Pedestrian Autonomous Localization Method Based on Inertial Sensors in Complex Environments

Abstract

Pedestrian autonomous positioning method based on inertial sensors in complex environments. 1) Considering the corresponding parameters of a single gyroscope, determine the number of redundant inertial sensors. 2) After determining the number of inertial sensors, study the configuration scheme of the redundant inertial sensors to obtain an inertial sensor configuration scheme that can simultaneously optimize the navigation performance and fault detection and isolation performance of the pedestrian navigation system. 3) Use a data fusion algorithm to optimally fuse the data measured by the inertial sensor configuration scheme obtained in steps 1 and 2. 4) Input the fused inertial motion information obtained in step 3 into the inertial navigation system calculation module to calculate various motion parameters of the pedestrian. The present invention is based on a microelectromechanical system inertial measurement unit, realizes high-precision autonomous positioning of pedestrians in complex environments, and adopts the redundancy technology of inertial sensors to solve the problem that the noise of inertial sensors accumulates multiple times, resulting in rapid divergence of the trajectory.

Description

Technical Field

[0001] The present invention belongs to the field of pedestrian autonomous positioning of inertial sensors, and specifically relates to a method for pedestrian autonomous positioning based on inertial sensors in complex environments. Background Art

[0002] Intelligent location services have become an important research direction at home and abroad today, playing a crucial role in fields such as artificial intelligence, emergency rescue, and smart cities. The Global Navigation Satellite System (GNSS) can provide precise positioning capabilities and can basically meet the needs for high-precision position information in outdoor open scenarios. However, in indoor environments such as warehouses, inside high-rise buildings, and basements, GNSS is difficult to complete positioning due to the obstruction of satellite signals and the influence of multipath effects. Therefore, researching indoor positioning technologies that do not rely on GNSS has high practical significance.

[0003] Currently, most indoor positioning uses technologies such as radio frequency identification (RFID), ZigBee, Bluetooth, Ultra-wideband (UWB), Ultrasound, Wi-Fi, and pseudolites. These indoor positioning solutions are all wireless positioning systems based on certain infrastructure, and various sensors need to be installed in advance to assist in positioning. Special personnel are also required for maintenance later, which requires a large amount of manpower and material resources and has high requirements for the real environment. Therefore, an independent positioning system that does not require the prior deployment of complex equipment has become an urgent need.

[0004] The Inertial Navigation System (INS) does not need to receive external information, has strong concealment, does not emit any signals to the outside world, and is not restricted by weather conditions. It can operate all-weather globally and achieve completely independent navigation. Since inertial navigation mainly relies on its own inertial sensors and does not depend on any external information. The Inertial Measurement Unit (IMU) based on Micro Electro Mechanical System (MEMS) has the advantages of small size, simple structure, and low cost, and has been widely used in pedestrian inertial navigation systems. The pedestrian inertial navigation system can provide the position and direction (roll, pitch, yaw) of a pedestrian. However, long-term operation will cause the noise of the inertial sensors to accumulate multiple times, resulting in rapid divergence of the trajectory and reducing the positioning accuracy of the pedestrian inertial navigation system. Therefore, improving the accuracy of inertial sensors is very important for the pedestrian inertial navigation system. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a pedestrian autonomous positioning method based on inertial sensors in a complex environment. To achieve high-precision autonomous positioning of pedestrians in a complex environment, a Micro ElectroMechanical System (MEMS)-based inertial measurement unit is used. To solve the problem that the noise of inertial sensors accumulates multiple times, resulting in rapid divergence of the trajectory, the redundancy technology of inertial sensors is adopted.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A pedestrian autonomous positioning method based on inertial sensors in a complex environment includes the following steps:

[0008] Step 1: Considering the mean time between failures (MTBF), relative MTBF, relative MTBF change amount of a single gyroscope, the volume, weight, and cost of the pedestrian inertial navigation system, determine the number of redundant inertial sensors;

[0009] Step 2: On the basis of determining the number of inertial sensors in Step 1, through research on the configuration scheme of redundant inertial sensors, an inertial sensor configuration scheme that can simultaneously optimize the navigation performance and fault detection and isolation performance of the pedestrian navigation system is obtained.

[0010] Step 3: Optimally fuse the data measured in Step 1 and Step 2 through a data fusion algorithm to achieve the purpose of improving the accuracy of the pedestrian inertial navigation system;

[0011] In the optimal fusion algorithm based on the standard Kalman filter algorithm, replace the standard Kalman filter algorithm with an adaptive filter algorithm with a system noise estimator, that is, form an adaptive optimal fusion algorithm;

[0012] Adopt an enhanced adaptive optimal fusion algorithm, which introduces a fading factor into the prediction process of the covariance matrix, improves the ability to cope with state mutations, suppresses the divergence of the filter over time to a certain extent, and improves the accuracy of the filtering algorithm;

[0013] Step 4: Input the fused inertial motion information obtained in Step 3 into the inertial navigation system solution module to calculate various motion parameters of the pedestrian (including three-dimensional attitude, speed, and position information).

[0014] As a further improvement of the present invention, the specific steps of Step 1 are as follows:

[0015] In the pedestrian inertial navigation system, at least three gyroscopes or accelerometers are required to measure the angular rate or acceleration in the inertial space. Assume the same reliability R econfigured for n inertial devices, the system reliability R a is

[0016]

[0017] Therefore, the MTBF of the entire pedestrian inertial navigation system is expressed as

[0018]

[0019] By calculation, the MTBF of a single gyroscope is 1 / λ. The more the number of inertial sensors, the higher the reliability of the inertial navigation system. By calculation, the MTBF of a single gyroscope is 1 / λ, and the MTBF of a non-redundant system with three inertial sensors installed along the orthogonal coordinate system 3 is 1 / 3λ. Define:

[0020]

[0021]

[0022]

[0023] where is the MTBF of the redundant navigation system formed by the inclined placement of inertial devices n and the MTBF of the non-redundant system 3 ratio, also known as the relative MTBF; is the change amount of the relative MTBF; F is called the reliability performance index of the inertial navigation system;

[0024] By changing the number of inertial devices, calculate respectively and the reliability performance index F.

[0025] As a further improvement of the present invention, the specific steps of step 2 are as follows:

[0026] The inertial sensor uses a redundant inertial sensor with 6 identical sensors. When the redundant inertial sensor with 6 identical sensors adopts the regular dodecahedron configuration method, the navigation performance and the fault detection and isolation performance FDI of the inertial navigation system reach the optimal at the same time;

[0027] In this configuration scheme, at least three sensors are required to measure the motion information of the X, Y, and Z axes. The corresponding redundant configuration matrix in this scheme is:

[0028]

[0029] In the formula, α = 31.72°, then the specific configuration matrix is:

[0030]

[0031] When the measurement matrix of the inertial navigation system satisfies the following equation, it is considered that the navigation performance of the navigation system and the FPI reach the optimal;

[0032]

[0033] where h i is the row vector of the redundancy configuration matrix H, and the redundancy configuration matrix H satisfies

[0034] From formula (8), it can be obtained that when the dodecahedron configuration method is adopted, the value of H op is 0.4472. Therefore, when the redundant navigation system with 6 homogeneous sensors adopts the dodecahedron configuration method, the navigation performance of the system and the fault detection and isolation performance FDI reach the optimal at the same time.

[0035] As a further improvement of the present invention, the specific steps of the adaptive optimal fusion algorithm in step 3 are as follows:

[0036] Project the output vector of the redundant inertial sensor onto the left null space of the configuration matrix to obtain the redundant observation of the fusion algorithm, and the maximum utilization of the performance of each sensor can be realized through the optimal estimation of the redundant observation;

[0037] In this pedestrian inertial navigation system, the error of the inertial sensor is selected as the state vector, and the output of the inertial sensor is selected as the measured quantity, that is

[0038] X = [x 1 x 2 …x n T

[0039] Z = [y 1 y 2 …y n T (9)

[0040] where x i represents the error of the i-th inertial sensor, and y i represents the measured output of the i-th inertial sensor;

[0041] Therefore, the state equation and the observation equation of the system are expressed as:

[0042] X k = A k / k-1 X k-1 + B k / k-1 W k-1 (10)

[0043] Z k = C​​k X k +Hu k +V k (11)

[0044] In the formula, A k / k-1 , B k / k-1 , C k are coefficient matrices, H is an installation matrix, W k-1 and V k are noise matrices;

[0045] Let where T k H = 0, and T k is called the left null space basis of H, is the orthogonal complement space of T k , that is Left-multiply T by equation (11) to get:

[0046] TZ k = TC k X k + THu k + TV k = TC k X k + TV k (12)

[0047] Therefore, the system model is expressed as

[0048]

[0049] Estimate this model using a Kalman filter, and the recurrence formula is as follows:

[0050] One-step state prediction:

[0051]

[0052] One-step state prediction mean square error:

[0053]

[0054] Filter gain:

[0055] K k = P k / k-1 (TC k ) T ((TC k )P k / k-1 (TC k ) T + R k ) -1 (16)

[0056] State estimation:

[0057]

[0058] Mean square error of state estimation:

[0059] P k =(I - K k TC k )P k / k-1 (18)

[0060] In the process of updating the Kalman filter, the initial state quantity X 0 and the initial variance P 0 need to be given first. Equations (14) and (15) are called time updates; the processes included in equations (16), (17) and (18) are called measurement updates. After the time update is completed, it is detected whether there is measurement information. If there is, measurement update and state estimation are performed to obtain the optimal estimation output; otherwise, the measurement information is used as the optimal estimation output. According to the Kalman filter, can be solved. In equation (14), V k satisfies the Gaussian distribution, that is, V k ~(0, R k ), and the redundancy configuration matrix H is full rank. Therefore, u k can be obtained through weighted least squares estimation, and

[0061]

[0062] As a further improvement of the present invention, in step 3, by combining the adaptive filtering algorithm with the Huber generalized maximum likelihood estimation method, the problem of filter model distortion caused by non-Gaussian measurement noise is solved;

[0063] By transforming the measurement update in the adaptive optimal algorithm into a linear regression problem between the state prediction and the measurement value, an enhanced adaptive filtering algorithm is obtained;

[0064] Let the true value of the state be X k , and the observed value be Then the state error is expressed as

[0065]

[0066] The linear regression problem is described as

[0067]

[0068] Define the following variables

[0069]

[0070]

[0071]

[0072]

[0073] Therefore, the linear regression problem is transformed into

[0074] y k = M k X k + ζ k (26)

[0075] wherein is the identity matrix. The above equation can be solved by the generalized maximum likelihood estimation algorithm, and its solution can be obtained by solving the cost function, which is

[0076]

[0077] where ξ i is the i-th component of ξ, called the residual vector, and this vector satisfies ξ = M k - y k , n is the dimension of the residual vector ξ, and the p function is the well-known Huber convex function, which has the following form:

[0078]

[0079] where r is the adjustment parameter. The estimated value obtained by using the p function in the above form has strong robustness. If the p function is differentiable, it conforms to formula (27);

[0080] Therefore, the solution of the linear regression problem is obtained by taking the partial derivative of formula (27):

[0081]

[0082]

[0083] To solve equation (29), first define

[0084]

[0085] Ψ(ξ i ) = diag[ψ(ξ i )] (32)

[0086] Substitute ξ i = (M k X k - y k ) i into equation (29), and we get

[0087] M k Ψ(M k X k -y k ) = 0 (33)

[0088] From equation (33), we can obtain

[0089]

[0090] where the superscript (j) represents the iteration number. The initialization is performed using the least squares method, that is

[0091]

[0092] The convergence value of the iteration process can be considered as the state estimate value after measurement update The final state error covariance update matrix is calculated using the following formula

[0093]

[0094] The above formula utilizes the Ψ matrix when the system state estimate value reaches convergence

[0095] As a further improvement of the present invention, the specific implementation process of step 4 is as follows

[0096] (1) Initial parameter setting: k = 0;

[0097] (2) Time update: Update the equations using the standard Kalman filter algorithm to update the state prediction value and the state error covariance matrix

[0098] (3) Linear regression problem: Construct a linear regression problem as in equation (26) through the variables defined by equations (22)-(25);

[0099] Measurement update: Define the cost function J(X k ), then solve it using the least squares algorithm. Finally, the state update value and the state error update matrix are obtained from equations (34) and (36) respectively

[0100] Beneficial effects:

[0101] The present invention discloses a pedestrian autonomous positioning method based on inertial sensors in a complex environment. In a redundant pedestrian inertial navigation system, the navigation performance and reliability of the navigation system improve with the increase in the number of inertial sensors. However, when there are too many devices, the integration difficulty of the system will increase significantly, and the cost will also increase significantly. Therefore, this application defines a performance index related to the system reliability to quantitatively describe the relationship between the number of redundant sensors and the reliability of the pedestrian inertial navigation system. Through the analysis and calculation of the reliability performance index, the number of sensors that can optimize the system reliability and economy is obtained. On the basis of determining the number of sensors, by studying the configuration scheme of redundant sensors, a redundant sensor configuration scheme that can simultaneously optimize the navigation performance and fault detection and isolation performance (FPI) of the navigation system is obtained.

[0102] The present invention optimally fuses the data measured by the inertial sensor configuration scheme through a data fusion algorithm. To solve the problem that the filtering performance drops sharply due to the unknown system noise characteristic parameters and non-Gaussian measurement noise in the standard Kalman filter algorithm, an enhanced adaptive optimal fusion algorithm is adopted. This algorithm introduces a fading factor into the prediction process of the covariance matrix, improves the ability to cope with state mutations, suppresses the divergence of the filter over time to a certain extent, and improves the accuracy of the filtering algorithm; by combining the adaptive filtering algorithm with the Huber generalized maximum likelihood estimation method, the problem of filter model distortion caused by non-Gaussian measurement noise is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 is the change curve of the present invention relative to MTBF;

[0104] Figure 2 is the change amount of the present invention relative to MTBF;

[0105] Figure 3 is the change curve of the reliability performance index of the present invention;

[0106] Figure 4 is the dodecahedron configuration scheme of the present invention;

[0107] Figure 5 is the flow chart of the adaptive optimal algorithm of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0108] The present invention will be further described in detail below in conjunction with the drawings and the specific embodiments:

[0109] As a specific embodiment of the present invention, the present invention provides a pedestrian autonomous positioning method based on inertial sensors in a complex environment, including the following steps:

[0110] Step 1: Determine the number of redundant inertial sensors by considering the mean time between failures (MTBF), relative MTBF, relative MTBF variation, volume, weight, and cost of a single gyroscope and the pedestrian inertial navigation system.

[0111] Define a performance metric related to system reliability to quantitatively describe the relationship between the number of redundant inertial sensors and the reliability of the pedestrian inertial navigation system. Through the analysis and calculation of the reliability performance metric, the number of sensors that can optimize system reliability and economy is obtained.

[0112] In a pedestrian inertial navigation system, at least three gyroscopes or accelerometers are required to measure the angular rate or acceleration in the inertial space. Assume that there are n inertial devices with the same reliability R e configured, then the system reliability R a is

[0113]

[0114] Therefore, the MTBF of the entire pedestrian inertial navigation system can be expressed as

[0115]

[0116] It can be seen from the above formula that the more inertial sensors there are, the higher the reliability of the inertial navigation system. Through calculation, the MTBF of a single gyroscope is 1 / λ. The more inertial sensors there are, the higher the reliability of the inertial navigation system. Through calculation, the MTBF of a single gyroscope is 1 / λ, and the MTBF 3 of a non-redundant system with three inertial sensors installed along the orthogonal coordinate system is

[0117]

[0118]

[0119]

[0120] Among them, the MTBF of the redundant navigation system formed by obliquely arranging n inertial devices and the MTBF 3 of the non-redundant system, the ratio is also called the relative MTBF; is the variation of the relative MTBF; F is called the reliability performance metric of the inertial navigation system.

[0121] By changing the number of inertial devices, calculate and the reliability performance metric F respectively, and the variation curves are as shown in Figure 1, 2 as shown in FIGS. 3.

[0122] From the analysis of the above figures, it can be seen that when there are six inertial sensors, the reliability performance index F reaches the maximum value, that is, the reliability and economy of the system reach the optimum.

[0123] Step 2: On the basis of determining the number of inertial sensors in Step 1, by studying the configuration scheme of redundant inertial sensors, an inertial sensor configuration scheme that can simultaneously optimize the navigation performance and fault detection and isolation performance (Fault detection and isolation performance, FPI) of the pedestrian navigation system is obtained.

[0124] When the redundant inertial sensors containing six similar sensors adopt the regular dodecahedron configuration, the navigation performance and fault detection and isolation performance (FDI) of the inertial navigation system reach the optimum simultaneously.

[0125] The regular dodecahedron configuration scheme is as Figure 4 shown. In this configuration scheme, at least three sensors are required to measure the motion information of the X, Y, and Z axes. The corresponding redundant configuration matrix in this scheme is:

[0126]

[0127] where α = 31.72°. Then the specific configuration matrix is:

[0128]

[0129] When the measurement matrix of the inertial navigation system satisfies the following equation, it can be considered that the navigation performance and FPI of the navigation system reach the optimum.

[0130]

[0131] where h i is the row vector of the redundant configuration matrix H, and the redundant configuration matrix H satisfies k = 1, 2, 3, ….

[0132] From formula (8), when the regular dodecahedron configuration is adopted, the value of H op is 0.4472. Therefore, when the redundant navigation system containing six similar sensors adopts the regular dodecahedron configuration, the navigation performance and fault detection and isolation performance (FDI) of the system reach the optimum simultaneously.

[0133] Step 3: Through the data fusion algorithm, the data measured by the inertial sensor configuration schemes obtained in Step 1 and Step 2 are optimally fused to achieve the purpose of improving the accuracy of the pedestrian inertial navigation system.

[0134] To solve the problem that the system noise characteristic parameters of the standard Kalman filter algorithm are unknown in complex environments, an enhanced adaptive optimal fusion algorithm is adopted. This algorithm introduces a fading factor into the prediction process of the covariance matrix, improves the ability to cope with state mutations, suppresses the divergence of the filter over time to a certain extent, and improves the accuracy of the filtering algorithm.

[0135] In the optimal fusion algorithm based on the standard Kalman filter algorithm, the standard Kalman filter algorithm is replaced with an adaptive filtering algorithm with a system noise estimator, that is, an adaptive optimal fusion algorithm is formed. The flowchart of this algorithm is as Figure 5 shown:

[0136] Project the output vector of the redundant inertial sensor onto the left null space of the configuration matrix to obtain the redundant observation of the fusion algorithm, and the maximum utilization of the performance of each sensor can be achieved through the optimal estimation of the redundant observation.

[0137] In this pedestrian inertial navigation system, the error of the inertial sensor is selected as the state vector, and the output of the inertial sensor is used as the measurement, that is

[0138] X = [x 1 x 2 …x n T

[0139] Z = [y 1 y 2 …y n T (9)

[0140] where x i represents the error of the i-th inertial sensor, and y i represents the measurement output of the i-th inertial sensor.

[0141] Therefore, the state equation and the observation equation of the system can be expressed as

[0142] X k = A k / k-1 X k-1 + B k / k-1 W k-1 (10)

[0143] Z k = C k X k + Hu k + V k (11)

[0144] where A k / k-1 , B k / k-1 , C​​k is the coefficient matrix, H is the installation matrix, W k-1 and V k are the noise matrices.

[0145] Let where T k H = 0, and T is called k the basis of the left null space of H, and k is the orthogonal complement space of T, that is Left multiplying T by equation (11) gives

[0146] TZ k = TC k X k + THu k + TV k = TC k X k + TV k (12) Therefore, the system model can be expressed as

[0147]

[0148] Estimate this model using the Kalman filter, and the recurrence formula is as follows:

[0149] One-step state prediction:

[0150]

[0151] One-step state prediction mean square error:

[0152]

[0153] Filter gain:

[0154] K k = P k / k-1 (TC k ) T ((TC k )P k / k-1 (TC k ) T + R k ) -1 (16)

[0155] State estimation:

[0156]

[0157] State estimation mean square error:

[0158] P k = (I - K k TCk )P k / k-1 (18)

[0159] In the process of updating the Kalman filter, it is first necessary to give the initial state quantity X 0 and the initial variance P 0 . Equations (14) and (15) are called time updates; the processes included in equations (16), (17), and (18) are called measurement updates. After the time update is completed, it is detected whether there is measurement information. If there is, measurement update and state estimation are performed to obtain the optimal estimation output; otherwise, the measurement information is used as the optimal estimation output. According to the Kalman filter, can be solved. In equation (14), V k satisfies the Gaussian distribution, that is, V k ~(0, R k ), and the redundant configuration matrix H is full rank. Therefore, u k can be obtained by weighted least squares estimation, and

[0160]

[0161] To solve the problem that the measurement noise of the standard Kalman filter algorithm in a complex environment does not satisfy the Gaussian distribution, resulting in a sharp decline in filtering performance, the adaptive filtering algorithm is combined with the Huber generalized maximum likelihood estimation method to solve the problem of filtering model distortion caused by non-Gaussian measurement noise.

[0162] The standard attitude estimation measurement sensor has non-Gaussian characteristics and uncertain noise characteristics. When the error / noise statistical distribution follows a non-Gaussian distribution, the estimation performance of the adaptive optimal fusion algorithm will rapidly decrease. Therefore, this algorithm needs to be improved. By transforming the measurement update in the adaptive optimal algorithm into a linear regression problem between the state prediction and the measurement value, an enhanced adaptive filtering algorithm is obtained.

[0163] Let the true value of the state be X k , and the observed value be Then the state error can be expressed as

[0164]

[0165] The linear regression problem can be described as

[0166]

[0167] Define the following variables

[0168]

[0169]

[0170]

[0171]

[0172] Therefore, the linear regression problem can be transformed into

[0173] y k = M k X k + ζ k (26)

[0174] where is the identity matrix. The above equation can be solved by the generalized maximum likelihood estimation algorithm,

[0175] and its solution can be obtained by solving the cost function, which is

[0176]

[0177] where ξ i is the i-th component of ξ, called the residual vector. This vector satisfies ξ = M k - y k , n is the dimension of the residual vector ξ, and the p function is the well-known Huber convex function, which has the following form:

[0178]

[0179] where r is the adjustment parameter, and the estimated value obtained by using the p function in the above form has strong robustness. If the p function is differentiable, it conforms to formula (27). Therefore, the solution of the linear regression problem can be obtained by taking the partial derivative of formula (27):

[0180]

[0181]

[0182] To solve equation (29), first define

[0183]

[0184] Ψ(ξ i ) = diag[ψ(ξ i )] (32)

[0185] Substitute ξ i = (M k X k - y k ) i into equation (29), and we get

[0186] Mk Ψ(M k X k -y k ) = 0 (33)

[0187] From equation (33), we can obtain

[0188]

[0189] where the superscript (j) represents the iteration number. The initialization is performed using the least squares method, that is

[0190]

[0191] The convergence value of the iteration process can be considered as the state estimation value after measurement update The final state error covariance update matrix can be calculated using the following formula

[0192]

[0193] The above formula utilizes the Ψ matrix when the system state estimation value reaches convergence

[0194] Step 4: Input the fused inertial motion information obtained in Step 3 into the inertial navigation system solution module to calculate various motion parameters (three-dimensional attitude, velocity, position information) of the pedestrian

[0195] The specific implementation process is as follows

[0196] (1) Initial parameter setting k = 0

[0197] (2) Time update: Update the state prediction value using the standard Kalman filter algorithm update equation and the state error covariance matrix

[0198] (3) Linear regression problem: Construct a linear regression problem as in equation (26) through the variables defined by equations (22)-(25)

[0199] Measurement update: Define the cost function J(X k ), and then solve it using the least squares algorithm. Finally, the state update value and the state error update matrix are obtained from equations (34) and (36) respectively

[0200] The above is only a preferred embodiment of the present invention, and it is not a limitation of the present invention in any other form. Any modification or equivalent change made according to the technical essence of the present invention still belongs to the scope protected by the present invention

Claims

1. A pedestrian autonomous positioning method based on inertial sensors in a complex environment, characterized in that, it includes the following steps: Step 1: Considering the mean time between failures (MTBF), relative MTBF, relative MTBF variation of a single gyroscope, the volume, weight, and cost of the pedestrian inertial navigation system, determine the number of redundant inertial sensors; The specific steps of Step 1 are as follows: In a pedestrian inertial navigation system, measuring the angular rate or acceleration in the inertial space requires at least three gyroscopes or accelerometers. Suppose there are n inertial devices with the same reliability R e configured, then the system reliability R a is Therefore, the MTBF of the entire pedestrian inertial navigation system is expressed as It can be calculated that the MTBF of a single gyroscope is 1 / λ. The more the number of inertial sensors, the higher the reliability of the inertial navigation system. It can be calculated that the MTBF of a single gyroscope is 1 / λ, and the MTBF of a non-redundant system with three inertial sensors installed along the orthogonal coordinate system 3 is 1 / 3λ. Definition: where θ n is the MTBF of a redundant navigation system composed of n (n≥3) inertial devices arranged obliquely n and the MTBF of a non-redundant system 3 The ratio, also known as the relative MTBF; Δθ is the change in the relative MTBF; F is called the reliability performance index of the inertial navigation system; Calculate θ separately by changing the number of inertial devices n , Δθ and the reliability performance index F; Step 2: Based on the number of inertial sensors determined in Step 1, by studying the configuration schemes of redundant inertial sensors, obtain an inertial sensor configuration scheme that can simultaneously optimize the navigation performance and fault detection and isolation performance of the pedestrian navigation system; Step 3: Optimally fuse the data measured in Steps 1 and 2 through a data fusion algorithm to achieve the purpose of improving the positioning accuracy of the pedestrian inertial navigation system; In the optimal fusion algorithm based on the standard Kalman filter algorithm, replace the standard Kalman filter algorithm with an adaptive filter algorithm with a system noise estimator, that is, form an adaptive optimal fusion algorithm; Adopt the adaptive optimal fusion algorithm, which introduces a fading factor into the prediction process of the covariance matrix, improves the ability to handle state mutations, suppresses the divergence of the filter over time to a certain extent, and improves the accuracy of the filtering algorithm; The specific steps of the adaptive optimal fusion algorithm in Step 3 are as follows: Project the output vector of the redundant inertial sensors onto the left null space of the configuration matrix to obtain the redundant observations of the fusion algorithm, and maximize the utilization of the performance of each sensor through the optimal estimation of the redundant observations; In this pedestrian inertial navigation system, select the error of the inertial sensors as the state vector and the output of the inertial sensors as the measured quantity, that is where x i represents the error of the i-th inertial sensor, and y i represents the measurement output of the i-th inertial sensor; Therefore, the state equation and the measurement equation of the system are expressed as: X k = A k / k-1 X k-1 + B k / k-1 W k-1 (10) Z k = C k X k + Hu k + V k (11) where A k / k-1 , B k / k-1 , C k is the coefficient matrix, H is the installation matrix, W k-1 and V k are the noise matrices; Let where T k H = 0, and call T k the basis of the left null space of H, is the orthogonal complement space of T k That is, Left-multiply equation (11) by T to get: So the system model is expressed as Use the Kalman filter to estimate this model, and the recurrence formula is as follows: One-step state prediction: One-step state prediction mean square error: Filter gain: K k = P k / k-1 (TC k ) T ((TC k )P k / k-1 (TC k ) T + R k ) -1 (16) State estimation: State estimation mean square error: P k = (I - K k TC k )P k / k-1 (18) In the process of updating the Kalman filter, the initial state quantity X needs to be given first 0 and the initial variance P 0 . Equations (14) and (15) are called time updates; the process included in equations (16), (17) and (18) is called measurement update. After the time update is completed, it is detected whether there is measurement information. If there is, the measurement update and state estimation are carried out to obtain the optimal estimation output; otherwise, the measurement information is used as the optimal estimation output. According to the Kalman filter, can be solved. In equation (14), V k satisfies the Gaussian distribution, that is, V k ~(0, R k ). The redundant configuration matrix H is full rank, so u k can be obtained by weighted least squares estimation, and Step 4: Input the fused inertial motion information obtained in Step 3 into the inertial navigation system solution module to calculate various motion parameters of the pedestrian, including three-dimensional attitude, speed, and position information.

2. The pedestrian autonomous positioning method based on inertial sensors in a complex environment according to claim 1, characterized in that: The specific steps of Step 2 are as follows: The inertial sensors use redundant inertial sensors with 6 similar sensors. When the redundant inertial sensors with 6 similar sensors adopt the regular dodecahedron configuration, the navigation performance and fault detection and isolation performance (FDI) of the inertial navigation system reach the optimal at the same time; In this configuration scheme, at least three sensors are required to measure the motion information of the X, Y, and Z axes. The corresponding redundant configuration matrix in this scheme is: In the formula, α = 31.72°, then the specific configuration matrix is: When the measurement matrix of the inertial navigation system satisfies the following equation, it is considered that the navigation performance and FPI of the navigation system reach the optimal; where h i is the row vector of the redundancy configuration matrix H, and the redundancy configuration matrix H satisfies According to formula (8), when the regular dodecahedron configuration is adopted, the value of H op is 0.4472. Therefore, when the redundant navigation system with 6 homogeneous sensors adopts the regular dodecahedron configuration, both the navigation performance and the fault detection and isolation performance FDI of the system reach the optimum simultaneously.

3. The pedestrian autonomous positioning method based on inertial sensors in a complex environment according to claim 1, characterized in that: In step 3, by combining the adaptive filtering algorithm with the Huber generalized maximum likelihood estimation method, the problem of filter model distortion caused by non-Gaussian measurement noise is solved; The enhanced adaptive filtering algorithm is obtained by transforming the measurement update in the adaptive optimal algorithm into a linear regression problem between the state prediction and the measurement value; Let the true value of the state be X k , and the observed value be Then the state error is expressed as The linear regression problem is described as Define the following variables Therefore, the linear regression problem is transformed into y k = M k X k + ζ k (26) In the formula, is the identity matrix. The above formula can be solved by the generalized maximum likelihood estimation algorithm, and its solution can be obtained by solving the cost function, which is where ξ i is the I-th component of ξ, called the residual vector, which satisfies ξ = M k - y k , n is the dimension of the residual vector ξ, and the p function is the well-known Huber convex function, having the following form: where r is a tuning parameter, and the estimated value obtained by using the p function in the above form has strong robustness. If the p function is differentiable, it conforms to formula (27); Therefore, the solution of the linear regression problem is obtained by taking the partial derivative of formula (27): To solve equation (29), first define Ψ(ξ i ) = diag[ψ(ξ i )] (32) Substitute ξ i =(M k X k -y k ) i into Equation (29), and we get M k Ψ(M k X k -y k ) = 0 (33) It can be obtained from equation (33) that where the superscript (j) represents the number of iterations, and the least squares method is used for initialization, that is The convergence value of the iterative process can be considered as the state estimate value after measurement update The last state error covariance update matrix is calculated using the following formula The above formula utilizes the Ψ matrix when the system state estimate reaches convergence.

4. The pedestrian autonomous positioning method based on inertial sensors in a complex environment according to claim 1, characterized in that: The specific implementation process of step 4 is as follows: (1) Initial parameter setting: (2) Time update: Update the equation using the standard Kalman filter algorithm to update the state prediction value and the state error covariance matrix (3) Linear regression problem: By the variables defined in equations (22)-(25), construct a linear regression problem such as equation (26); Measurement update: Define the cost function \(J(X k \)), then solve it using the least squares algorithm. Finally, the state update value and the state error update matrix are obtained from equations (34) and (36), respectively.

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