An Improved sRGB Optical Algorithm Considering Thermal Effects and Adaptability for Low-Cost Automotive-Grade Dedicated LED Chips

Abstract

Achieving a stable color output across wide temperature ranges in automotive LED applications is challenging, especially when using cost-sensitive chips with limited computational resources. This study proposes an improved temperature model that integrates Fourier heat conduction and thermal resistance concepts to more accurately capture self-heating and power dissipation effects. To accommodate the constraints of low-cost automotive-grade microcontrollers (MCUs), the associated optical algorithm is converted from floating-point to a 16.16 fixed-point format, reducing both memory usage and computational overhead. Experimental results conducted from −40 °C to 120 °C show that the improved model predicts LED temperatures within 5 °C of measured values, reducing errors by up to 30% compared to conventional PN-junction-based methods. Furthermore, by comparing the chromaticity points generated under the new and traditional models—and implementing an additional three-duty-cycle offset at 1% brightness—the improved approach reduces chromaticity drift by approximately 0.0052 in the CIE 1931 xy color space. These findings confirm the superior stability and accuracy of the new model for both thermal management and chromaticity compensation, offering a cost-effective solution for automotive LED systems requiring precise color control under constrained MCU resources.

1. Introduction

With the widespread adoption of automotive-grade LED chips, low-cost chips have become the preferred choice due to their excellent cost-effectiveness and low power consumption. However, these systems are often constrained by limited processing power and hardware resources, which results in significant shortcomings in existing LED thermal compensation methods—primarily based on PN-junction thermal models—in handling self-heating effects and achieving real-time temperature control. Currently, traditional methods not only exhibit significant errors in temperature prediction accuracy but also perform poorly in computational efficiency and low-brightness chromaticity compensation, failing to meet the demands of practical automotive applications [1].

Temperature control is crucial in embedded systems since temperature fluctuations directly affect chip stability and overall performance. Traditional temperature modeling methods tend to be overly complex and computationally intensive, making them difficult to implement efficiently on low-cost microcontrollers [2]. Moreover, previous studies have not sufficiently revealed and addressed the trade-off between prediction accuracy and computational resources, nor have they proposed effective compensation measures for chromaticity drift under low-brightness conditions.

In response to these issues, this study proposes a novel temperature prediction (TP) model. Unlike existing methods, we have adopted a strategy of converting the optical algorithm from floating-point to 16.16 fixed-point arithmetic, which significantly reduces memory usage and computational load while improving prediction accuracy. The improved model consistently maintains LED temperature prediction errors within approximately 5 °C over the range from −40 °C to 120 °C, reducing errors by as much as 30% compared to conventional PN-junction models. Furthermore, by incorporating an additional three-duty-cycle PWM compensation strategy, the method significantly reduces chromaticity drift under low-brightness conditions, thereby enhancing overall LED performance [3].

To visually illustrate the key differences between traditional LED compensation methods and our proposed TP model in terms of performance parameters such as temperature prediction accuracy, computational efficiency, MCU hardware compatibility, chromaticity compensation, and cost-effectiveness, we have introduced

Table 1. Key parameter comparison: PN-Junction, RC, TP Models.

Parameter	Traditional PN-Junction Thermal Model	RC Thermal Model	Proposed TP Model
Temperature Prediction Accuracy	Errors up to 15 °C	Moderate accuracy, not specifically optimized for real-time performance	Error controlled within approximately 5 °C (improved by about 67%)
Computational Efficiency	Relies on floating-point arithmetic, high computational overhead	Complex parameter extraction, moderate computational load	Employs 16.16 fixed-point arithmetic, significantly reducing memory usage and computational burden
MCU Hardware Compatibility	Not suitable for resource-constrained low-cost MCUs	Limited by computational complexity, difficult to deploy	Optimized for low-cost automotive-grade MCUs (RAM < 3 KB, clock < 50 MHz)
Chromaticity Compensation	Lacks effective compensation measures; significant chromaticity drift under low brightness	Not optimized for chromaticity drift	Introduces PWM compensation strategy (compensating 3 duty cycle units), reducing chromaticity drift from approximately 0.025 to 0.006 under low brightness conditions
Cost-Effectiveness	Low hardware cost but poor performance	Moderate cost with significant application limitations	Achieves a good balance between performance and resource consumption, offering high cost-effectiveness

for a detailed comparison [4].

In summary, the main contributions of this study are as follows:

• Developed a novel temperature prediction model that combines physical modeling with 16.16 fixed-point arithmetic to effectively address LED self-heating and power dissipation issues;
• Through experimental validation, demonstrated that the model can maintain a prediction error within approximately 5 °C in the range of −40 °C to 120 °C, significantly enhancing real-time performance and the adaptability of low-cost MCUs;
• Introduced a PWM compensation strategy that effectively mitigates chromaticity drift under low-brightness conditions, thereby providing a robust and cost-effective solution for automotive LED systems.

By addressing the limitations of previous research in prediction accuracy, computational efficiency, and low-brightness compensation, this study not only provides a new technical approach for automotive LED thermal management and chromaticity stabilization but also points the way for future developments in related technologies.

2. Temperature Prediction Considering Thermal Effects

2.1. PN Method

The PN junction (P-type and N-type semiconductor junction) forward voltage method is currently the mainstream approach for measuring LED junction temperature due to its simplicity, low cost, and direct correlation with semiconductor temperature characteristics. This method utilizes the approximately linear relationship between the PN junction forward voltage drop and the junction temperature, making it an effective technique for real-time LED temperature monitoring [5]. The relationship between the PN junction forward voltage V and temperature T can be expressed as [6]:

$$V_f=V_{g_0}-{\displaystyle \frac{kT}{q}}\ln \left({\displaystyle \frac{I}{I_S}}\right)$$

(1)

where $V_{g_0}$ represents the bandgap voltage of the semiconductor material (for silicon at 0 K, $V_{g_0}$ ≈ 1.17 V), k = 1.38 × 10⁻²³ J/K is the Boltzmann constant, q = 1.6 × 10⁻¹⁹ C denotes the elementary charge, T is the absolute temperature of the PN junction (in Kelvin), I is the measured current flowing through the junction (typically ranging from 10 μA to 10 mA), and I_s is the reverse saturation current, which is determined by the doping concentration, junction area, and temperature (for silicon devices at 300 K, Is ≈ 10⁻¹⁴ A).

This formula indicates that V_f decreases approximately linearly with increasing T, with a theoretical temperature coefficient of about −2 mV/°C. However, in practical measurements, the junction temperature shift $\Delta T_{self-heating}$ induced by Joule heating must be considered, which is primarily governed by I²Rs (where Rs is the series resistance). Additionally, a key challenge of the PN junction forward voltage temperature measurement method is that it requires measurement at low currents. When an LED operates at a constant power output for brightness control, an intermittent low-current measurement must be inserted to determine the temperature, which consequently reduces the overall brightness of the LED.

2.2. Model Development

To improve the accuracy of temperature prediction, this study proposes a novel temperature prediction model, the Temperature-Power Prediction Model (TP Model), for quantitatively analyzing the relationship between heat generation and power consumption in electronic components. For most electronic components, heat generation typically increases linearly with current and voltage, indicating a positive correlation with power. By evaluating the effect of power—calculated through ADC (Analog-to-digital converter) and PWM (Pulse Width Modulation)—on heat generation, this study investigates the influence of power on LED temperature and further explores its role in driving LED temperature variations.

A separated thermal model is developed to analyze the impact of self-heating on temperature in electronic components while independently assessing the thermal contribution of PCB (Printed Circuit Board) heat dissipation. The relationship between self-heating power, input power, and output power of electronic components can be accurately described by the following mathematical expression [7]:

$$P_{origin\_t}=P_{origin\_in}-P_{origin\_out}$$

(2)

where $P_{origin\_t}$ represents the self-heating power, $P_{origin\_in}$ is the input power of the heat source, and $P_{origin\_out}$ is the output power. The expression for $P_{origin\_out}$ is given by [8]:

$$P_{origin\_out}=\eta P_{origin\_in}$$

(3)

where $\eta$ represents the mechanical efficiency. Thus, the self-heating power $P_{origin\_t}$ of the electronic component can be rewritten as:

$$P_{origin\_t}=\left(1-\eta \right)P_{origin\_in}$$

(4)

According to Fourier’s law of heat conduction:

$$Q_{cond}={\displaystyle \frac{kA\Delta T_{cond}}{d}}$$

(5)

where $k$ is the thermal conductivity, which is material-dependent and obtained experimentally, $A$ is the cross-sectional area of heat conduction, and $d$ is the length or thickness of the thermal conduction path. $\Delta T_{cond}$ represents the temperature difference caused by heat conduction between all electronic components on the PCB and the target electronic component. The expression is given by [8]:

$$\Delta T_{cond}=\left(T_h-T_l\right)$$

(6)

where $T_h$ is the PCB temperature and $T_l$ is the electronic component temperature.

According to the second law of thermodynamics, heat always transfers from the higher-temperature region to the lower-temperature region. A constant current source generates power dissipation while supplying a stable current, with the resulting heat concentrated inside the chip, making it the primary heat source. However, the self-heating effect may interfere with the accurate measurement of thermal conduction parameters. Therefore, this study proposes an improved method that isolates the electronic component from the PCB, connecting them via conducting wires and measuring the solder pad temperature. This effectively separates the self-heating effect. Based on this method, the corrected expression for the thermal conduction temperature difference is given by:

$$\Delta {T^{\prime }}_{cond}=\left(T_J-T_P\right)$$

(7)

where $\Delta {T^{\prime }}_{cond}$ represents the temperature difference between the built-in constant current source chip and the electronic component, $T_J$ is the chip junction temperature, and $T_P$ is the solder pad temperature of the electronic component.

Under steady-state conditions, the system follows the principle of energy conservation. For a heat-generating source, the total generated thermal power $P_t$ must equal the total dissipated thermal power. In an ideal scenario where no other heat dissipation paths exist, all heat is dissipated through thermal conduction. Therefore, the self-heating power of the PCB is equivalent to the heat power lost through thermal conduction, given by [9]:

$$P_{origin\_t}=Q_{cond}$$

(8)

From Equations (4)–(6), it follows that [9]:

$$\Delta {T^{\prime }}_{cond}={\displaystyle \frac{\left(1-\eta \right)d}{kA}}{P}_{origin\_in}$$

(9)

Since $\eta$, $d$, $k$, and $A$ are constants, let the self-heating proportional coefficient be defined as $\alpha ={\displaystyle \frac{\left(1-\eta \right)d}{kA}}$, then:

$$\Delta {T^{\prime }}_{cond}=\alpha P_{origin\_in}$$

(10)

The thermal resistance formula is an essential theoretical tool in electronic engineering and thermal management. It is widely used to analyze and predict temperature variations in electronic devices, chips, and systems caused by power dissipation during operation. It provides a critical quantitative basis for studying heat transfer paths and optimizing thermal design [9].

$$\Delta T_{self}=R_{\theta }{P}_{self\_t}$$

(11)

where $\Delta T_{self}$ represents the self-heating temperature difference, $R_{\theta }$ is the thermal resistance, and $P_{self\_t}$ is the self-power dissipation of the electronic component. Based on Equation (17), it can be rewritten as:

$$\Delta T_{self}=R_{\theta }\left(1-\eta \right)P_{self\_in}$$

(12)

where $\eta$ represents the mechanical efficiency of the electronic component. Since $R_{\theta }$ and $\eta$ are constants, let the thermal conduction coefficient be defined as $\beta =R_{\theta }\left(1-\eta \right)$, then:

$$\Delta T_{self}=\beta P_{self\_in}$$

(13)

Based on Equations (10) and (13), the relationship between the corrected heat generation $Q$ and power $P$ can be expressed as:

$$T=T_J+\beta P_{self\_in}-\alpha P_{origin\_in}$$

(14)

Since mixed-light LEDs require switching between different colors and brightness levels, their temperature is affected by power variations, leading to changes in self-heating power. The relationship between the self-heating temperature rise of the LED and the input power can be expressed as:

$$\Delta T_{Diode}={\beta }_{Diode}{P}_{Diode\_in}$$

(15)

where $\Delta T_{Diode}$ represents the self-heating temperature rise, ${\beta }_{Diode}$ is the self-heating coefficient of the LED, and $P_{Diode\_in}$ is the input power of the LED. The relationship can be expressed as:

$$P_{Diode\_in}=V_{Diode}{I}_{Diode}$$

(16)

where $V_{Diode}$ represents the LED voltage, which can be obtained through ADC, and $I_{Diode}$ is the current. Since mixed-light LEDs typically consist of three RGB LEDs, the expression can be written as:

$$I_{Diode}=I_r+I_g+I_b$$

(17)

where $I_r$, $I_g$, and $I_b$ represent the currents of the red, green, and blue LEDs, respectively. Their corresponding calculation formulas are as follows [10]:

$$I_i={\displaystyle \frac{PW{M}_i}{PW{M}_{\max }}}{I}_{\max }$$

(18)

where the value of $i$ is r, g, or b, $I_{\max }$ is the peak current of the built-in constant current source of the chip.

Since mixed-light LEDs are relatively low-cost, the chip typically contains a built-in constant current source. During the process of supplying a stable current, power dissipation occurs, primarily in the form of heat generated inside the chip. As a result, the heat source is concentrated within the chip itself. To eliminate the impact of self-heating on the measurement of thermal conduction parameters, a new measurement method is proposed, where the electronic component is isolated from the PCB and connected via conductive wires, allowing the solder pad temperature to be measured.

$$\Delta T_{MCU}={\alpha }_{MCU}{P}_{MCU\_in}$$

(19)

where $\Delta T_{MCU}$ represents the temperature difference between the chip junction and the LED solder pad, ${\alpha }_{MCU}$ is the thermal conduction coefficient of the chip, and $P_{MCU\_in}$ is the input power of the MCU (Microcontroller Unit). The expression can be written as:

$$P_{MCU\_in}=V_{MCU}{I}_{MCU}$$

(20)

where $V_{MCU}$ represents the input voltage of the MCU, and $I_{MCU}$ is the input current of the chip. Since they are connected in series, it follows that $I_{MCU}=I_{Diode}$. The expression for $V_{MCU}$ can be written as:

$$V_{MCU}=V_{BAT}-V_{Diode}$$

(21)

where $V_{BAT}$ represents the power supply voltage.

Thus, the temperature of the LED is given by:

$$T=T_J+\left(\beta V_{Diode}-\alpha \left(V_{BAT}-V_{Diode}\right)\right)I_{\max }{\displaystyle \frac{PW{M}_r+PW{M}_g+PW{M}_b}{PW{M}_{\max }}}$$

(22)

2.3. Model Validation

2.3.1. Spot Temperature Parameter Measurement

To eliminate the interference of the self-heating effect on the thermal conductivity measurement experiments of electronic components, an improved measurement method is proposed. This method isolates the LED from the PCB and connects it via wires to another PCB, with a thermocouple fixed to the LED solder pad for temperature measurement. Since the LED solder pad is thermally isolated from other components on the PCB, the thermocouple can accurately capture the self-heating characteristics of the LED, avoiding measurement deviations caused by PCB heat conduction.

The spot temperature box, temperature chamber, and PCB wiring are shown in Figure 1. During the experiment, a spot temperature probe (point temperature line) was connected to the LED solder pad and interfaced with the Spot Temperature Box to accurately read the real-time junction temperature of the LED. Meanwhile, the temperature chamber was used to precisely regulate the ambient temperature from −40 °C to 120 °C. This setup enabled a reliable comparison between the temperature model predicted by the software and the actual temperature measured via the point temperature line. The parameter measurement results at 25 °C are presented in

Table 2. PCB experimental data and measured temperature data of 25 °C.

	LED Solder Pad Temperature (°C)	LED Temperature (°C)	Voltage (V)	$\mathit{P}\mathit{W}\mathit{M}$	${\mathit{T}}_{\mathit{m}\mathit{c}\mathit{u}}$ (°C)	$\mathit{P}\mathit{W}{\mathit{M}}_{\mathbf{max}}$	${\mathit{I}}_{\mathbf{max}}$ (mA)	${\mathit{V}}_{\mathit{B}\mathit{A}\mathit{T}}$ (V)
R	34.1	27.1	1.951 V	12,800	35.4	32,000	36.5	12.13
G	33.5	26.94	2.639 V	12,800	35.8	32,000	36.5
B	33.2	26.7	2.875 V	12,800	35.6	32,000	36.5
LED Off	28.7	25.1	/	0	27.1	32,000	/

. Based on Equations (10) and (13), $\alpha =17.58458615$, ${\beta }_r=92.245813$, ${\beta }_g=50.6826145$, and ${\beta }_b=42.538945$.

2.3.2. Experimental Results Analysis

Based on the value of $\alpha$, ${\beta }_r$, ${\beta }_g$, and ${\beta }_b$, the software is first compiled to generate the corresponding HEX (Hexadecimal Number System) file, which is then programmed into the chip. Based on the above research, we conducted a temperature measurement experiment on a printed circuit board and employed both the TP model and the PN model to predict the light-emitting diode’s (LED) temperature. The LED’s actual temperature was measured using the spot temperature box(Purchased from Duohe Test Equipment (Shanghai) Co., Ltd., Shanghai, China), and the experimental results are presented in Figure 2.

Compared to the PN method, the proposed improved temperature model demonstrates higher accuracy in predicting temperature variations. The error between the TP model prediction and the measured values is within 5 °C, fully validating the effectiveness of the improved model in enhancing prediction accuracy. This result indicates its broad applicability and potential value in complex system temperature prediction. By comparing the experimental data with the predicted results, the theoretical validity and engineering feasibility of the model are further supported.

3. Incompatibility Between Optical Algorithms and Low-Cost Chips

In automotive electronics, LED-equipped chips generally utilize LIN communication, feature built-in constant current sources, operate at relatively low clock frequencies (typically below 50 MHz), have limited computational speed, and do not support floating-point arithmetic. Additionally, these low-cost chips often have constrained RAM (Random Access Memory) that is typically less than 3 KB, leading to tight stack space and Flash memory sizes generally below 32 KB. Examples of such cost-effective automotive-grade chips include Infineon’s newly released TLD4020, Elmos 31/36/39 series, and Melexis 81108/81113.

However, optical algorithms involve extensive floating-point calculations, including chromaticity coordinate computations and equation solving, which are not supported by these low-cost chips. To adapt to the computational constraints of these chips, improve processing speed, and optimize memory usage, this section first introduces a floating-point to fixed-point conversion algorithm. Subsequently, optimizations are applied to each step of the sRGB (standard Red Green Blue) algorithm to enhance efficiency.

3.1. Floating-Point to Fixed-Point Conversion

In automotive electronics, LED driver chips are low-cost components with limited performance, often lacking support for floating-point operations. Directly applying floating-point optical algorithms significantly increases RAM and ROM (Read-Only Memory) usage, which is detrimental to system optimization. This study employs a floating-point to fixed-point conversion approach to optimize the computational process to address the limitation of low-cost LED driver chips that do not support floating-point operations. Adjusting scaling factors and managing precision in key computational steps significantly improves computational efficiency, reduces power consumption and resource usage, and achieves high-precision calculations in LED color adjustment and temperature compensation within embedded systems. It provides essential support for the stability and performance optimization of optical systems.

The 16.16 fixed-point arithmetic method is used, where 32-bit integers represent values, as illustrated in Figure 3. The upper 16 bits store the integer part, while the lower 16 bits store the fractional part, achieving an approximation of floating-point numbers through a fixed decimal point position. This method balances computational accuracy in embedded systems while simplifying hardware implementation, making it an essential tool for efficient algorithm design in resource-constrained environments.

This study provides a detailed description of how multiplication and division are implemented to achieve efficient 16.16 fixed-point arithmetic. The fixed-point number is divided into its upper 16 bits and lower 16 bits for multiplication. The partial products are computed separately and then combined through bit-shifting and addition. Finally, carry propagation and rounding are applied to maintain the 16.16 format, as illustrated in Figure 4a.

For division, after initializing the dividend and divisor, the function returns the minimum possible value if the divisor is zero. If the divisor is a power of two, the computation is simplified using bit shifts. Otherwise, long division is performed iteratively, calculating the quotient bit by bit, followed by rounding and sign processing, as shown in Figure 4b. This implementation ensures both efficiency and accuracy of fixed-point arithmetic in embedded systems.

3.2. sRGB to xyY: Target Color Determination

sRGB is a standard RGB color space commonly used to represent color information in display devices. The xyY color space is derived from the CIE 1931 XYZ model and is frequently used in chromaticity diagrams to describe color hue (x, y) and luminance (Y). Converting sRGB to xyY involves the following steps: gamma decoding, color space transformation, and normalization [11].

sRGB input is typically represented as an eight-bit integer, with each channel ranging from 0 to 255. As shown in Figure 5, consider the color gamut of a certain LED (note that each LED has different luminous efficacy, so the gamut triangle varies accordingly). The coordinates of the red, green, and blue vertices in the CIE xy chromaticity space are R (0.55, 0.35), G (0.2, 0.65), and B (0.15, 0.16), respectively. At the same time, these vertices correspond to the following RGB representations on the LED device: R (255, 0, 0), G (0, 255, 0), and B (0, 0, 255). Let a, b, and c be non-negative decimals satisfying a + b + c = 1; then, any point within the gamut can be expressed as a combination: P = a × R + b × G + c × B.

For example, when a = 0.2, b = 0.4, and c = 0.4, the point P in the xy chromaticity space can be written as P = 0.2 × (0.55, 0.35) + 0.4 × (0.2, 0.65) + 0.4 × (0.15, 0.16) = (0.25, 0.394). Meanwhile, its value in the device’s RGB representation is P = 0.2 × (255, 0, 0) + 0.4 × (0, 255, 0) + 0.4 × (0, 0, 255) = (51, 102, 102).

Therefore, the color located at the gamut coordinates (0.25, 0.394) can be represented in the LED’s RGB space as (51, 102, 102).

For computational convenience, normalization is required, which is expressed by the following formula [12]:

$$R^{\prime }={\displaystyle \frac{R}{255}},G^{\prime }={\displaystyle \frac{G}{255}},B^{\prime }={\displaystyle \frac{B}{255}}$$

(23)

where $R$, $G$ and $B$ are the original sRGB input values, ranging from [0, 255], $R^{\prime }$, $G^{\prime }$ and $B^{\prime }$ are the normalized sRGB values, ranging from [0, 1].

sRGB is designed based on the human eye’s nonlinear perception of light. Specifically, sRGB applies a gamma correction algorithm to encode linear RGB values into nonlinear values, enhancing detail representation in darker regions. However, for accurate color conversion, the nonlinear sRGB values must be restored to linear RGB values. This step is achieved using the following piecewise function [13]:

$$C_{\mathrm{linear}}=\left\{\begin{array}{ll}{\displaystyle \frac{C}{12.92}},\hfill & C\le 0.04045\hfill \\ {\left({\displaystyle \frac{C+0.055}{1.055}}\right)}^{2.4},\hfill & C>0.04045\hfill \end{array}\right.$$

(24)

where $C$ represents the normalized sRGB value ($R^{\prime }$, $G^{\prime }$ and $B^{\prime }$), and $C_{\mathrm{linear}}$ represents the linear RGB value. This piecewise function is used to accurately model the human eye’s nonlinear response to light.

Since low-cost chips do not support power function operations with non-integer exponents, this study proposes an optimized interpolation point selection and training method for high-precision sRGB to CIE 1931 xyY color space conversion, enabling more accurate curve fitting. This method generates random interpolation points and constructs corresponding cubic spline curves, systematically evaluating the maximum absolute error between each spline and the target function. The optimal spline model is then selected based on the minimum error. The entire training process is illustrated in Figure 6.

Through optimized interpolation point training, the results are as follows:

$$C_{\mathrm{linear}}=\left\{\begin{array}{ll}{\displaystyle \frac{C}{12.92}},\hfill & C\le 0.04045\hfill \\ 0.2919C^3+0.7106C^2-0.0046C+0.0027,\hfill & C>0.04045\hfill \end{array}\right.$$

(25)

Figure 7a shows the absolute error distribution after 1,000,000 training iterations using the cubic spline interpolation method, with a maximum error of 0.000698 and an average error of 0.000428. In contrast, Figure 7b illustrates the absolute error distribution for the least squares method under the same training iterations, where the maximum error is 0.001217, and the average error is 0.000560. The results demonstrate that the proposed cubic spline interpolation method significantly outperforms the traditional least squares method in error control, validating its effectiveness in improving accuracy and robustness.

The CIE XYZ color space was defined by the International Commission on Illumination (CIE) in 1931 based on the perceptual characteristics of the human visual system. It aims to provide a device-independent color representation. The linearized sRGB values can be converted into the XYZ color space using a 3 × 3 matrix transformation. This matrix is defined by the tristimulus values of the sRGB primary colors in the CIE 1931 standard observer model. The conversion formula is as follows [14]:

$$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{ccc}0.4124564& 0.3575761& 0.1804375\\ 0.2126729& 0.7151522& 0.0721750\\ 0.0193339& 0.1191920& 0.9503041\end{array}\right]\left[\begin{array}{c}{R}_{\mathrm{linear}}\\ G_{\mathrm{linear}}\\ B_{\mathrm{linear}}\end{array}\right]$$

(26)

where $R_{\mathrm{linear}}$, $G_{\mathrm{linear}}$, and $B_{\mathrm{linear}}$ are the linearized RGB values, and $X$, $Y$, and $Z$ are the tristimulus values in the CIE XYZ color space, representing overall luminance and the components in the red, green, and blue perception channels. The coefficients in the transformation matrix are defined based on measurements under the D65 standard illuminant, ensuring physical consistency in the conversion.

The CIE xyY color space is a derivative of XYZ, where $x$ and $y$ describe the chromaticity of the color, while $Y$ etains the luminance information. Through a normalization process, $xyY$ values can be computed from $XYZ$ using the following equations [15]:

$$x={\displaystyle \frac{X}{X+Y+Z}}$$

(27)

$$y={\displaystyle \frac{Y}{X+Y+Z}}$$

(28)

$$Y=Y$$

(29)

where $x$ and $y$ are the chromaticity values, representing the hue and saturation of the color, independent of luminance. $Y$ is the luminance component, directly inherited from the $Y$ value in the $XYZ$ space. In the special case where $X+Y+Z=0$, $x=0,y=0$, [16].

3.3. Chromaticity Coordinate Temperature Compensation

To visually demonstrate the variation in light intensity of multi-wavelength LEDs at different junction temperatures, this section first presents the normalized light intensity measurements over the temperature range of −40 °C to 120 °C.

Multi-wavelength LEDs are composed of red, green, and blue chips, each emitting at different wavelengths. Due to differences in their material bandgap structures and internal quantum efficiencies, these chips exhibit varying degrees of light intensity attenuation and chromaticity shift under the same junction temperature. Generally, red light (around 620 nm) is the most sensitive to temperature changes, with significant brightness degradation at high temperatures and a potential redshift in wavelength. Green light (around 525 nm) experiences a moderate decrease in intensity as temperature rises, while blue light (around 450 nm) typically falls between the two in terms of thermal sensitivity.

To quantitatively study this phenomenon, we measured the light intensity of the red, green, and blue channels across a temperature range of −40 °C to 120 °C. The LED module was placed in a programmable temperature chamber, and a thermocouple was attached to the solder pad to monitor real-time junction temperature. After the LED stabilized at each target temperature, an integrating sphere was used to measure the luminous output of each color channel. The recorded intensities were then compared with their baseline values at 25 °C and normalized to facilitate the observation and quantification of temperature-induced changes in optical output.

Based on these measurements, Figure 8 plots the normalized light intensity curves of the three channels over the −40 °C to 120 °C range. It is evident that the red channel undergoes the most pronounced attenuation as temperature increases, while the green and blue channels also show noticeable decreases at higher temperatures. Given that automotive LEDs often operate under wide temperature fluctuations, these thermal characteristics impose higher demands on subsequent temperature modeling and optical compensation strategies. The following subsection further explores how chromaticity coordinate and luminance compensation formulas can be used to achieve more stable LED color output under varying thermal conditions.

As shown in Figure 8, the red LED exhibits significant attenuation with increasing temperature, while noticeable gain occurs in the low-temperature range [17]. This highlights the critical importance of accurate junction temperature monitoring and prediction in maintaining LED light output and reliability. The optical intensity of multi-wavelength LEDs varies significantly with junction temperature from −40 °C to 120 °C. This effect is particularly pronounced in red LEDs, where the optical intensity at 120 °C drops to only 30% of its value at room temperature, while at −40 °C, it increases to 140%. This phenomenon highlights the importance of accurate junction temperature assessment. However, embedding temperature sensors directly into LEDs would increase costs and affect performance, necessitating the development of a high-precision temperature prediction model.

The color and luminance of red LEDs exhibit drift at different temperatures, primarily reflected in the changes of chromaticity coordinates (x, y) and luminance Y. Figure 9 illustrates the LED gamut shift in the CIE 1931 chromaticity diagram, where the solid line represents the state at 25 °C, and the dashed line indicates the shift at elevated temperatures. Noticeable changes occur in the chromaticity coordinates of red, green, and blue light. To ensure that the target chromaticity and luminance of LEDs remain stable across different temperatures, temperature compensation is required. The compensation formula calculates the actual chromaticity coordinates and luminance at a given temperature by adding a temperature offset to the reference values [18].

The color and brightness compensation formulas for the red, green and blue LEDs at the current temperature are as follows [18]:

$$x_r=x_{r0}+\Delta x_r,x_g=x_{g0}+\Delta x_g,x_b=x_{b0}+\Delta x_b$$

(30)

$$y_r=y_{r0}+\Delta y_r,y_g=y_{g0}+\Delta y_g,y_b=y_{b0}+\Delta y_b$$

(31)

$$Y_r=Y_{r0}+\Delta Y_r,Y_g=Y_{g0}+\Delta Y_g,Y_b=Y_{b0}+\Delta Y_b$$

(32)

where $x_r,x_g,x_b$ are the x chromaticity coordinates of red, green, and blue LEDs after temperature-induced shift at the LED temperature of the current temperature $T$, and $x_{r0},x_{g0},x_{b0}$ represents their x chromaticity coordinate at the LED temperature of 25 °C. $\Delta x_r,\Delta x_g,\Delta x_b$ represent the shifts in the x chromaticity coordinates at the LED temperature of the current temperature $T$. $y_r,y_g,y_b$ are the y chromaticity coordinates of red, green, and blue LEDs after temperature-induced shift at the LED temperature of the current temperature $T$, $y_{r0},y_{g0},y_{b0}$ represent their y chromaticity coordinates at the LED temperature of 25 °C, $\Delta y_r,\Delta y_g,\Delta y_b$ represent the shifts in the y chromaticity coordinates at the LED temperature of the current temperature $T$. $Y_r,Y_g,Y_b$ are the luminance values of red, green, and blue LEDs after temperature-induced shift at the current temperature $T$, and $Y_{r0},Y_{g0},Y_{b0}$ are their luminance values at the LED temperature of 25 °C. The luminance shifts at an LED temperature of the current temperature $T$ are represented by $\Delta Y_r,\Delta Y_g,\Delta Y_b$.

3.4. PWM Calculation

Following the compensation of chromaticity coordinates and luminance in Section 3.3, the corrected values represent the LED’s chromaticity coordinates at the current temperature. To convert these compensated chromaticity coordinates into actual light output, the target color must be mapped to the RGB space of the new color gamut, and the duty cycle for each RGB channel must be calculated. By determining the proportion of each RGB channel, the corresponding PWM values are obtained to control the luminance output of each LED. Finally, the PWM signals adjust the operation of the three RGB LEDs, achieving the mixing and output of the target color [18].

At the current temperature, the standard chromaticity coordinates of the red, green, and blue LED channels are denoted as $(x_r,y_r)$, $(x_g,y_g)$, and $(x_b,y_b)$, with luminance values $Y_r,Y_g,Y_b$, respectively. In the CIE color representation, a three-dimensional coordinate system $\left(x,y,z\right)$ is commonly used [18], where:

$$z=1-x-y$$

(33)

Therefore, the z-coordinate of the three primary colors can be expressed as:

$$z_r=1-x_r-y_r z_g=1-x_g-y_g z_b=1-x_b-y_b$$

(34)

If a target chromaticity coordinate $(x_t,y_t)$ and target luminance $Y_t$ need to be achieved, they can be similarly expressed as:

$$z_t=1-x_t-y_t$$

(35)

Assuming the relative weights of the three channels are $D_{red}$, $D_{green}$ and $D_{blue}$, in order to match the mixed light coordinates with $(x_t,y_t,z_t)$, the following matrix equation can be used to solve for the weights [18]:

$$\left[\begin{array}{c}{D}_{\mathrm{red}}\\ D_{\mathrm{green}}\\ D_{\mathrm{blue}}\end{array}\right]={\left[\begin{array}{ccc}{\displaystyle \frac{Y_r}{y_r}}{x}_r& {\displaystyle \frac{Y_g}{y_g}}{x}_g& {\displaystyle \frac{Y_b}{y_b}}{x}_b\\ {\displaystyle \frac{Y_r}{y_r}}{y}_r& {\displaystyle \frac{Y_g}{y_g}}{y}_g& {\displaystyle \frac{Y_b}{y_b}}{y}_b\\ {\displaystyle \frac{Y_r}{y_r}}{z}_r& {\displaystyle \frac{Y_g}{y_g}}{z}_g& {\displaystyle \frac{Y_b}{y_b}}{z}_b\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_{\mathrm{t}}\\ y_{\mathrm{t}}\\ z_{\mathrm{t}}\end{array}\right]$$

(36)

Since the matrix of this equation system cannot be solved using mathematical libraries on low-cost chips, it is necessary to derive the solution in advance and embed it into the algorithm. Let the abstract form of the equation system be:

$$x=A^{-1}b$$

(37)

Since the matrix A is invertible, it follows that:

$$Ax=b$$

(38)

By Cramer’s rule, it follows that:

$$D_{red}={\displaystyle \frac{\left|A_1\right|}{\left|A\right|}}, D_{green}={\displaystyle \frac{\left|A_2\right|}{\left|A\right|}}, D_{blue}={\displaystyle \frac{\left|A_3\right|}{\left|A\right|}}$$

(39)

Performing elementary transformations on the determinant and expanding it, we obtain:

$$D_{red}={\displaystyle \frac{\left(x_t-x_b\right)\left(y_g-y_b\right)-\left(x_g-x_b\right)\left(y_t-y_b\right)}{\left(X_r+Y_r+Z_r\right)\left[\left(x_r-x_b\right)\left(y_g-y_b\right)-\left(x_g-x_b\right)\left(y_r-y_b\right)\right]}}$$

(40)

$$D_{green}={\displaystyle \frac{\left(x_r-x_b\right)\left(y_t-y_b\right)-\left(x_t-x_b\right)\left(y_r-y_b\right)}{\left(X_g+Y_g+Z_g\right)\left[\left(x_r-x_b\right)\left(y_g-y_b\right)-\left(x_g-x_b\right)\left(y_r-y_b\right)\right]}}$$

(41)

$$D_{blue}={\displaystyle \frac{\left(x_r-x_t\right)\left(y_g-y_t\right)-\left(x_g-x_t\right)\left(y_r-y_t\right)}{\left(X_b+Y_b+Z_b\right)\left[\left(x_r-x_b\right)\left(y_g-y_b\right)-\left(x_g-x_b\right)\left(y_r-y_b\right)\right]}}$$

(42)

After the above calculations, the computed PWM color ratios have been transformed into an explicit function form, requiring only one division operation, thereby significantly reducing computation time. This is because the CPU execution time for division operations is at least 10 times that of addition, subtraction, and multiplication operations [19]. After obtaining the duty cycle weights $D_{red}$, $D_{green}$, and $D_{blue}$, if the system must also meet the target luminance $Y_{target}$, considering the brightness percentage $i$ and PWM period $PW{M}_{\max }$, the final duty cycle for each channel $\left(PW{M}_r, PW{M}_g, PW{M}_b\right)$ can be expressed as [19]:

$$PW{M}_i={\displaystyle \frac{Y_{\mathrm{target}}}{Y_r{D}_{\mathrm{red}}+Y_g{D}_{\mathrm{green}}+Y_b{D}_{\mathrm{blue}}}}\times i\times PW{M}_{\max }\times D$$

(43)

where the value of $i$ is the brightness percentage, which is derived from the LIN bus signal. $D$ represents the duty cycle weight $D_{red}$, $D_{green}$, and $D_{blue}$.

4. Model Validation and Discussion

As shown in Figure 10, the experiment utilizes an LED automatic thermal control optoelectronic analysis system, in conjunction with a spectrometer, to test the PCB’s luminous performance. The experiment targets a 200 Hz PWM signal with a period of 5 ms, setting the integration time to 140 ms to ensure complete measurement coverage of multiple PWM cycles. This setup avoids the fluctuation effects caused by cycle truncation, ensuring the stability and accuracy of the spectrometer measurement results.

4.1. Optical Compensation Parameter Measurement

In order to investigate changes in the optical characteristics of LEDs under different temperatures, this experiment was conducted in an integrating sphere while maintaining a constant duty cycle (40% of the maximum PWM). By adjusting the ambient temperature and using a temperature sensing line to monitor the LED junction temperature in real time, the system measured the LED’s luminous performance under various thermal conditions. Figure 11a shows the measured brightness ratios for the red, green, and blue channels as a function of temperature, along with their fourth-order polynomial fitting curves. Figure 11b displays the scatter plots and corresponding fits for the x and y chromaticity coordinates of the three channels. To ensure data reliability, luminous flux and chromaticity information were recorded at each temperature point only after the LED reached steady-state operation, with the real-time LED temperature being monitored simultaneously.

The measured parameter offsets are summarized in

Table 3. Brightness variation relative to 25 °C (percentage).

Temperature (°C)	Red Brightness Ratio	Green Brightness Ratio	Blue Brightness Ratio
−40	138.30%	106.80%	91.40%
−20	126.30%	104.50%	93.40%
−10	120.20%	103.30%	94.40%
0	113.0%	101.40%	93.30%
25	100%	100%	100%
50	85.20%	97.00%	101.60%
85	48.30%	92.20%	103.50%
120	31.70%	88.40%	107.40%

and

Table 4. Chromaticity coordinate shifts (x and y).

Temperature (°C)	Red X Coordinate	Red Y Coordinate	Green X Coordinate	Green Y Coordinate	Blue X Coordinate	Blue Y Coordinate
−40	−0.006	0.0063	−0.0203	0.012	0.003	−0.004
−20	−0.006	0.0045	−0.0139	0.0082	0.0021	−0.0029
−10	−0.0032	0.0035	−0.0107	0.0062	0.0016	−0.0023
0	−0.0025	0.003	−0.0072	0.0038	0.001	−0.002
25	0	0	0	0	0	0
50	0.0026	−0.0024	0.0085	−0.0051	−0.0013	0.001
85	0.0056	−0.0053	0.0196	−0.0121	−0.0031	0.0028
120	0.0087	−0.0085	0.0308	−0.0189	−0.0047	0.0049

, covering the brightness changes (expressed as a percentage relative to 25 °C) and the shifts in x and y chromaticity coordinates. The results indicate that as temperature increases, the brightness ratios and chromaticity coordinates of the red, green, and blue channels exhibit varying degrees of drift. Through multi-point calibration and fourth-order polynomial fitting, more accurate relationships between temperature and these parameters can be established. Ultimately, all of the fitted polynomial functions will be integrated into the control code to enable temperature compensation and real-time corrections of LED chromaticity and brightness in practical applications.

4.2. Optical Experiment Validation Result and Discussion

To improve the accuracy of the experimental measurements, this paper integrates the temperature model with the optical algorithm model and uses a spectrometer to verify the LED’s chromaticity coordinates. By conducting chromaticity coordinate tests on mixed-light LEDs and comparing them with the PN method, the prediction accuracy of the improved model is verified. In order to achieve more comprehensive measurements, brightness levels of 100%, 70%, 35%, and 1% are selected, with measurements taken sequentially from high to low brightness. Brightness adjustment is realized by modifying the brightness signal value in the LIN (Local Interconnect Network) message frame, the format of which is shown in

Table 5. LIN control message frame format for LED.

ID (PID)	Data1	Data2	Data3	Data4	Data5	Data6	Data7	Data8
0 × 29	R	G	B	intensity	dimming	address	address	ENABLE

:

Where R, G, and B represent the color information, while intensity denotes the brightness percentage with a range of [0, 100]. For instance, an intensity value of 99 corresponds to 99% of the maximum brightness. Using this message format, 30 sets of target color values (R, G, and B) are input sequentially and transmitted to the LED device’s slave node as inputs to the optical algorithm model described in Section 3, which then computes the corresponding color. Finally, the overall PWM values are scaled according to the intensity information contained in data4, thereby achieving proportional brightness adjustment. The 30 test color datasets are shown in

Table 6. sRGB color space RGB to xy chromaticity mapping.

R	G	B	x	y
255	0	0	0.64	0.33
255	24	0	0.634352	0.334486
255	48	0	0.622377	0.343995
255	72	0	0.603611	0.358897
255	96	0	0.579528	0.378022
255	120	0	0.552343	0.39961
255	143	0	0.525463	0.420956
255	167	0	0.498286	0.442537
255	191	0	0.473154	0.462495
255	215	0	0.450656	0.480362
255	239	0	0.430951	0.49601
247	255	0	0.413771	0.509652
223	255	0	0.396966	0.522997
199	255	0	0.380221	0.536295
175	255	0	0.363979	0.549193
151	255	0	0.348736	0.561298
255	64	64	0.573533	0.329802
255	82	64	0.560152	0.343019
255	100	64	0.544591	0.358391
255	118	64	0.527604	0.375171
255	135	64	0.510939	0.391632
255	153	64	0.49328	0.409076
255	171	64	0.476131	0.426016
255	189	64	0.459876	0.442073
255	207	64	0.444751	0.457014
255	225	64	0.430873	0.470722
255	243	64	0.418273	0.483168
249	255	64	0.40639	0.493708
231	255	64	0.393773	0.502549

, where the error calculation result for each measured color is $\Delta UV$. The expressions for the chromaticity coordinates $U$, $V$ and the chromaticity error $\Delta UV$ are as follows:

$$U={\displaystyle \frac{4x}{-2x+12y+3}}$$

(44)

$$V={\displaystyle \frac{4y}{-2x+12y+3}}$$

(45)

$$\Delta UV={\left(U-U_m\right)}^2+{\left(V-V_m\right)}^2$$

(46)

where $U$ and $V$ represent the chromaticity coordinates of the standard color, while $U_m$ and $V_m$ denote the chromaticity coordinates of the measured color.

The chromaticity errors of the measurement results for 30 colors at different brightness levels are shown in Figure 12.

From the results shown in Figure 12, it is evident that the improved TP temperature model predicts LED chromaticity parameters more accurately than the traditional PN-junction model in the medium-to-high brightness range. However, due to a hardware-induced delay of three duty-cycle units, once the system enters the low-brightness region (with PWM duty cycles under 100), these rise and fall edge delays—previously only three duty-cycle units—become critically important. For high brightness levels, where PWM duty cycles typically exceed 1000, a three-duty-cycle delay is negligible and has virtually no effect on either the luminous flux or the ratio among the three color channels. For instance, if the theoretical algorithmic values for the RGB channels are (3000, 1500, 2000), subtracting three duty cycles yields (2997, 1497, 1997), leaving the RGB ratio essentially unchanged.

In contrast, under low-brightness conditions, suppose a particular RGB channel ratio is set to (20, 35, 5), corresponding to duty cycles of 4:7:1. If three duty cycles are effectively lost, these values shift to (17, 32, 2), causing a substantial deviation from the original RGB balance and resulting in significant chromaticity error. To resolve this issue, a fixed compensation of three duty-cycle units can be introduced at the algorithmic level, offsetting the missing pulses during startup and shutdown so that the pulse waveform at low brightness remains closer to the theoretical target. This compensation considerably reduces chromaticity errors within this brightness range. Through these corrective measures, the TP temperature model maintains a more favorable level of predictive accuracy across the entire brightness spectrum.

When operating at low duty cycles, the rising and falling edges of the PWM signal each introduce approximately a 3 ns delay. This physical characteristic significantly shortens the effective on-time and, consequently, causes a relatively large deviation in the LED drive current for small pulse widths. Since LED brightness is proportional to the drive current, and the pulse width represents only a tiny fraction of the overall period at low duty cycles, any additional delay is magnified and directly impacts both luminous output stability and chromatic consistency.

To compensate for the errors introduced by these delays, one can apply a duty cycle correction to the PWM signal at the algorithmic level. Specifically, an additional three duty-cycle units (i.e., 3 ns of compensation) is added to the original pulse width to offset the loss in conduction time caused by the rising and falling edges. Figure 13 provides an example of this compensation strategy: for an original 100 ns pulse, an extra 3 ns is added so that the actual on-time is restored to 103 ns. As a result, the compensated pulse area aligns with the theoretically calculated value. Experimental results Figure 14 indicate that, at a 1% brightness level, the compensated PWM signal output closely matches the algorithmic prediction, greatly improving the LED’s brightness accuracy and color uniformity at low duty cycles. Compared to the PN method, the TP model exhibits a higher degree of alignment with the standard chromaticity coordinates, with an error of less than 0.0052, thereby validating the effectiveness of the improved model.

However, if the PN-junction method is used to measure temperature for determining the compensation value, inaccuracies in temperature prediction lead to a mismatch between the true thermal characteristics and the compensation applied. In low duty-cycle scenarios, this imprecision is amplified, causing larger brightness and chromatic errors. Therefore, achieving stable and accurate LED output at low brightness levels hinges on precisely compensating for the rising and falling edge delays and maintaining sufficiently accurate thermal characterization. Overall, in low duty-cycle operation, applying slight but accurate PWM compensation not only effectively reduces brightness errors but also significantly enhances the stability and color consistency of the LED’s optical output.

5. Discussion

In this study, we propose a comprehensive thermal-optical compensation method for automotive RGB LEDs, which centers on integrating Fourier heat conduction theory with thermal resistance theory to establish a temperature prediction (TP) model. Within the temperature range from −40 °C to 120 °C, this model consistently maintains the temperature prediction error within 5 °C. Moreover, by employing 16.16 fixed-point arithmetic, the model effectively overcomes the inherent computational resource limitations of low-cost automotive-grade microcontrollers, thereby achieving real-time precise control without relying on floating-point operations.

Compared with the conventional thermal model based on the PN junction, the method proposed in this study demonstrates significant advantages across several key indicators. The traditional PN junction thermal model exhibits substantial shortcomings in temperature prediction accuracy, chromaticity drift, and system resource utilization, especially under low brightness conditions (approximately 1% PWM duty cycle), where significant chromaticity deviations often occur. To visually illustrate the differences between the two methods,

Table 7. Comparative analysis of TP and PN-junction thermal models.

Metric	TP Model	Traditional PN-Junction-Based Thermal Model
Temperature Prediction Error (°C)	≤5 °C	Up to 15 °C
Prediction Error Reduction (%)	Reduced from 15 °C to 5 °C, approximately a 67% reduction (some literature reports a 30% reduction depending on measurement conditions)	Error remains high
Chromaticity Drift Error (CIE 1931 xy)	At medium-to-high brightness: error < 0.0052; at low brightness, after PWM compensation, error is reduced from 0.025 to 0.006	Significant chromaticity deviation at low brightness; error can reach 0.025
Computational Implementation	Employs 16.16 fixed-point arithmetic to reduce memory usage and computational overhead	Relies on floating-point arithmetic, leading to higher resource consumption
MCU Resource Adaptability	Optimized for low-cost automotive-grade MCUs (RAM < 3 KB, clock frequency < 50 MHz)	Not suitable for low-cost, resource-constrained embedded systems
PWM Signal Compensation	Introduces PWM pulse width compensation (compensating 3 duty cycle units), significantly enhancing chromaticity stability at low brightness	No compensation for PWM rise/fall delays, resulting in notable chromaticity errors at low brightness

provides a detailed comparison in terms of temperature prediction error, chromaticity drift, computational implementation, MCU resource adaptability, and PWM signal compensation.

The results indicate that the proposed TP model not only outperforms the conventional model in temperature prediction accuracy but also offers notable benefits in chromaticity stability, computational efficiency, and adaptability for low-cost embedded systems. This, in turn, robustly supports the real-time and stability requirements of automotive LED systems operating under harsh conditions. However, the current TP model is primarily optimized for chips that use built-in constant-current sources, a strategy that may limit its direct application to high-power LEDs that rely on constant-voltage sources and PWM switching control.

Additionally, the chromaticity compensation component depends on empirical polynomial fitting methods, which might require recalibration under different thermal conditions or with alternative LED packaging configurations. Therefore, future research could explore adaptive learning algorithms based on real-time sensor feedback to dynamically update compensation parameters, while also expanding the scope of validation to encompass a broader range of LED technologies and packaging solutions. Furthermore, integrating predictive control strategies and multi-sensor data fusion techniques holds promise for further enhancing the overall performance of automotive LED thermal management and chromaticity stability.

6. Conclusions

This study conducted an in-depth investigation into temperature modeling and optical compensation for mixed-light LEDs. By integrating Fourier heat conduction principles with thermal resistance theory, a higher-accuracy temperature prediction model was proposed. In addition, a conventional optical algorithm was converted from floating-point to fixed-point arithmetic to meet the computational and memory limitations of low-cost automotive-grade MCUs.

Experimental results demonstrate that, within the −40 °C to 120 °C temperature range, the proposed model keeps the temperature prediction error within approximately 5 °C, whereas traditional PN-junction-based methods exhibit errors up to 15 °C, resulting in a 67% reduction in prediction error. Moreover, at medium-to-high brightness levels, the model reduces chromaticity deviation by approximately 58%. Under extremely low brightness conditions (1% duty cycle), by compensating for the rising and falling edge delays of the PWM waveform, the average chromaticity deviation in the CIE 1931 xy color space is reduced from approximately 0.025 to 0.006, achieving an improvement of about 76%, thereby significantly enhancing color consistency in resource-constrained automotive environments.

It is worth noting that the current experiments focused primarily on conventional RGB tricolor LEDs, and further exploration is needed for multi-wavelength or alternative LED packaging configurations. Additionally, the limited computational precision and memory capacity of low-cost MCUs still pose challenges for more complex temperature management applications. Future work may incorporate multi-sensor fusion, intelligent optical control, and advanced LED packaging technologies to strike a balance between cost-effectiveness and performance, while continuously enhancing thermal management and chromatic stability of LED systems.