output digital pressure value U can be determined. This allows the actual pressure output of the sensor to be derived based on the measured pressure output voltage and temperature output voltage signals. Additionally, a multi-point two-dimensional calibration test is required. Using the calibrated input and output values, the polynomial coefficients of the surface equation are determined based on the principle of least squares. This results in a surface-fitting correction polynomial equation that can be used for linear correction and temperature compensation of the sensor.

As can be seen from Figure 13, the linearity of temperature signal acquisition at various temperature and pressure points is excellent, especially at fixed pressure points, where the linearity remains consistent. However, across the entire pressure range, the cross-coupling of pressure signals introduces some influence on the accuracy of temperature signal measurement. Nevertheless, this coupling effect also exhibits linearity, as shown in Figure 14. In the figure, Series 1 to 9 represent the AD output value curves at temperature points ranging from −28 °C to 65 °C. It can be observed that, at the same temperature, the output value of the temperature signal increases with the increase in pressure, reaching its maximum and minimum at the upper and lower limits of the pressure calibration points, respectively. The maximum output error for temperature occurs between these two pressure points. In the measurements at each temperature point, the coupling error of temperature at the upper and lower pressure calibration points is ∼1 °C. This error can be mitigated through simple linear correction, thereby improving the accuracy of temperature signal acquisition.

Figure 13.

Output curve of temperature signal of each pressure point with temperature change.

Figure 14.

Output curve of temperature signal with pressure change at each temperature point.

Compared to the pressure signal acquisition, the temperature signal acquisition of the sensor does not require extremely high precision. Moreover, the coupling error of the temperature signal across the entire pressure range is relatively small. Through general linear correction, the coupling effect of the pressure signal on the temperature signal can be reduced to a minimal level, which essentially does not affect the temperature compensation of the pressure signal. The specific method to eliminate the cross-coupling error of the pressure signal in the temperature signal is as follows: First, acquire the temperature and pressure signals of the sensor. Input the pressure signal into the polynomial equation derived at room temperature to obtain the measured pressure value. The measurement error of this pressure value at the upper and lower temperature limits has a very small impact on the temperature, and thus can be practically ignored. Then, calculate the coupling error of the pressure on the temperature at this point using the obtained pressure value, and correct the acquired temperature signal accordingly. The corrected temperature signal is then used as the parameter for pressure temperature compensation.

The temperature characteristic curve of each pressure point is shown in Figure 15. Due to the temperature compensation in the hardware, the temperature characteristic surface of the experimentally acquired pressure data has been improved to some extent, but it can still be seen that the graph as a whole exhibits a poor nonlinearity of the response of the sensor pressure with respect to the change in temperature.

Figure 15.

Temperature characteristic curve of each pressure point.

The overall workflow of the temperature calibration of the sensor is shown in Figure 16. In the field working environment, using a certain accuracy of the standard equipment, the pressure sensor in accordance with the standard specification for online calibration, calibration of the “true value” of the input quantities given by the standard equipment. The sensor has a variety of calibration modes, the calibration method is to use a standard manometer, to the pressure sensor to apply a series of equal differences in the standard pressure, and at the same time, the use of dynamic acquisition instrumentation to collect the standard pressure value and the sensor’s output pressure value, and after the calculation, to assess the sensor’s error, linearity, and other basic parameters. The number of calibration repetitions should be not <3, and the calibration process should be a smooth pressure increase or decrease, to avoid overshooting or callback (Figure 17).

Figure 16.

Flow chart of online calibration.

Figure 17.

Schematic diagram of function selection for sensor in calibration mode.

When the sensor is powered up, it first detects the host computer signal to determine whether the operating mode is calibration mode or measurement mode. Measurement mode consists of the A/D chip collecting and inputting the core output signal into the microprocessor, combining with the temperature detection data, performing digital temperature compensation, and outputting the pressure value. Calibration mode, on the other hand, requires uploading the corresponding detection data according to the control signal from the host computer and accepting the calibration parameters input from the host computer.

As is shown in Figure 8, when working in the calibration mode, according to the input signal from the host computer, the sensor has a variety of calibration functions, which can communicate with the host computer for sending and receiving to complete different calibration tasks.

After completing the above work on the calibration function, the sensor will receive a reset signal from the host computer to reset the parameters of the compensated fit curve polynomial and complete the calibration work.

Analysis of test results

According to the application needs, the static test at room temperature as well as the high and low temperature environment working test were carried out, respectively. In order to make it easier to observe, the sensor was pressure-depth converted (10 kPa is 1 m), and the test results before and after compensation are shown in Tables 1 and 2.

Table 1.

Test results (before calibration).

Depths (m)	−28 °C	0 °C	25 °C	65 °C
0	0.00	0.00	0.00	0.00
20	19.13	19.23	19.24	19.64
60	58.89	59.16	59.14	59.56
100	98.82	99.04	99.11	99.46
200	198.35	198.52	198.85	199.04
300	298.05	298.25	298.45	298.81
400	397.12	397.84	398.14	398.61
500	497.21	497.76	498.06	498.24
610	607.09	607.39	607.99	608.13

Table 2.

Test results (after calibration).

Depths (m)	−28 °C	0 °C	25 °C	65 °C
0	0.02	0.01	0.01	0.01
20	20.00	20.00	20.00	19.98
60	60.03	60.01	60.01	59.99
100	100.05	100.05	100.03	100.01
200	199.89	199.89	199.88	199.83
300	299.92	299.91	299.93	299.81
400	399.91	399.92	399.94	399.89
500	499.81	499.81	499.82	499.81
610	609.85	609.88	609.94	609.91

The errors before and after calibration are compared in Table 3.

Table 3.

Comparison of errors before and after calibration.

Depths (m)	−40 °C		0 °C		25 °C		60 °C
	Before	After	Before	After	Before	After	Before	After
0	0	0.02	−0.77	0.01	−0.8	0.01	−0.36	0.01
20	−0.87	0	−0.84	0	−0.9	0	−0.44	−0.02
60	−1.11	0.03	−0.96	0.01	−0.9	0.01	−0.54	−0.01
100	−1.18	0.05	−1.48	0.05	−1.2	0.03	−0.96	0.01
200	−1.65	−0.11	−1.75	−0.11	−1.6	−0.1	−1.19	−0.17
300	−1.95	−0.08	−2.16	−0.09	−1.9	−0.1	−1.39	−0.19
400	−2.88	−0.09	−2.24	−0.08	−1.9	−0.1	−1.76	−0.11
500	−2.79	−0.19	−2.61	−0.19	−2	−0.2	−1.87	−0.19
610	−2.91	−0.15	−0.77	−0.12	−0.8	−0.1	−0.36	−0.09

A comparison of the error curves is shown in Figure 18.

Figure 18.

Error curve before and after pressure on-line calibration: (a) before calibration of pressure points and (b) after calibration of pressure points.

It can be observed from the above graphs that the accuracy of the sensor output is greatly improved after calibration, especially over the entire temperature range, and the improvement in performance before and after calibration is very significant. As can be seen in the graph, before calibration at −28 °C, the error in the sensor pressure output is significantly larger than at other temperature conditions. It is difficult to achieve full temperature accuracy compensation by means of hardware alone. At the same time, the error of the sensor pressure output increases with the increase of pressure, showing a certain regularity, which also provides a certain basis for the feasibility of software compensation. After the software algorithm compensation, the maximum error of the sensor output at each temperature and pressure point is 0.19 m, which is remarkable.

Conclusion

In this design, a series of experimental studies were carried out on the basis of completing the design and manufacture of the online calibrated CAN bus depth sensor, and the following conclusions were obtained:

The sensor delivers exceptional measurement accuracy with a maximum error of only 0.19 m, combined with outstanding long-term operational stability. Its robust design ensures consistent performance even under varying environmental conditions, making it ideal for applications requiring reliable and precise continuous monitoring.

By integrating real-time temperature compensation directly into its pressure output processing, the sensor achieves high precision, low temperature drift, and fully digitized signal conversion. Its built-in digital interface enables direct communication with host systems, eliminating the need for external signal conditioning and simplifying system integration.

A distinctive feature of this sensor is its in-situ calibration capability, which allows recalibration without disassembly or return to the factory. This innovation significantly enhances equipment supportability, reduces maintenance downtime, and ensures sustained accuracy and reliability over extended operational periods.

Together, these attributes highlight the sensor’s novel integration of high accuracy, intelligent compensation, and field-maintainable calibration in a compact and system-ready form, offering a compelling solution for modern precision measurement and control systems.

Footnotes

Handling Editor: Shaemili Pandian

ORCID iD

Xiaodong Wu

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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