Development and Experimentation of a Real-Time Greenhouse Positioning System Based on IUKF-UWB

Abstract

To mitigate the challenges posed by the confined spatial environment of greenhouses and various obstacles that frequently cause non-line-of-sight (NLOS) communication issues in ultra-wideband (UWB) localization systems, leading to localization difficulties and low accuracy, we propose a real-time greenhouse localization system that recognizes UWB ranging values prior to correction. First, the initial ranging value is obtained through double-sided two-way ranging (DS-TWR). Subsequently, a communication state identifier is designed based on the residual distribution of ranging values across two UWB communication modes. A correction model is then established by analyzing the causes of ranging value deviations. Finally, the NLOS localization deviation is corrected using an improved unscented Kalman filter (IUKF) algorithm. Experimental results in the greenhouse environment demonstrate that the proposed algorithm enhances positioning accuracy by 68% compared to the uncorrected localization method, offering a valuable reference for localization services in greenhouse settings.

1. Introduction

The swift advancement of intelligent agricultural facilities and greenhouse Internet of Things (IoT) technology has significantly heightened the demand for real-time, reliable, and high-precision Location-Based Services (LBSs) within greenhouse environments [1,2,3]. For instance, the autonomous navigation agricultural robots used for crop protection [4] and agricultural machinery require rapid positioning for task scheduling [5,6,7]. In outdoor environments, the Real-Time Kinematic (RTK) can deliver centimeter-level positioning services for agricultural machinery [8]. However, the rapid signal attenuation of GPS in indoor environments renders it incapable of providing precise positioning services for greenhouses [9]. The primary technologies employed to offer positioning services in greenhouse environments include WiFi [10], Bluetooth [11], ZigBee [12], and ultra-wideband (UWB) [13,14,15]. WiFi positioning technology offers lower accuracy and necessitates the prior deployment of numerous Access Point (AP) devices, making it challenging to adapt to complex environments with numerous obstacles, such as greenhouses. Bluetooth positioning technology offers low power consumption and cost benefits, but it is vulnerable to environmental interference, leading to reduced positioning accuracy in complex indoor environments. ZigBee positioning technology also boasts low power consumption and cost efficiency but suffers from reduced positioning accuracy and data security. Conversely, UWB technology offers high precision, strong penetration capabilities, and robust interference resistance. This makes it highly promising for positioning in greenhouse environments [16,17]. The integration of greenhouse IoT technology with UWB positioning technology can facilitate efficient data collection, communication, and display. This integration enables the real-time acquisition of location information for objects of interest [18,19]. This fusion is essential to improve the stability of fully automated navigation, the accuracy of path planning, and the efficiency of scheduling agricultural machinery in greenhouse environments.

Under line-of-sight (LOS) conditions, UWB exhibits exceptional positioning performance, achieving centimeter-level accuracy. However, in non-line-of-sight (NLOS) conditions, UWB modules suffer from multipath effects, resulting in a significant decrease in positioning accuracy [20,21,22]. Compared to other indoor positioning services, the complex interference from plants and metal frameworks within greenhouse environments presents a more severe NLOS challenge for UWB positioning technology. Therefore, accurately identifying UWB communication status and designing appropriate correction models are crucial measures to further enhance UWB positioning accuracy in NLOS environments. To address the challenge posed by NLOS ranging interference in UWB positioning systems, scholars have proposed the following effective methods. On the one hand, a hybrid ranging method based on time of arrival (TOA) and time difference of arrival (TDOA), combined with angle of arrival (AOA), is utilized to enhance UWB ranging accuracy and thereby mitigate system positioning errors [23,24]. On the other hand, extracting useful signal properties from channel impulse response (CIR) through machine learning methods such as support vector machines (SVM) [25], multilayer perceptron (MLP) [26] and convolutional neural networks (CNNs) [27] can identify and reject NLOS signals. However, these methods necessitate extensive initial data collection and substantial computational power. Therefore, some scholars have proposed a cooperative localization method [28] that reduces NLOS range errors using an inertial navigation system (INS) and offsets the rapid cumulative error of the INS with a UWB inertial navigation system. On one hand, wireless distributed IoT technology in greenhouse environments has limited energy capacity [29]. When UWB positioning data are reliable, this collaborative positioning method enhances navigation accuracy and provides more comprehensive attitude data. Additionally, in greenhouse environments, the energy capacity of wireless distributed IoT technology is limited. Therefore, it is imperative to develop a UWB real-time positioning correction algorithm that maintains stable accuracy and conserves computing power in continuous non-line-of-sight greenhouse environments.

In this study, an IUKF-UWB based real-time greenhouse localization system is proposed using IoT and UWB communication technologies. This localization system aims to improve the robot localization accuracy in greenhouse crop growing intensive environments. In this study, our main work is as follows:

(1)

A real-time greenhouse IoT positioning system with a three-tier architecture is designed to upload the collected ranging information to the cloud for processing and computation in order to reduce the energy consumption of distributed wireless IoT terminals in greenhouses and to enhance the system’s life cycle.

(2)

Using DS-TWR to obtain real-time distance information between the anchor and the tags carried by the robot, and designing the communication type identification method to recognize the ranging communication type of the UWB in the current state.

(3)

Based on the ranging deviation propagation characteristics of UWB signals in a greenhouse environment, IUKF is proposed to construct the error compensation function in the non-line-of-sight state in order to improve the positioning accuracy of the localization system in the NLOS situation.

2. Materials and Methods

2.1. System Composition and Design

In this study, we present a three-layer architecture IoT localization system for the real-time remote localization of greenhouse plant protection robots. The IUKF-UWB algorithm is designed to improve the positioning accuracy and stability of the greenhouse robot. As shown in Figure 1, the three-layer architecture designed in this study includes a greenhouse equipment layer, network transmission layer, and remote application layer.

As illustrated in Figure 2a, the greenhouse equipment layer in a real-time greenhouse positioning system utilized four UWB wireless transceivers designated as anchors. Additionally, one UWB wireless transceiver, referred to as a tag, was installed on the greenhouse mobile carrier for localization. The anchors were positioned at the corners of the perimeter edges of the greenhouse localization area.

This study has integrated and developed a low-power UWB wireless transceiver development board for the system, as shown in Figure 2b. This development board features an STM32F103T8U6 MCU (STMicroelectronics, Geneva, Switzerland) as the main control chip, a DWM1000 module (Decawave, Dublin, Ireland) for the UWB signal transceiver, and an ESP8266 (Espressif, Shenzhen, China) for remote communication. The DWM1000 module operates at a center frequency of 6489.6 MHz, suitable for civilian use, with a bandwidth of 499.2 to 900 MHz and a data output rate of 6.8 Mbps. To optimize UWB signal transmission and reception in greenhouse conditions, the development board is equipped with an external rod antenna, providing an effective range of up to 80 m.

The UWB positioning system comprises three or more localization anchors and a mobile tag that requires localization. By measuring the distances between the tag and each anchor, the location of the tag can be determined through the geometric relationships, achieving localization. The UWB ranging method employed in this experiment is based on the double-sided two-way ranging (DS-TWR) technique. This technique utilizes the time-of-flight (ToF) of signals propagated between anchors and tags to measure the distance between them, theoretically mitigating the time synchronization issue between devices without relying on clock synchronization. The working principle of the DS-TWR algorithm is illustrated in Figure 3. As illustrated in Figure 3, the ranging process begins with the tag to be positioned, sending a UWB signal (Poll) sequentially to the four anchors. Upon receiving the signal, each anchor responds with a signal (Resp) back to the tag. The tag then delays for a specified period before sending a final signal (Final), which the anchors receive, thus completing a DS-TWR cycle.

According to the ranging principle of DS-TWR in Figure 3, the ToF between the tag and the four anchors can be derived from the following equation.

$$\left\{\begin{array}{c}{\mathrm{T}}_{\mathrm{tof}0}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{round}10}{\mathrm{T}}_{\mathrm{round}20}-{\mathrm{T}}_{\mathrm{reply}10}{\mathrm{T}}_{\mathrm{reply}20}}{{\mathrm{T}}_{\mathrm{round}10}+{\mathrm{T}}_{\mathrm{round}20}+{\mathrm{T}}_{\mathrm{reply}10}+{\mathrm{T}}_{\mathrm{reply}20}}}\\ {\mathrm{T}}_{\mathrm{tof}1}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{round}11}{\mathrm{T}}_{\mathrm{round}21}-{\mathrm{T}}_{\mathrm{reply}11}{\mathrm{T}}_{\mathrm{reply}21}}{{\mathrm{T}}_{\mathrm{round}11}+{\mathrm{T}}_{\mathrm{round}21}+{\mathrm{T}}_{\mathrm{reply}11}+{\mathrm{T}}_{\mathrm{reply}21}}}\\ {\mathrm{T}}_{\mathrm{tof}2}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{round}12}{\mathrm{T}}_{\mathrm{round}22}-{\mathrm{T}}_{\mathrm{reply}12}{\mathrm{T}}_{\mathrm{reply}22}}{{\mathrm{T}}_{\mathrm{round}12}+{\mathrm{T}}_{\mathrm{round}22}+{\mathrm{T}}_{\mathrm{reply}12}+{\mathrm{T}}_{\mathrm{reply}22}}}\\ {\mathrm{T}}_{\mathrm{tof}3}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{round}13}{\mathrm{T}}_{\mathrm{round}23}-{\mathrm{T}}_{\mathrm{reply}13}{\mathrm{T}}_{\mathrm{reply}23}}{{\mathrm{T}}_{\mathrm{round}13}+{\mathrm{T}}_{\mathrm{round}23}+{\mathrm{T}}_{\mathrm{reply}13}+{\mathrm{T}}_{\mathrm{reply}23}}}\end{array}\right.$$

(1)

where T_round1i is the return time from the tag sending a signal to the anchors, and T_reply1i is the response time from the anchors sending a signal to the tag.

The distance information between the tag and the four anchors can be derived from

$$\mathrm{d}={\mathrm{T}}_{\mathrm{tof}i}\times \mathrm{c}$$

(2)

where c is the velocity of electromagnetic wave propagation in the standard state.

2.2. UWB Ranging Correction Model

The complexity of crop growth in greenhouse environments may cause obstructions between UWB anchors and tags during communication, resulting in a significant increase in time of flight. Hence, the real-time monitoring of communication between UWB anchors and tags, the accurate identification of the current communication state, and the application of different models to correct various communication states are feasible for achieving precise real-time positioning in the greenhouse system. The block diagram of the UWB-IUKF algorithm is shown in Figure 4. In this study, the residuals of the ranging values are calculated to achieve the discrimination of the LOS and NLOS of the system; second, the discrimination results are corrected by using the NLOS correction model and the NLOS correction model, respectively; and finally, the optimal estimation of the coordinate values of the greenhouse robot is obtained.

2.2.1. UWB Communication State Discrimination Method

During communication in the LOS state, the error term of the ranging result obtained by UWB only contains Gaussian noise with a mean of zero; when communicating in the NLOS state, the error term of the ranging result obtained by UWB includes both Gaussian noise with a mean of zero and varying nonlinear random errors [30]. Consequently, in LOS conditions, the overall measurement residuals of the system are relatively small; however, in NLOS states, the estimated Euclidean range from the tags to the anchors will generally deviate from the true range. Hence, in NLOS conditions, the system will exhibit larger measurement residuals.

In practical applications, leveraging this characteristic, this study has designed a UWB communication state discriminator, resulting in overall residuals greater than those observed under LOS conditions when NLOS measurements are present in the system. The communication state discriminator and the tag coordinate calculation algorithm are described as follows:

Firstly, as illustrated in Figure 3, under the DS-TWR algorithm, each anchor communicates sequentially with the tag, recording time differences. Assuming the coordinates of the four localization anchors are (x₁, y₁, z₁), (x₂, y₂, z₂), (x₃, y₃, z₃) and (x₄, y₄, z₄), and the coordinates of the mobile tag to be localized are (x, y, z), a set of nonlinear equations can be derived based on their spatial relationships:

$$\left\{\begin{array}{c}{(\mathrm{x}-{\mathrm{x}}_1)}^2+{(\mathrm{y}-{\mathrm{y}}_1)}^2+{(\mathrm{z}-{\mathrm{z}}_1)}^2={\mathrm{d}}_1^2\\ {(\mathrm{x}-{\mathrm{x}}_2)}^2+{(\mathrm{y}-{\mathrm{y}}_2)}^2+{(\mathrm{z}-{\mathrm{z}}_2)}^2={\mathrm{d}}_2^2\\ {(\mathrm{x}-{\mathrm{x}}_3)}^2+{(\mathrm{y}-{\mathrm{y}}_3)}^2+{(\mathrm{z}-{\mathrm{z}}_3)}^2={\mathrm{d}}_3^2\\ {(\mathrm{x}-{\mathrm{x}}_4)}^2+{(\mathrm{y}-{\mathrm{y}}_4)}^2+{(\mathrm{z}-{\mathrm{z}}_4)}^2={\mathrm{d}}_4^2\end{array}\right.$$

(3)

where d₁, d₂, d₃, and d₄ represent the original UWB ranging values.

To facilitate calculation, Equation (2) can be simplified into the following linear matrix:

$$ax=b$$

(4)

where a is $\left[\begin{array}{ccc}2({\mathrm{x}}_1-{\mathrm{x}}_2)& 2({\mathrm{y}}_1-{\mathrm{y}}_2)& 2({\mathrm{z}}_1-{\mathrm{z}}_2)\\ 2({\mathrm{x}}_1-{\mathrm{x}}_3)& 2({\mathrm{y}}_1-{\mathrm{y}}_3)& 2({\mathrm{z}}_1-{\mathrm{z}}_3)\\ 2({\mathrm{x}}_1-{\mathrm{x}}_4)& 2({\mathrm{y}}_1-{\mathrm{y}}_4)& 2({\mathrm{z}}_1-{\mathrm{z}}_4)\end{array}\right]$. x is ${\left[\begin{array}{ccc}\mathrm{x}& \mathrm{y}& \mathrm{z}\end{array}\right]}^{\mathrm{T}}$, which is the matrix representation of the mobile tag coordinate values. b is $\left[\begin{array}{c}{\mathrm{x}}_1^2-{\mathrm{x}}_2^2+{\mathrm{y}}_1^2-{\mathrm{y}}_2^2+{\mathrm{z}}_1^2-{\mathrm{z}}_2^2+{\mathrm{d}}_2^2-{\mathrm{d}}_1^2\\ {\mathrm{x}}_1^2-{\mathrm{x}}_3^2+{\mathrm{y}}_1^2-{\mathrm{y}}_3^2+{\mathrm{z}}_1^2-{\mathrm{z}}_3^2+{\mathrm{d}}_3^2-{\mathrm{d}}_1^2\\ {\mathrm{x}}_1^2-{\mathrm{x}}_4^2+{\mathrm{y}}_1^2-{\mathrm{y}}_4^2+{\mathrm{z}}_1^2-{\mathrm{z}}_4^2+{\mathrm{d}}_4^2-{\mathrm{d}}_1^2\end{array}\right]$.

By using the maximum likelihood estimation to solve Equation (4), the estimated position of the tag can be obtained:

$$\widehat{x}={\left(a^{\mathrm{T}}a\right)}^{-1}{a}^{\mathrm{T}}b$$

(5)

Since the positions of the four anchors were known, the range between the currently estimated position of the tag and the four anchors can be calculated using the estimated position of the tag.

$${ \widehat{\mathrm{d}}}_i=‖\widehat{x}-p_i‖,i=1,2,3,4$$

(6)

where p_i represents the coordinates of the anchors, which are specifically denoted as ${\left[\begin{array}{ccc}{\mathrm{x}}_i& {\mathrm{y}}_i& {\mathrm{z}}_i\end{array}\right]}^{\mathrm{T}},i=1,2,3,4$.

The residual of range measurement can be written as

$${\epsilon }_i=\left|{\widehat{\mathrm{d}}}_i-{\mathrm{d}}_i\right|$$

(7)

The overall range measurement residual of the UWB system is

$$\epsilon =\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\epsilon }_i^2}}$$

(8)

Hence, the residual threshold differentiating between LOS and NLOS communications can be determined through practical greenhouse experiments. The communication status discrimination model can be written as

$$\mathrm{M}=\left\{\begin{array}{c}0\\ 1\end{array}\right.\begin{array}{c}(\epsilon <\alpha {\mathrm{T}}_{\epsilon })\\ (\epsilon <\alpha {\mathrm{T}}_{\epsilon })\end{array}$$

(9)

where M represents the communication status between the UWB anchors and tag, where M = 0 corresponds to an LOS communication status and M = 1 corresponds to an NLOS communication status. ${\mathrm{T}}_{\epsilon }$ denotes the discrimination threshold value, which is the maximum range measurement residual under LOS conditions for the current environment. This threshold value does not change with the growth of greenhouse crops. $\epsilon$ represents the discrimination coefficient, which is used to adjust the sensitivity of the discrimination model to NLOS conditions. The specific value of $\alpha$ can be adjusted according to the actual positioning scenario.

2.2.2. LOS Correction Model

Under LOS conditions, UWB signals propagate in a straight line through the air, and the range between the UWB anchor and the positioning tag is directly proportional to the signal flight time. Formula (1) can be used to calculate the range measurement result by multiplying the UWB signal flight time by the propagation speed. However, in practical measurement scenarios, due to factors such as latitude and longitude, air quality, etc., the propagation speed of UWB signals in the air is not exactly equal to the speed of light. Therefore, there still exists an error in the range measurement results of UWB under LOS communication. Before proceeding with positioning, it is necessary to correct this error.

After modifying Formula (1), an LOS condition UWB range correction model can be established. The mathematical relationship between the UWB ranging result d and the corrected result d₀ can be represented by the following linear polynomial:

$$\mathrm{d}= {\mathrm{c}}^{\prime }{\mathrm{d}}_0+\mathsf{\beta }$$

(10)

where c’ is the ratio of the electromagnetic wave propagation speed in the current environment to the propagation speed in a vacuum. Moreover, the constant term β represents the zero offset for the measured range. These two parameters need to be determined according to the actual usage scenarios of UWB and can be estimated through experiments.

Based on Equation (9), the corrected model under LOS conditions can be written as

$${\widehat{\mathrm{d}}}_{\mathrm{i}}={\displaystyle \frac{1}{ {\mathrm{c}}^{\prime }}}{\mathrm{d}}_{\mathrm{i}}-{\displaystyle \frac{\mathsf{\beta }}{ {\mathrm{c}}^{\prime }}}$$

(11)

where ${\widehat{\mathrm{d}}}_{\mathrm{i}}$ is the corrected ranging value between the tag and anchor i, while ${\mathrm{d}}_{\mathrm{i}}$ is the original ranging values between the tag and anchor i.

2.2.3. NLOS Correction Model

To alleviate the error in the original ranging values caused by NLOS communication due to obstructions between tags and anchors in the complex greenhouse environment, this paper presents a modified unscented Kalman filter (UKF) algorithm as an NLOS correction model. When the communication status discriminator identifies non-line-of-sight conditions in the current TOF ranging measurements, the NLOS correction model is applied for correction.

The UKF algorithm is a filtering technique applicable to nonlinear systems. Similar to the classic Kalman filter (KF) and the extended Kalman filter (EKF), it computes the difference between the predicted estimate and the actual measurements to obtain the optimal Kalman gain. It then acquires an accurate state vector and covariance matrix. The standard UKF algorithm calculation process is divided into the following steps [31,32,33]:

Step 1: Initialization.

For different times t, the initial ranging values measured by UWB are selected as the observation vector Z_t, and the state vector is X_t. The UWB nonlinear system can be described as follows:

$$\left\{\begin{array}{l}{\mathrm{X}}_{\mathrm{t}}=\mathrm{F}({\mathrm{X}}_{\mathrm{t}-1})+{\mathsf{\omega }}_{\mathrm{t}-1}\hfill \\ {\mathrm{Z}}_{\mathrm{t}}=\mathrm{H}({\mathrm{X}}_{\mathrm{t}})+{\mathrm{\nu }}_{\mathrm{t}}\hfill \end{array}\right.$$

(12)

where ${\mathrm{\omega }}_{t-1}$ represents the process noise at time t; ${\mathrm{\nu }}_t$ is the measurement noise; F(x) is the state transition equation; and H(x) is the observation equation.

Step 2: Obtain sigma points.

First, given the initial values of the state vector X(t − 1) and the initial covariance matrix Z(t − 1), generate a set of Sigma sampling points as follows:

$$\left\{\begin{array}{l}{\mathsf{\xi }}^0(\mathrm{t}-1)=\mathrm{X}(\mathrm{t}-1)\hfill \\ {\mathsf{\xi }}^i(\mathrm{t}-1)=\mathrm{X}(\mathrm{t}-1)+{(\sqrt{(n+\mathsf{\lambda })\mathrm{Z}(\mathrm{t}-1)})}_i,i=1,\cdots n\hfill \\ {\mathsf{\xi }}^i(\mathrm{t}-1)=\mathrm{X}(\mathrm{t}-1)-{(\sqrt{(n+\mathsf{\lambda })\mathrm{Z}(\mathrm{t}-1)})}_i,i=n+1,\cdots 2n\hfill \end{array}\right.$$

(13)

where n represents the dimensionality of the system; ${\mathsf{\xi }}^i(\mathrm{t}-1)$ is the number of i sampling points at the moment t − 1; $\lambda$ is a scaling factor to reduce the total prediction error.

Step 3: Prediction process.

The next-step predictive value of the Sigma sampling points ${\mathsf{\xi }}^i(t)$ can be described as

$${\xi }^i(\mathrm{t})=\mathrm{F}{\xi }^i(\mathrm{t}-1),i=0,1,\cdots 2n$$

(14)

The one-step predictive value of the state vector $\mathrm{X}(\mathrm{t}\left|\mathrm{t}-1\right.)$ and the covariance $\mathrm{Z}\left(\left.\mathrm{t}\right|t-1\right)$ can be written as

$$\mathrm{X}(\mathrm{t}\left|\mathrm{t}-1\right.)=\sum _{i=0}^{2n}{\mathrm{W}}_i^m{\mathsf{\xi }}^i(\mathrm{t})$$

(15)

$$\mathrm{Z}(\left.\mathrm{t}\right|\mathrm{t}-1)=\sum _{\mathrm{i}=0}^{2\mathrm{n}}{\mathrm{W}}_i^c[{\mathsf{\xi }}^i(\mathrm{t})-\mathrm{X}(\left.\mathrm{t}\right|\mathrm{t}-1)][{\mathsf{\xi }}^i(\mathrm{t})-\mathrm{X}{(\left.\mathrm{t}\right|\mathrm{t}-1)}^{\mathrm{T}}]+\mathrm{Q}(\mathrm{t}-\mathrm{1})$$

(16)

where $\mathrm{Q}(\mathrm{t}-1)$ represents the covariance matrix of the process noise. ${\mathrm{W}}_i^m$ and ${\mathrm{W}}_i^c$ are the mean weight factor and the variance weight factor, respectively, in the UKF.

Step 4: Utilize the unscented transformation (UT), and generate a new set of Sigma points based on the one-step predictive values.

$$\left\{\begin{array}{l}{\mathsf{\xi }}^{\prime \left(0\right)}(\left.\mathrm{t}\right|\mathrm{t}-1)=\mathrm{X}(\left.\mathrm{t}\right|\mathrm{t}-1)\hfill \\ {\mathsf{\xi }}^{\prime \left(i\right)}(\left.\mathrm{t}\right|\mathrm{t}-1)=\mathrm{X}(\left.\mathrm{t}\right|\mathrm{t}-1)+{(\sqrt{(n+\mathsf{\lambda })\mathrm{Z}(\left.\mathrm{t}\right|\mathrm{t}-1)})}_{i^{\prime }},i^{\prime }=1,\cdots n\hfill \\ {\mathsf{\xi }}^{\prime \left(i\right)}(\left.\mathrm{t}\right|\mathrm{t}-1)=\mathrm{X}(\left.\mathrm{t}\right|\mathrm{t}-1)-{(\sqrt{(n+\mathsf{\lambda })\mathrm{Z}(\left.\mathrm{t}\right|\mathrm{t}-1)})}_{i^{\prime }},i^{\prime }=n+1,\cdots 2n\hfill \end{array}\right.$$

(17)

Step 5: Update process.

Bring the new set of sigma points into the observation equation to obtain the following predicted observations.

$$\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.)=\mathrm{H}\left({ {\mathsf{\xi }}^{\prime }}^{\left(\mathrm{i}\right)}(\mathrm{t})\right)$$

(18)

Utilize weighted summation to calculate the mean and covariance of the system’s predicted values.

$$\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)=\sum _{\mathrm{i}=0}^{2n}({\mathrm{W}}_i^m\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.))$$

(19)

$${\mathrm{P}}_{{\mathrm{Z}}_{\mathrm{t}}{\mathrm{Z}}_{\mathrm{t}}}=\sum _{i=0}^{2n}{\mathrm{W}}_i^c[\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.)-\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)]{[\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.)-\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)]}^{\mathrm{T}}+\mathrm{R}(\mathrm{t})$$

(20)

$${\mathrm{P}}_{{\mathrm{X}}_{\mathrm{t}}{\mathrm{Z}}_{\mathrm{t}}}=\sum _{i=0}^{2n}{\mathrm{W}}_i^c[\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.)-\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)]{[\mathrm{Z}(\mathrm{t}\left|\mathrm{t}-1\right.)-\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)]}^{\mathrm{T}}$$

(21)

The unscented Kalman filter gain can be written as

$$\mathrm{K}(\mathrm{t})={\mathrm{P}}_{{\mathrm{X}}_{\mathrm{t}}{\mathrm{Z}}_{\mathrm{t}}}{{\mathrm{P}}_{{\mathrm{Z}}_{\mathrm{t}}{\mathrm{Z}}_{\mathrm{t}}}}^{-1}$$

(22)

Calculate the updated system state and covariance.

$$\widehat{\mathrm{X}}(\mathrm{t})=\widehat{\mathrm{X}}(\left.\mathrm{t}\right|\mathrm{t}-1)+\mathrm{K}(\mathrm{t})\left(\mathrm{Z}\left(\mathrm{t}\right)-\widehat{\mathrm{Z}}(\mathrm{t}\left|\mathrm{t}-1\right.)\right)$$

(23)

$$\mathrm{P}(\mathrm{t})=\mathrm{P}(\left.\mathrm{t}\right|\mathrm{t}-1)-\mathrm{K}(\mathrm{t}){\mathrm{P}}_{{\mathrm{Z}}_{\mathrm{t}}{\mathrm{Z}}_{\mathrm{t}}}\mathrm{K}{(\mathrm{t})}^{\mathrm{T}}$$

(24)

In a previous study, when four UWB anchors were used for localization in a greenhouse environment, the closer the tags were to the geometric center of the height planes of the four anchors, the smaller the deviation of the measured ranging values from the actual range, and the further they were from the geometric centers, the larger the deviation from the actual range [34]. The improved untraceable Kalman filter algorithm (IUKF) constructs a state error compensation function based on the characteristics of UWB measurement error and the actual greenhouse positioning environment. When the communication state discriminator recognizes the NLOS communication, it adopts the measurement value of the current estimated value of the previous moment value as the reference of the UKF state, calculates the amount of compensation for the state error at this time, and compensates for the amount of the UKF state.

Assuming the geometric center of the horizontal plane formed by the four anchors is (x₀, y₀), and the measured coordinates of the tag at the previous moment are (x_t−1, y_t−1), the deviation of the tag’s position from the geometric center at that moment can be calculated as the difference between the two points:

$$\left\{\begin{array}{c}\mathsf{\Delta }\mathrm{x}={\mathrm{x}}_{\mathrm{t}-1}-{\mathrm{x}}_{\mathrm{c}}\\ \mathsf{\Delta }\mathrm{y}={\mathrm{y}}_{\mathrm{t}-1}-{\mathrm{y}}_{\mathrm{c}}\end{array}\right.$$

(25)

Taking into account the size of the deviation in the coordinates on the horizontal plane and the error characteristics of UWB in the greenhouse environment, correction coefficients K_x and K_y are set separately. The compensation for the tag’s coordinates is determined as

$${\mathrm{T}}_{\mathrm{offset}}={\left[{\mathrm{K}}_{\mathrm{X}}\Delta \mathrm{x},{\mathrm{K}}_{\mathrm{y}}\Delta \mathrm{y}\right]}^{\mathrm{T}}$$

(26)

Using the tag’s coordinate compensation, the original nonlinear system of UWB can be written as

$$\left\{\begin{array}{l}{\mathrm{X}}_{\mathrm{t}}=\mathrm{F}({\mathrm{X}}_{\mathrm{t}-1})+{\mathrm{T}}_{\mathrm{offset}}+{\omega }_{\mathrm{t}-1}\hfill \\ {\mathrm{P}}_{\mathrm{t}}=\mathrm{H}({\mathrm{X}}_{\mathrm{t}})+{\nu }_{\mathrm{t}}\hfill \end{array}\right.$$

(27)

The next-step prediction value for Sigma points in Step 3 of the UKF is modified as follows, while the other steps remain as per the standard UKF filtering algorithm.

$${\mathsf{\xi }}^i(\mathrm{t})=\mathrm{F}{\mathsf{\xi }}^i(\mathrm{t}-1)+{\mathrm{T}}_{\mathrm{offset}},i=0,1,\cdots 2n$$

(28)

To characterize the positioning accuracy of the proposed greenhouse remote positioning system presented in this paper, the study introduces Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) as evaluation criteria. MAE and RMSE can be solved by the following equations:

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left(\left|{ \hat{\mathrm{x}}}_i-{\mathrm{x}}_i\right|+\left|{\widehat{\mathrm{y}}}_i-{\mathrm{y}}_i\right|\right)}$$

(29)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{i=1}^n\left({\left({\widehat{\mathrm{x}}}_i-{\mathrm{x}}_i\right)}^2+{\left({\widehat{\mathrm{y}}}_i-{\mathrm{y}}_i\right)}^2\right)}}$$

(30)

2.3. Remote Operation Interface

As shown in Figure 5, to facilitate remote visualization of the localization process and acquisition of experimental data, this study has orchestrated a web-based operation interface utilizing Visual Studio Code (version 1.71). The interface predominantly comprises: an anchor coordinates setup zone that allows for the definition of initial anchor coordinates; a map attribute configuration zone capable of inserting positioning background maps and adjusting relevant parameters to align with the actual deployment environment; a positioning mode setting zone that offers the ability to switch between tagging modes, initiate positioning functions, and output logs of tag positioning; a real-time display area for tag coordinate information; and a visual display area for the relative range between tags and anchors. In an endeavor to minimize the energy consumption of the distributed UWB node network and thus elongate the lifespan of the greenhouse positioning system, the firmware programmed into the UWB development boards is solely responsible for measuring the TOF between each anchor and tag and then relaying this information to an ESP8266 module via a TTL serial port. Subsequently, the ESP8266 module employs the TCP protocol to transmit the TOF data to an Alibaba Cloud server, where the communication status determination, correction processes, and computation of positioning coordinates are executed.

3. Results

3.1. Test Environment and Equipment

In order to verify the positioning accuracy of the UWB correction model proposed in this paper and the robustness of the IUKF algorithm in the NLOS environment, this study carried out static accuracy test experiments and dynamic accuracy test experiments in the pepper planting area of the Venlo greenhouse at the Institute of Agricultural Mechanization, Xinjiang Academy of Agricultural Sciences (IAAS), respectively. This study only considered the positioning results on a two-dimensional plane, with base station A0 as the origin, the direction of the line connecting A0 to A1 as the positive x-axis direction, and the direction of the line connecting A0 to A3 as the positive y-axis direction. A two-dimensional Cartesian positioning system coordinate system was established, and the coordinate markers of each point in the coordinate system were all in meters (m). As shown in Figure 6, the experimental site in the greenhouse is 7 × 7 m, in which 6 rows of chili peppers using soilless cultivation were uniformly planted. The height of the top of the chili pepper plants ranged from 1.5 to 1.85 m, and the height of the metal support used for soilless cultivation was 0.7 m. The deployment location of the base station in the greenhouse is shown in Figure 6, where the heights of A0 (0,0), A1 (0,7), and A2 (7,7) are set to 1.7 m; the height of A3 (0,7) is 1.9 m; and the test plant protection robot uses a DC power supply to drive four motor tires to move forward in a straight line. Each motor tire is equipped with a steering motor above it to drive the motor tire to turn, enabling the plant protection robot to turn at right angles in place. The height of the label carried on the plant protection robot is 1.1 m. The log output includes the raw ranging values during the positioning process through the remote operation interface.

The static accuracy test experiment adopts the five-point sampling method, and five target points are selected as the monitoring points of the static accuracy test among the soilless cultivated pepper crops in the greenhouse. The horizontal and vertical range between each target point and the origin A0 are taken as the actual coordinates of the target point, and the real coordinates of the selected target points can be referred to the blue markers in Figure 6, which are labeled tag target1 to tag target5 according to the direction of the trajectory exercise. The plant protection robot is operated to the target points by controlling the plant protection robot, and the time of the localization test for each target point is one minute. The localization system measures the average coordinate value at the target point in one minute as the measurement value for the static accuracy test, and the final positioning errors were calculated by comparing the measured values with the real coordinate values.

In the dynamic accuracy test experiment, the mobile cart carrying the UWB tag started from the yellow marked point (1.1, 1), as shown in Figure 6. It moved at a constant speed of 0.5 m/s through all the crop rows within the UWB coverage area following the path planned in Figure 6. The UWB positioning data during the experiment were downloaded via the log button on the web operation interface. The actual test scene is as shown in Figure 7.

3.2. Analysis of Experiment Results

The analyzed localization errors data of the static accuracy test experiment are shown in

Table 1. Static positioning errors.

Target Points		Longitudinal Deviation			Lateral Deviation
		Max (m)	MAE (m)	RMSE (m)	Max (m)	MAE (m)	RMSE (m)
Tag	1	0.153	0.094	0.101	0.155	0.097	0.106
	2	0.138	0.090	0.094	0.146	0.093	0.097
	3	0.125	0.072	0.076	0.128	0.070	0.079
	4	0.144	0.096	0.104	0.141	0.093	0.098
	5	0.159	0.097	0.103	0.138	0.098	0.092

; in the localization of each target point, the maximum longitudinal deviation comes from the target point 5, with a localization error of 0.159 m, the maximum lateral deviation comes from the localization of the target point 1, with a localization error of 0.155 m, and the root mean square error of localization for each point is less than 0.15 m. At the same time, by the localization error data given in Table 1, it is not difficult to find that during the localization process, the closer the tag is to the geometric centers of the four anchors, the errors are smaller.

In the dynamic accuracy test experiment, we use the traditional least squares (LS), EKF, UKF, and IUKF algorithms for coordinate resolution of the tags, respectively, and the performance results of the four localization resolution algorithms as well as the real reference trajectory of the plant protection robot’s motion are shown in Figure 8.

As shown in the positioning results of Figure 8, due to the obstruction from the pepper plants as the experiment progresses, using the least squares method to directly analyze the UWB positioning coordinates leads to significant nonlinear deviations in the cart’s positioning results. Compared to the least squares method, the nonlinear filtering algorithms EKF and UKF provide more ideal filtering effects on the cart’s trajectory, resulting in a smaller overall error in the output positioning trajectory data.

Moreover, as clearly demonstrated in the enlarged parts a and b of Figure 9, the IUKF algorithm shows an advantage in processing the UWB positioning system by producing trajectories that are closer to the true path and displaying better filtering performance even under significant fluctuations in UWB positioning. This indicates that when there is a large residual between the measurement predictive value and the actual value, the IUKF algorithm compensates for the ranging errors in NLOS conditions by improving the correction coefficients. Additionally, the trajectory produced by the IUKF algorithm is smoother compared to the standard UKF algorithm, better balancing the contributions of compensation and measurements to the filtering estimate overall.

In the dynamic accuracy test experiment, the positioning results of the trolley in the positioning coordinate system under the x-axis and y-axis changes are shown in Figure 9a. As can be seen from the figure, as the test proceeds, the coordinate value of the cart in the x-axis shows a step-like increase, and the coordinate of the y-axis remains basically unchanged during the x-axis increase; the coordinate value of the y-axis varies back and forth between 1 and 6 m. The trend of the cart coordinate value is consistent with the planning path in Figure 6. The time period selected by the red box in Figure 9a is the time period when the mobile tag is affected by a serious NLOS due to passing through the vegetated area, which leads to a large deviation from the actual coordinates when the least squares method is directly used to solve the coordinate values. Figure 9b shows a zoom-in view of the x-axis localization results of the mobile tag in 30~46 s. The localization error of the uncorrected localization algorithm reaches the maximum when the test is carried out to the 36.25 s. After calculation of the point relative to the real trajectory under the localization coordinate system, the Euclidean range error is 0.684 m, while the maximum Euclidean range error of the IUKF algorithm near that moment is only 0.225 m.

To visually demonstrate the effectiveness of the IUKF algorithm proposed in this paper in suppressing UWB positioning errors, this paper introduces a Cumulative Distribution Function (CDF) graph, as shown in Figure 10, which records the probability distribution of error variables. The horizontal axis represents the location error, and the vertical axis represents the cumulative distribution function, indicating the percentage of a certain range of errors in the total error. From Figure 9, it can be seen that the IUKF algorithm proposed in this paper reaches the maximum error point the fastest and converges quickly. By introducing a correction coefficient in the filtering process to update the measurement noise, the IUKF algorithm effectively suppresses the fluctuation of UWB positioning points and has a stronger ability to predict and update noise. Compared to the least squares method, which does not correct ranging values, nonlinear filtering algorithms such as EKF and UKF are better at suppressing positioning errors; compared to the EKF and UKF algorithms, the accuracy of the IUKF algorithm improved by 42% and 34%, respectively.

Table 2. Dynamic positioning errors.

Positioning Method	Max (m)	MAE (m)	RMSE (m)
LS	0.684	0.383	0.416
EKF	0.312	0.214	0.235
UKF	0.264	0.183	0.203
IUKF	0.205	0.114	0.134

presents the statistical analysis results of the positioning errors from the dynamic accuracy testing experiment, including the maximum error, minimum error, MAE, and RMSE. The maximum error using the least squares method reached 0.684 m with an MAE of 0.383 m and an RMSE of 0.416 m. The positioning errors under the EKF and UKF algorithms are similar, with RMSE values of 0.235 m and 0.203 m, respectively. The IUKF algorithm achieved a maximum error, MAE, and RMSE of 0.225 m, 0.114 m, and 0.134 m, respectively. Therefore, it can be concluded that in an actual greenhouse environment, the IUKF algorithm proposed in this paper outperforms the traditional EKF and UKF algorithms in terms of root mean square error, maximum error, and average error, and it significantly surpasses the traditional least-squares method, meeting the practical requirements of greenhouse applications.

4. Discussion

The dense vegetation environment of a greenhouse brings serious continuous non-line-of-sight interference, and the UWB will cause a decrease in ranging accuracy due to the multipath effect and signal attenuation during the localization process, which ultimately leads to bias in the localization results. This paper proposes a first recognition and then correction on the basis of non-line-of-sight recognition of the untraceable Kalman filter algorithm to increase the correction coefficient and thus compensate for the measured value, in the actual greenhouse experiments, indicating the stability and accuracy of the performance, to meet the actual greenhouse plant protection robot’s location information needs.

The AliCloud server adopts advanced hardware equipment and optimized software architecture, with excellent performance and reliability, and it has a more mature application base in the greenhouse Internet of Things field. When selecting cloud servers, we can fully consider the configuration suitability and demand, cost and application environment, application background, and development prospects of cloud servers in the field. In this study, the remote Ali cloud computing service greatly reduces the energy consumption of the greenhouse environment terminal and further improves the use cycle of the greenhouse IoT.

In addition, among the filtering algorithms, the EKF algorithm can also be used for nonlinear filtering, but the UKF algorithm can approximate the posterior mean and covariance with second-order or more than second-order Taylor’s accuracy when using the UT transform to process the nonlinear filtering, whereas the EKF does not reach the second-order or more than second-order accuracy. And compared with the linearization process of EKF and the cumbersome Jacobi matrix calculation, the IUKF proposed in this study has higher filtering accuracy and less computational effort than EKF. Compared with the traditional EFK algorithm, the accuracy of this paper’s algorithm can be improved by 42%.

In future work, the fusion of UWB positioning technology with inertial sensors, LiDAR, and visual localization can be fully considered to achieve higher accuracy positioning in greenhouse environments. When taking into account the improvement of accuracy, the actual cost situation is fully considered so that the research results can be generalized.

5. Conclusions

In this paper, a greenhouse localization system based on IUKF-UWB is designed to realize the remote real-time localization service of a greenhouse plant protection robot under complex greenhouse conditions. The designed remote operating system can process the ranging data uploaded by the UWB positioning system and output the test logs. Under the same conditions of energy consumption, this study demonstrated longer usage time. In the greenhouse test, when the plant protection robot passes through the area with lush vegetation, the non-line-of-sight localization error is better mitigated, so that the localization result can be better close to the real movement trajectory; the analyzed test results show that the root mean square error of UWB localization without distance correction is 0.416 m, and after the correction of this paper’s method, the localization error is 0.134 m, which is a reduction of 68%, and it can provide reliable and stable localization information for continuous NLOS situations in a greenhouse environment.