A MEMS-IMU array measurement system based on central and staggered double ring configuration and a collaborative output method

Abstract

A MEMS-IMU array measurement system and cooperative output method based on a center-and-staggered double-ring configuration are disclosed, belonging to the field of inertial navigation and sensor measurement. This system addresses the problem that existing MEMS-IMU error models cannot eliminate common error components and structural system deviations. It comprises N MEMS-IMU units fixed to a rigid measurement substrate, forming a center-and-staggered double-ring physical configuration. One MEMS-IMU unit serves as the central reference unit, located at the center of the substrate. The remaining units are divided into two groups, distributed evenly around the circumference of the inner and outer rings centered on the central reference unit, with the corner positions of the inner and outer rings staggered. The main controller provides a synchronous sampling clock for all MEMS-IMU units and acquires raw measurement data. The data processing unit executes a cooperative output algorithm, processing the raw data based on observations and error models, and outputs fused inertial measurement data. This system is applicable to the field of inertial navigation.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation and sensor measurement technology, and in particular relates to a MEMS-IMU array measurement system based on a central and staggered double-ring configuration. Background Technology

[0002] In modern high-intensity combat and distributed warfare environments, numerous small platforms impose extremely stringent physical constraints on the size, weight, power consumption, and cost of Inertial Measurement Units (IMUs). While traditional high-precision fiber optic gyroscopes and laser gyroscopes possess excellent measurement accuracy and superior long-term zero-bias stability, their reliance on optical interference or resonant cavities results in bulky size, extremely high power consumption, and expensive manufacturing and maintenance costs, making them unsuitable for the miniaturization, low cost, and mass deployment demands of modern equipment. In contrast, micro-electro-mechanical system (MEMS) gyroscopes based on micro-nano fabrication processes have become the inevitable development direction for small inertial devices due to their advantages of small size, low power consumption, low cost, and ease of high integration. However, limited by current micro-nano fabrication technology, MEMS inertial measurement units generally suffer from zero-bias instability, scale factor error, and long-term drift due to the coupled effects of various physical factors such as manufacturing processes, packaging stress, temperature gradient changes, and thermal noise from internal mechanical structures. During inertial navigation system (INS) calculations, the attitude error obtained by integrating the angular velocity output from the gyroscope tends to diverge over time. In the short term, achieving a breakthrough in accuracy solely through improvements in single-chip manufacturing processes faces significant technological barriers. Therefore, constructing sensor arrays using multiple low-cost MEMS devices, and leveraging spatial redundancy, information redundancy in the observation dimensions, and processing redundancy in the estimation algorithms to effectively suppress errors, compensate for performance, and enhance fault tolerance, has become a core technological path for improving the performance of low-cost inertial systems.

[0003] In existing research on MEMS-IMU array geometry, the array layout design directly determines the system's observation performance and error propagation mechanism. Array geometry typically involves two core variables: first, directional geometry, which is the set of unit vectors of each single-axis gyroscope's sensing axis in the carrier coordinate system; and second, spatial structure geometry, which includes the absolute position of each sensor on the rigid substrate, layering relationships, packaging constraints, and interconnection and clock distribution topology. These two types of geometric variables act on different observation models and performance measurement systems. Directional geometry directly determines the rank, condition number, and dimension of the parity space of the gyroscope array's observation matrix; while spatial structure geometry enters the rigid body kinematics equations when the array fuses multi-point acceleration information or needs to estimate relative pose, thereby changing the system's Fisher information content and Cramer-Rao lower bound (CRLB).

[0004] Currently, the most common form in engineering implementation is the regular square or rectangular array. This planar layout is widely adopted because of its regular structure, high compatibility with existing printed circuit board (PCB) wiring technology, and greater friendliness to power supply and packaging constraints of large-scale nodes. However, the directional distribution of this regular planar layout exhibits a significant bias, with severely insufficient geometric isotropy. From an information theory perspective, when the array uses multi-point acceleration information to assist in angular velocity estimation, the rotation term in the model is related to the position vector. The Fisher information of the system increases with the square of the array size and with the increase of the angular velocity amplitude. This provides a direct physical basis for the design of non-equidistant, outer-ring-priority point placement. Traditional dense rectangular arrays fail to effectively utilize the maximum average radius under given board area or structural size constraints, thus failing to theoretically improve the identifiability of rotation-related parameters and making it difficult to improve the lower bound of the estimation variance in the CRLB sense. Furthermore, some existing research has turned to three-dimensional symmetrical layout design in pursuit of theoretical observation optimization. The core of this research lies in finding a configuration that satisfies the condition of the observation matrix (where is the number of sensors) to achieve the optimal condition in terms of navigation accuracy. While the uniform spatial distribution of sensor orientations in a 3D layout reduces the matrix condition number and improves fault detection and isolation performance, its practical engineering applications face significant obstacles. On one hand, the manufacturing complexity of 3D structures is high, assembly is difficult, and calibration is extremely labor-intensive. On the other hand, assembly errors in polyhedra or conical surfaces often introduce larger non-orthogonal error propagation, and it cannot be guaranteed that all sensors are in a consistent thermodynamic environment and power supply path. The negative impacts of these packaging complexities and assembly errors often offset the theoretical advantages brought by the orientation distribution.

[0005] Overall, existing technologies, whether planar arrays or three-dimensional stacked arrays, have failed to effectively elucidate the explicit correspondence between array geometry and internal information matrices. Especially for sensors located at different positions on the same substrate, structural mechanical disturbances caused by printed circuit board deformation or external high-frequency vibrations often manifest as strongly correlated common errors. Traditional array cooperative output models typically assume that the errors of each sensor are independent, directly employing mean filtering or simple covariance weighting, which makes it difficult to effectively decouple and suppress these structural common-mode errors mathematically, thus limiting the actual measurement accuracy of the array under complex mechanical environments. Summary of the Invention

[0006] In view of this, the present invention aims to propose a MEMS-IMU array measurement system and a collaborative output method based on a central and staggered double-ring configuration, in order to solve the problem that the existing single-unit MEMS-IMU error model ignores the statistical correlation between measurement channels in array applications, which leads to the inability of simple arithmetic averaging fusion methods to eliminate common error components and structural system deviations.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a MEMS-IMU array measurement system based on a central and staggered double-ring configuration, the system comprising: Rigid measuring substrate; N MEMS-IMU units are fixedly mounted on the rigid measurement substrate, forming a center-staggered double-ring physical configuration with spatial isotropic characteristics. One MEMS-IMU unit serves as the central reference unit, positioned at the center of the rigid measurement substrate. The remaining MEMS-IMU units are divided into two groups, respectively arranged on an inner ring and an outer ring centered on the central reference unit. The radius of the inner ring is... The radius of the outer ring is And satisfy The MEMS-IMU units deployed on the inner and outer rings are evenly distributed on the circumference, and the units on the inner and outer rings are staggered at the corner positions. The main controller is used to provide a synchronous sampling clock for all MEMS-IMU units and to acquire the raw measurement data of each unit; The data processing unit is used to execute the collaborative output algorithm, which processes the collected raw measurement data based on the observation model and error model corresponding to the center-staggered double-ring physical configuration, and outputs the fused inertial measurement data.

[0008] Furthermore, a preferred embodiment is proposed, wherein N=7, and three MEMS-IMU units are evenly distributed on both the inner and outer rings, with the units on the inner and outer rings differing by 120 degrees in angular position.

[0009] Furthermore, a preferred embodiment is proposed, wherein the main controller includes: Synchronous clock generation circuit, used to generate the main external clock signal; An impedance matching network is connected to the output of the synchronous clock generation circuit to perform impedance matching on the main external clock signal, so as to suppress signal reflection and edge ringing, and distribute the matched synchronous clock signal to all MEMS-IMU units. The data acquisition module is used to read the measurement data of all MEMS-IMU units in parallel via DMA when triggered by the synchronization clock signal.

[0010] Based on the same inventive concept, the present invention also proposes a cooperative output method, which is implemented based on the array measurement system described in any one of the above-mentioned methods, and the method includes: Construct an observation model corresponding to the central-staggered double-ring physical configuration, the observation model will... Observations of MEMS-IMU cells at time k Represented as a system state vector Linear functions: ,in The observation matrix is ​​related to the spatial location of the sensor. It should include at least the angular velocity ω to be estimated, the global common bias, and the spatial gradient mode. To observe noise; Establish a three-level error model of public-structure-individual, and then... The equivalent zero bias error of each MEMS-IMU unit Decomposed into:

[0011] in, This represents the global common bias acting on the entire array; This represents a structural perturbation term that is highly correlated with the spatial distribution of the array; A piecewise constant weighting function related to the spatial location of the MEMS; This represents the individual independent residual term of each MEMS unit; Based on the observation model corresponding to the center-interlaced double-ring physical configuration and the three-layer error model, the system state-space equation is constructed. Based on the Kalman filter framework, the observation model is used to perform online recursive estimation of the state in the system state space equation. The recursive estimation includes a measurement update step, which is used to correct the predicted state based on the array measurement values ​​at the current time. Based on the state estimation results, the estimated error components are subtracted from the average observation signals of all MEMS-IMU units to generate a collaborative fusion output.

[0012] Furthermore, a preferred method is proposed, wherein the weighting function For a piecewise constant function, the weight value for a cell located in the inner ring is... For the units arranged in the outer ring, their weight value is ,and and The inequality is used at the model level to distinguish the differences in error correlation between inner and outer loop units due to their different physical locations.

[0013] Furthermore, a preferred method is proposed, in which the steps of constructing the state-space equations of the system include: Construct a system state vector X, wherein X includes at least N individual independent residual terms, the global common deviation and its rate of change, and the structural disturbance term; Assign a second-order dynamic model to the global common deviation, assign a first-order Gauss-Markov process model to the structural disturbance term, and assign a random walk model to the individual independent residual term; Based on the dynamic model assigned to each error component, a state transition matrix A with a block diagonal structure and a process noise covariance matrix Q are constructed; at the same time, an equivalent observation matrix in non-identity matrix form is constructed.

[0014] Furthermore, a preferred method is proposed, wherein the equivalent observation matrix H is in the form of: ,in, Let be an N-dimensional identity matrix, where 1 represents an N-dimensional column vector of all 1s and 0 represents an N-dimensional column vector of all 0s. It is an N-dimensional column vector composed of the weight function values ​​of each MEMS-IMU unit.

[0015] Furthermore, a preferred method is proposed, wherein the generation of collaborative fusion output includes: Calculate the collaborative estimation bias :

[0016] in, Equivalent observation matrix The The row is used to map the system state estimation vector to the first row. The estimation error components corresponding to each MEMS-IMU unit; for The system state estimation vector obtained by recursive estimation using Kalman filtering at time 1; This represents the total number of MEMS-IMU units.

[0017] Generate fused output:

[0018] in, For the first Each MEMS-IMU unit in The original measurement value at time.

[0019] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a cooperative output method according to any of the preceding claims.

[0020] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a cooperative output method as described in any one of the above.

[0021] Compared with the prior art, the beneficial effects of the present invention are: Traditional planar rectangular array sensors suffer from uneven distribution of directional sensitive axes, leading to anisotropy in the system's sensitivity to the movement of the carrier in different directions. This results in poor conditional numbers in the observation matrix, and parameter estimation is prone to coupling and ill-conditioned problems. While three-dimensional symmetrical layouts theoretically pursue isotropy, they introduce uncontrollable assembly errors and thermal inconsistencies, undermining the fundamental assumptions of error modeling. This invention proposes a specific quasi-three-dimensional geometric configuration: a center-staggered double-ring structure. This configuration does not pursue absolute spatial symmetry in theory, but rather maximizes isotropy in the geometric sense of information within an engineering-feasible planar layout through a precise geometric relationship between a central reference point and the staggered, uniformly distributed points of the inner and outer rings. The core of this design lies in the fact that the Fisher information matrix, representing the identifiability of parameters, can be transformed into a diagonal matrix. This characteristic allows the estimated angular velocity parameter to be naturally decoupled from the spatial gradient error parameter caused by substrate deformation, temperature gradient, etc., in a statistical sense, fundamentally avoiding mutual interference between parameter estimates.

[0022] Traditional array fusion algorithms typically implicitly assume that the errors of each sensor are independent or simply correlated, using arithmetic mean or covariance weighting. This fails to handle common and structural errors with strong spatial correlation among sensors, caused by overall power fluctuations and PCB board bending. These errors are not suppressed during averaging but are instead retained as systematic biases. This invention breaks through the traditional model that treats sensor zero bias as a single random process, proposing a three-layer error physical model of common-structural-individual. Starting from the physical causes, this model explicitly decomposes the total zero bias of the sensors into global common bias, structural perturbation, and individual independent residuals. By directly encoding the physical geometric information of the array into the mathematical model through a position weight function, subsequent algorithms can utilize prior geometric constraints such as the absence of structural error in the central unit and the difference in structural error coefficients between the inner and outer rings to explicitly estimate and separate these three types of errors.

[0023] Existing methods often simply apply single-sensor dynamic models to arrays or use static weighting, ignoring the fundamental differences in the temporal evolution characteristics of error components at different levels. This invention, based on a three-layer error model, matches differentiated dynamic evolution models to error components with different physical characteristics and constructs a unified, hierarchical block diagonal state space model.

[0024] Within this framework, recursive estimation is performed using Kalman filtering, which enables tracking of the dynamic changes in error in the time dimension. At the same time, geometric constraints are used to decouple different error components in the spatial dimension, making it a true spatiotemporal joint dynamic optimal estimation.

[0025] Due to its unique geometric configuration, the information matrix is ​​diagonalized, resulting in optimal identifiability of the parameters to be estimated and the estimated variance approaching the theoretical lower bound. Simultaneously, the parameter decoupling characteristic significantly improves the numerical stability of the estimation process, exhibiting stronger robustness under highly dynamic or adverse observation conditions.

[0026] Unlike traditional mean filtering, which can only suppress independent noise, the three-layer model of this invention can explicitly estimate and subtract two types of systematic errors: global common bias and structural perturbation. This fully releases the theoretical potential of array redundancy information, resulting in a substantial improvement in fusion accuracy compared to simple mean fusion, with an actual accuracy improvement of 66.36%, surpassing the accuracy of traditional fusion methods. Attached Figure Description

[0027] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This invention relates to a MEMS-IMU array measurement system based on a central and staggered double-ring configuration. Figure 2 This is a schematic diagram of the spatial geometric configuration and physical arrangement described in this invention; Figure 3 This is a flowchart of the collaborative output and decoupling method described in this invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0029] Implementation Method 1: This implementation method addresses the problem that existing single-unit MEMS-IMU error models neglect the statistical correlation between measurement channels in array applications, leading to the inability of simple arithmetic averaging fusion methods to eliminate common error components and structural system biases. It proposes a MEMS-IMU array measurement system based on a central and staggered dual-ring configuration. The system includes: Rigid measuring substrate; N MEMS-IMU units are fixedly mounted on the rigid measurement substrate, forming a center-staggered double-ring physical configuration with spatial isotropic characteristics. One MEMS-IMU unit serves as the central reference unit, positioned at the center of the rigid measurement substrate. The remaining MEMS-IMU units are divided into two groups, respectively arranged on an inner ring and an outer ring centered on the central reference unit. The radius of the inner ring is... The radius of the outer ring is And satisfy The MEMS-IMU units deployed on the inner and outer rings are evenly distributed on the circumference, and the units on the inner and outer rings are staggered at the corner positions. The main controller is used to provide a synchronous sampling clock for all MEMS-IMU units and to acquire the raw measurement data of each unit; The data processing unit is used to execute the collaborative output algorithm, which processes the collected raw measurement data based on the observation model and error model corresponding to the center-staggered double-ring physical configuration, and outputs the fused inertial measurement data.

[0030] In this embodiment, N=7, and three MEMS-IMU units are evenly distributed on both the inner and outer rings, with the units on the inner and outer rings differing by 120 degrees in angular position.

[0031] In this embodiment, the main controller includes: Synchronous clock generation circuit, used to generate the main external clock signal; An impedance matching network is connected to the output of the synchronous clock generation circuit to perform impedance matching on the main external clock signal, so as to suppress signal reflection and edge ringing, and distribute the matched synchronous clock signal to all MEMS-IMU units. The data acquisition module is used to read the measurement data of all MEMS-IMU units in parallel via DMA when triggered by the synchronization clock signal.

[0032] The relationship between the existing layout and the accuracy of the final parameter estimation is ambiguous, and the design has a certain degree of blindness. Theoretically, a 3D layout can optimize the information matrix, but this sacrifices engineering feasibility and consistency with the error environment. This implementation method, through a specific design of a central and staggered double ring, directly ensures that the structure of the observation matrix satisfies the key condition of diagonalization of the Fisher information matrix without introducing 3D assembly complexity.

[0033] Implementation Method Two: This implementation method proposes a collaborative output method, which is implemented based on the array measurement system described in Implementation Method One. The method includes: On the same rigid body measurement base plate, set One MEMS-IMU unit (in this embodiment) Its physical location is configured as follows: a MEMS-IMU unit is placed at the center as the common-mode reference of the array, and its position vector in the local array coordinate system is set to... With this central reference point as the center, respectively... and Construct an inner and outer ring with a radius of , and Three MEMS-IMU units are evenly distributed on both the inner and outer rings, with the inner and outer rings located 120 degrees apart at their angular positions, forming an alternating distribution.

[0034] For the spatial location of any sensor node Under the condition of uniform angular distribution, the following must be strictly satisfied: .

[0035] in, For the first The MEMS-IMU cells on each ring are relative to the array coordinate system. Polar angle of the axis, For the first The corner positions of each MEMS-IMU unit are at Normalized projection along the axial direction, For the first The corner positions of each MEMS-IMU unit are at Normalized projection along the axis.

[0036] This geometric property makes the first position moments of the array itself mean zero, and the second position moments degenerate into a scalar multiple of the identity matrix, thereby ensuring that the array has a consistent gradient sensing capability in orthogonal directions, providing a rigid geometric constraint basis for the decoupling of subsequent parameter estimation.

[0037] Construct an observation model corresponding to the central-staggered double-ring physical configuration, the observation model will... Observations of MEMS-IMU cells at time k Represented as a system state vector Linear functions: ,in The observation matrix is ​​related to the spatial location of the sensor. It should include at least the angular velocity ω to be estimated, the global common bias, and the spatial gradient mode. To observe noise; Establish an array equivalent observation model for spatial gradient decoupling: Under the same rigid body motion, all sensors in the array observe the same physical quantity. Structural error terms related to spatial position are extracted. And perform a first-order Taylor expansion on it under the local plane approximation:

[0038] in, For spatial gradient modes that are linearly dependent on the position vector, Incorporate into global common deviation Substituting the above expansion into the measurement equation, a vector containing the parameters to be estimated is constructed. linear form ,in, for The common angular velocity components of the array to be estimated at any given time. This is the equivalent global common deviation after incorporating the zero-order spatial error term; The structural error field in the array coordinate system First-order spatial gradient along the axis; The structural error field in the array coordinate system The first-order spatial gradient along the axis. Due to the central reference node. The observations at this location do not contain spatial gradient terms, and when used in conjunction with the two-node point, they weaken the coupling between the common term and the gradient term. Due to triple rotational symmetry, its corresponding Fisher information matrix... This is strictly transformed into a diagonal structure. The symmetrical distribution of the central sensor and the ring array completely decouples the angular velocity estimation and spatial gradient estimation in the sense of Fisher information, fundamentally avoiding statistical coupling between parameter estimates. Furthermore, the outer ring contributes approximately four times more to the spatial gradient information than the inner ring, effectively boosting the diagonal terms corresponding to the gradient parameters in the information matrix.

[0039] Breaking through the limitation of traditional single-sensor error models that treat zero bias as a single random process, the first... The equivalent zero bias error of each MEMS cell In terms of physical causes, it can be explicitly decomposed into three dimensions, specifically: Establish a three-level error model of public-structure-individual, and then... The equivalent zero bias error of each MEMS-IMU unit Decomposed into:

[0040] in, This represents the global common bias affecting the entire array (originating from overall power drift or system-level temperature drift). This represents structural perturbation terms that are highly correlated with the spatial distribution of the array (originating from PCB package stress or temperature gradient). The piecewise constant weighting function is related to the spatial location of the MEMS, with a value of 0 for the center node and values ​​of 0 for the inner and outer nodes respectively. and This allows for the differentiation of the correlation between inner and outer circular ring errors at the model level; This represents the individual independent residual term of each MEMS unit; Based on the observation model corresponding to the center-interlaced double-ring physical configuration and the three-layer error model, the system state-space equation is constructed. Based on the Kalman filter framework, the observation model is used to perform online recursive estimation of the state in the system state space equation. The recursive estimation includes a measurement update step, which is used to correct the predicted state based on the array measurement values ​​at the current time. Based on the state estimation results, the estimated error components are subtracted from the average observation signals of all MEMS-IMU units to generate a collaborative fusion output.

[0041] In this embodiment, the weighting function For a piecewise constant function, the weight value for a cell located in the inner ring is... For the units arranged in the outer ring, their weight value is ,and and The inequality is used at the model level to distinguish the differences in error correlation between inner and outer loop units due to their different physical locations.

[0042] In this embodiment, the steps for constructing the system state-space equations include: Construct a system state vector X, wherein X includes at least N individual independent residual terms, the global common deviation and its rate of change, and the structural disturbance term; Assign a second-order dynamic model to the global common deviation, assign a first-order Gauss-Markov process model to the structural disturbance term, and assign a random walk model to the individual independent residual term; Based on the dynamic model assigned to each error component, a state transition matrix A with a block diagonal structure and a process noise covariance matrix Q are constructed; at the same time, an equivalent observation matrix in non-identity matrix form is constructed.

[0043] This implementation method addresses global common deviations. A second-order dynamic system is used to describe its strong time dependence and inertial smoothing characteristics; structural disturbance errors are also considered. A first-order Gauss-Markov process is used to model its slow time-varying correlation; individual residual terms are analyzed. Preserve the slow random walk property.

[0044] Based on this, a block diagonal state transition matrix exhibiting a "center-ring layer-individual" hierarchical structure is constructed. and process noise covariance matrix The equation of state and the array geometry form a strict one-to-one correspondence at the mathematical model level.

[0045] The multi-sensor observations must strictly correspond to the same discrete time. rigid body motion state Based on the derivation of rigid body kinematics, the sampling timing error... Under highly dynamic motion conditions, equivalent inertial measurement errors (including angular velocity error and specific force error) related to the dynamic derivative of the carrier will be introduced:

[0046] in, This represents the rate of change of a real physical quantity.

[0047] Therefore, the hardware synchronous clock link design of the array system must eliminate asymmetric transmission delay and ensure that spurious spatial gradient components caused by time asynchrony are suppressed below the equivalent individual residual level, so as to guarantee the effectiveness of the array equivalent observation model and the three-layer error model in pure physical space observation.

[0048] Furthermore, the equivalent observation matrix H is in the form of ,in, Let be an N-dimensional identity matrix, where 1 represents an N-dimensional column vector of all 1s and 0 represents an N-dimensional column vector of all 0s. It is an N-dimensional column vector composed of the weight function values ​​of each MEMS-IMU unit.

[0049] In this embodiment, generating the collaborative fusion output includes: Calculate the collaborative estimation bias :

[0050] in, Equivalent observation matrix The The row is used to map the system state estimation vector to the first row. The estimation error components corresponding to each MEMS-IMU unit; for The system state estimation vector obtained by recursive estimation using Kalman filtering at time 1; This represents the total number of MEMS-IMU units.

[0051] Generate fused output:

[0052] in, For the first Each MEMS-IMU unit in The original measurement value at time.

[0053] Traditional methods fail to distinguish between common errors and structural errors, either ignoring their correlation leading to biased estimations or using coarse models that cannot accurately characterize their spatiotemporal evolution. This implementation combines a three-layer error model, a matched dynamic equation, and the specific geometry of the array. The geometric layout provides the physical basis for spatially distinguishing common and structural errors; the differentiated dynamic model provides the mathematical tool for temporally distinguishing their evolutionary patterns. These two elements work collaboratively through a state-space model, enabling the Kalman filter algorithm to simultaneously and independently estimate the time-varying common bias and spatial gradient error. This deep integration of a physically interpretable model and an optimal estimation algorithm solves the problem of previous algorithms being disconnected from physical reality.

[0054] Most existing algorithm studies neglect the non-ideal characteristics of hardware. In practical systems, minute sampling time asynchrony can be misidentified as spatial gradients under high dynamic conditions, thus contaminating the model and causing algorithm failure. This implementation recognizes the premise of the aforementioned theoretical model and proposes targeted hardware synchronization constraints as an integral part of the method. Through specific hardware designs such as hierarchical power supply, star routing, and impedance-matched clock distribution, strict consistency of sampling times is ensured, severing the coupling path from time asynchrony error to spatial gradient estimation at the physical source. This combination of high-precision back-end algorithms and highly consistent front-end hardware design ensures the effectiveness and robustness of the entire technical solution in engineering applications.

[0055] Implementation Method 3, see below Figures 1 to 3 This embodiment describes a complete application example of the collaborative output method described in Embodiment 2, including: To ensure the physical effectiveness of the backend spatial correlation algorithm, the equivalent acceleration error caused by sampling timing errors must be eliminated at the hardware physical layer. This embodiment employs a tiered power supply and a strict hardware-level clock synchronization strategy, as detailed below: Step 1: Construct a two-stage LDO hierarchical power isolation network.

[0056] The system's external power supply is introduced from the USB Type-C interface (5V), first stepped down to 3.3V by a primary voltage regulator (such as an LDO) to power non-sensitive peripherals (such as the CH340E USB-to-serial chip). Subsequently, a two-stage high-performance precision LDO is used to independently power the main controller (STM32L431RCT6) and a seven-MEMS sensor array arranged in a "center-double-ring" configuration. On the printed circuit board (PCB) layout, the sensor power supply strictly adopts a symmetrical star topology, and a filter network consisting of large-capacity capacitors and multi-stage decoupling capacitors is configured at key nodes to suppress high-speed switching noise of the MCU, provide a clean 3.3V (AVDD) reference, and eliminate common-mode fluctuations caused by power supply ripple.

[0057] Step 2: Implement a hardware clock synchronization link based on impedance matching.

[0058] To prevent the clock signal from being misinterpreted as a spatial physical gradient by the algorithm due to microsecond-level delays during multi-node transmission, a main external clock (PWM signal) with a frequency of 32.768kHz and a duty cycle of 50% is generated by the main controller's internal timer (TIM2). To avoid waveform distortion caused by multiple loads disrupting sampling alignment, measures are taken considering the low output impedance of the buffer and the characteristic impedance of the PCB microstrip line. To address signal reflection and ringing issues caused by mismatch, a matching resistor is connected in series at the drive output of the clock buffer to achieve critical impedance matching. This physical design suppresses clock edge overshoot and ringing, ensuring that the sampling times of all MEMS sensors are strictly consistent on a nanosecond scale, thus cutting off the coupling path from time error to spatial gradient estimation at the hardware level.

[0059] Step 3: Perform DMA-based non-blocking data acquisition.

[0060] The main controller's timer periodically generates sampling trigger signals, using the SPI bus combined with DMA technology to read raw data from seven MEMS sensors in parallel via independent CS lines. After the DMA completes its callback, the data packets are precisely timestamped in SRAM and binary formatted. Finally, they are transferred in batches to the host computer via USART DMA, completely avoiding microsecond-level timing jitter caused by nested software interrupts.

[0061] After acquiring the raw multi-channel array data with strict time consistency, the host computer or embedded DSP executes the collaborative output algorithm. This algorithm follows a rigorous forward derivation based on the underlying physical mechanism, without relying on inverse fitting of standard results, and specifically includes the following calculation steps: Step 1: Initialize system and sensor parameters.

[0062] Set array sampling frequency Hz. Intrinsic noise parameters of individual MEMS devices are extracted based on Allan variance analysis, and the measurement noise variance is initialized. Individual random walk noise variance Common deviation process noise and structural error process noise .

[0063] Step 2: Spatial configuration and weight vector design.

[0064] against The “center-inner ring 3-outer ring 3” configuration is used to construct a spatial weight vector. Since the central unit does not contain spatial gradients, its weight is set to 0; the inner loop weights are set to... The outer ring weight is set as The model explicitly characterizes the differences in error correlation between different loops caused by physical factors such as encapsulation stress and temperature gradient at the underlying level.

[0065] Step 3: Construct the higher-order dynamic state space matrix.

[0066] Construction dimension State vector:

[0067] Among them, the former The term represents the individual residuals, and the last three terms are the global common deviation, the rate of change of the common deviation (second-order dynamic modeling), and the structural error (first-order Markov modeling), respectively. Based on this, stability control parameters are set. Correlation control parameters Construct the state transition matrix and the process noise covariance matrix in block diagonal form Simultaneously, an equivalent observation matrix in non-identity matrix form is constructed. This allows for a precise description of the coupling effect of error terms at each level on the observed physical quantities.

[0068] Step 4: Perform Kalman filter time update. Use the system's high-order dynamic model for state prediction.

[0069] Predicted state vector :

[0070] in, This is the system state estimate vector obtained by Kalman filtering at the previous time step.

[0071] Prediction error covariance matrix :

[0072] in, Let be the state estimation error covariance matrix of the previous time step.

[0073] Step 5: Perform Kalman filter measurement update.

[0074] Introducing the array measurement vector at the current moment Calculate the Kalman gain and correct the state.

[0075] Calculate the Kalman gain:

[0076] in, To measure the noise covariance matrix.

[0077] Update the state vector:

[0078] Update the error covariance matrix:

[0079] Through the above recursion, the system achieves real-time stripping and joint estimation of common bias, structural disturbances, and individual random walks in the spatiotemporal dimensions.

[0080] Step Six: Generate Co-fusion Output. Using the state estimation results, accurately identified comprehensive error terms are removed from the average observations of the array to generate the final high-precision angular velocity or acceleration output.

[0081] Calculation of co-estimation bias:

[0082] Fusion output generation:

[0083] Through comparative simulation and static experimental verification, the collaborative output method proposed in this embodiment demonstrates significant effectiveness. Experimental data shows that, while preserving the dynamic characteristics of the original measurement signal, the residual error after collaborative fusion remains stable near the zero axis, with a significantly reduced fluctuation range. Specifically, the root mean square error (RMSE) of the central sensor unit is 0.4128, the RMSE of the traditional array arithmetic mean method is 0.1855, while the RMSE of the collaborative fusion model generated using the above steps of this invention is reduced to 0.0624. Compared to a single sensor, the accuracy is improved by 84.88%; compared to traditional arithmetic mean fusion, the accuracy is improved by 66.36%. These results fully verify the effectiveness and robustness of this system in suppressing long-term zero-bias drift and filtering out complex high-frequency structural noise.

[0084] Implementation Method 4: This implementation method proposes a computer device, including a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a cooperative output method according to Implementation Method 2.

[0085] Implementation Method 5: This implementation method provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a cooperative output method as described in any one of Implementation Method 2.

[0086] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0088] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

Claims

1. A MEMS-IMU array measurement system based on a central and staggered double torus configuration, characterized by, The system includes: Rigid measuring substrate; N MEMS-IMU units are fixedly mounted on the rigid measurement substrate, forming a center-staggered double-ring physical configuration with spatial isotropic characteristics. One MEMS-IMU unit serves as the central reference unit, positioned at the center of the rigid measurement substrate. The remaining MEMS-IMU units are divided into two groups, respectively arranged on an inner ring and an outer ring centered on the central reference unit. The radius of the inner ring is... The radius of the outer ring is And satisfy The MEMS-IMU units deployed on the inner and outer rings are evenly distributed on the circumference, and the units on the inner and outer rings are staggered at the corner positions. The main controller is used to provide a synchronous sampling clock for all MEMS-IMU units and to acquire the raw measurement data of each unit; The data processing unit is used to execute the collaborative output algorithm, which processes the collected raw measurement data based on the observation model and error model corresponding to the center-staggered double-ring physical configuration, and outputs the fused inertial measurement data.

2. The MEMS-IMU array measurement system based on a central and staggered double-ring configuration according to claim 1, characterized in that, The number N is 7. Three MEMS-IMU units are evenly distributed on both the inner and outer rings, and the units on the inner and outer rings are 120 degrees apart at their angular positions.

3. The MEMS-IMU array measurement system based on a central and staggered double-ring configuration according to claim 1, characterized in that, The main controller includes: Synchronous clock generation circuit, used to generate the main external clock signal; An impedance matching network is connected to the output of the synchronous clock generation circuit to perform impedance matching on the main external clock signal, so as to suppress signal reflection and edge ringing, and distribute the matched synchronous clock signal to all MEMS-IMU units. The data acquisition module is used to read the measurement data of all MEMS-IMU units in parallel via DMA when triggered by the synchronization clock signal.

4. A collaborative output method, characterized in that, The method is implemented based on the array measurement system according to any one of claims 1 to 3, and the method includes: Construct an observation model corresponding to the central-staggered double-ring physical configuration, the observation model will... Each MEMS-IMU unit in Observations at time Represented as a system state vector Linear functions: ,in The observation matrix is ​​related to the spatial location of the sensor. It should include at least the angular velocity ω to be estimated, the global common bias, and the spatial gradient mode. To observe noise; Establish a three-level error model of public-structure-individual, and then... The equivalent zero bias error of each MEMS-IMU unit Decomposed into: in, This represents the global common bias acting on the entire array; This represents a structural perturbation term that is highly correlated with the spatial distribution of the array; A piecewise constant weighting function related to the spatial location of the MEMS; This represents the individual independent residual term of each MEMS unit; Based on the observation model corresponding to the center-interlaced double-ring physical configuration and the three-layer error model, the system state-space equation is constructed. Based on the Kalman filter framework, the observation model is used to perform online recursive estimation of the state in the system state space equation. The recursive estimation includes a measurement update step, which is used to correct the predicted state based on the array measurement values ​​at the current time. Based on the state estimation results, the estimated error components are subtracted from the average observation signals of all MEMS-IMU units to generate a collaborative fusion output.

5. The collaborative output method according to claim 4, characterized in that, The weighting function For a piecewise constant function, the weight value for a cell located in the inner ring is... For the units arranged in the outer ring, their weight value is ,and and The inequality is used at the model level to distinguish the differences in error correlation between inner and outer loop units due to their different physical locations.

6. The collaborative output method according to claim 4, characterized in that, The steps for constructing the state-space equations of the system include: Construct a system state vector X, wherein X includes at least N individual independent residual terms, the global common deviation and its rate of change, and the structural disturbance term; Assign a second-order dynamic model to the global common deviation, assign a first-order Gauss-Markov process model to the structural disturbance term, and assign a random walk model to the individual independent residual term; Based on the dynamic model assigned to each error component, a state transition matrix A with a block diagonal structure and a process noise covariance matrix Q are constructed; at the same time, an equivalent observation matrix in non-identity matrix form is constructed.

7. A collaborative output method according to claim 6, characterized in that, The equivalent observation matrix H is in the form of ,in, Let be an N-dimensional identity matrix, where 1 represents an N-dimensional column vector of all 1s and 0 represents an N-dimensional column vector of all 0s. It is an N-dimensional column vector composed of the weight function values ​​of each MEMS-IMU unit.

8. The collaborative output method according to claim 4, characterized in that, The generation of collaborative fusion output includes: Calculate the collaborative estimation bias : in, Equivalent observation matrix The The row is used to map the system state estimation vector to the first row. The estimation error components corresponding to each MEMS-IMU unit; for The system state estimation vector obtained by recursive estimation using Kalman filtering at time 1; This represents the total number of MEMS-IMU units. Generate fused output: in, For the first Each MEMS-IMU unit in The original measurement value at time.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a cooperative output method according to any one of claims 4-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a cooperative output method as described in any one of claims 4-8.

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