CN104793182B - Indoor positioning method based on particle filtering under condition of non-Gaussian noises - Google Patents
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/10—Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements, e.g. omega or decca systems
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Abstract
The invention discloses an indoor positioning method based on particle filtering under the condition of non-Gaussian noises. The indoor positioning method comprises the following steps of modeling movement accelerated speed of an object and measurement noises into random vectors which obey Gaussian mixture distribution in a training stage by using a particle filtering method based on a suboptimum important function; and performing local linearization on a non-linear observation equation in a positioning state so as to obtain a suboptimum important function and a weight coefficient, change a degradation phenomenon in particle filtering and implement optimum estimation on state vectors. The indoor positioning method has the advantages that on one hand, compared with Gaussian noises, modeling of the Gaussian mixture model is close to actual conditions, and errors caused by model approximation can be reduced effectively; and on the other hand, the degradation speed of the weight coefficient in the particle filtering process can be increased through the solved suboptimum important function, the algorithm efficiency and the algorithm precision are improved, and the positioning precision is improved effectively.
Description
Technical Field
The invention belongs to the technical field of wireless positioning.
Background
How to realize accurate positioning and tracking of a moving target in an indoor environment is one of the important points of indoor positioning research. Among the existing positioning technologies, Ultra Wide Band (UWB) technology can achieve centimeter-level ranging accuracy. Because of the influence of the indoor environment on the transmission of electromagnetic waves, the actual distance measurement value is influenced by non-gaussian noise, so that a large deviation is generated. Therefore, the observation noise is approximated to a normal distribution, and although the amount of calculation can be reduced, it is difficult to accurately estimate the actual state, and therefore, the above method approximates the ranging noise by mixing gaussian variables.
In addition, the traditional ultra-wideband (UWB) positioning algorithm adopts a trilateration method to obtain a least square solution satisfying conditions, but when some anchor nodes have a small deviation, the positioning result has a large deviation; and the moving target has the motion states of acceleration, deceleration, uniform speed and the like in the motion process, so the acceleration of the object motion cannot follow unimodal normal distribution.
Standard particle filter algorithms select the prior probability density as the significant density function, but since the current measurement is not taken into account, the samples sampled from the significant density function have a large deviation from the samples sampled from the true posterior probability density. The variance of the importance weights also randomly increases over time, so that the weight of the particles is concentrated on a few particles, giving rise to a degradation problem. In order to overcome the degradation phenomenon, a good important density function needs to be selected, but in the actual process, the observation equation is nonlinear, and the optimal density function cannot be directly obtained, so that the efficiency and the precision of calculation cannot be guaranteed.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides an indoor positioning method based on particle filtering under the condition of non-Gaussian noise, which improves the particle degradation phenomenon in the particle filtering, realizes the optimal estimation of a state vector and improves the positioning precision.
The technical scheme is as follows: an indoor positioning method based on particle filtering under the condition of non-Gaussian noise models acceleration in a state equation and measurement noise in an observation equation into Gaussian mixture random variables, and conducts local linearization on the observation equation to obtain a suboptimal importance function, thereby conducting particle filtering and obtaining the optimal estimation of the state quantity, and the method specifically comprises the following steps:
(1) establishing a state equation and an observation equation of the motion of the moving target, approximating the probability distribution of the acceleration vector in the state equation by mixed Gaussian distribution, and approximating the distribution of the distance measurement noise and the inertia measurement noise in the observation equation by the mixed Gaussian distribution;
(2) performing local linearization on a nonlinear observation equation to obtain a suboptimal importance function and a weight coefficient at any moment, wherein two parameters, namely values of a mean value and a variance are obtained by recursion;
(3) measuring the distance between the current moment of the moving target and an observation node, the motion azimuth angle of the current moment of the moving target and the distance between the current moment of the moving target and the position of the previous moment, and obtaining optimal estimation by adopting particle filtering based on a suboptimal importance function on a measured value;
(4) and positioning and tracking the moving target according to the distance and the azimuth angle between the filtered moving target and the observation point, and updating two parameters, namely the mean value and the variance.
Further, in the step (1), the acceleration term of the state equation is modeled as a random vector that follows a mixed gaussian distribution, and the noise term in the observation equation is also modeled as a random vector that follows a mixed gaussian distribution by anticipating statistics of the ranging error and the azimuth measurement error.
Further, the mobile object carrying terminal in the step (1) includes an Ultra Wideband (UWB) and an Inertial Sensor Unit (ISU), compares a true value and a measured value according to an actual scene to obtain a measurement error, and approximates the measurement error by using a mixed gaussian distribution according to a statistical characteristic of the measurement error.
Furthermore, the acceleration of the state equation is modeled according to the acceleration, deceleration and uniform motion states in the walking process of a normal person, and is approximated by adopting a mixed Gaussian distribution with the collection number of 3.
Furthermore, the mean value and the variance are statistics in the weight coefficient in the particle filtering process, have memory, can obtain a value required by the current moment through iteration according to a value of the previous moment, and the recursive process is linear operation.
Further, the ultra-wideband (UWB) anchor node is single, locating a single user.
Has the advantages that: compared with the prior art, the invention has the advantages that:
1. by adopting a particle filtering method based on a suboptimal importance function, the acceleration of the motion of the object and the measurement noise are modeled into random vectors obeying mixed Gaussian distribution, so that the situation is closer to the real situation.
2. By carrying out local linearization on the observation equation, a suboptimal important density function is obtained, the degradation phenomenon of particle filtering is improved, the calculation efficiency and precision are improved, and the high-precision positioning and tracking functions in an indoor environment are realized.
3. By comprehensively using the ultra-wideband (UWB) ranging technology and the measurement information of an Inertial Sensor Unit (ISU), on one hand, the number of anchor nodes required by UWB positioning can be reduced, the dependence on UWB is reduced, and the cost is greatly reduced; on the other hand, the error of the measured value of the inertial sensor is modeled into a mixed Gaussian variable, so that the positioning precision can be improved.
Drawings
FIG. 1 is a block diagram of an overall scheme implementation;
FIG. 2 is a positioning scene diagram;
FIG. 3 is a schematic diagram of a mobile terminal carried by a mobile object;
FIG. 4 is a flow chart of a particle filtering algorithm based on a suboptimal importance function.
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description.
As shown in fig. 1-2, an indoor positioning method based on particle filtering under non-gaussian noise condition, a single Ultra Wide Band (UWB) anchor node is used to position a single user. The method models acceleration in a state equation and measurement noise in an observation equation into a Gaussian mixture random variable, carries out local linearization on the observation equation, obtains a suboptimal importance function, carries out particle filtering and obtains the optimal estimation of the state quantity, and comprises the following specific steps:
(1) establishing a state equation and an observation equation of the motion of the moving target, approximating the probability distribution of the acceleration vector in the state equation by mixed Gaussian distribution, and approximating the distribution of the distance measurement noise and the inertia measurement noise in the observation equation by the mixed Gaussian distribution;
the method comprises the steps that an acceleration term of a state equation is modeled into a random vector which obeys mixed Gaussian distribution, and a noise term in an observation equation is modeled into the random vector which obeys the mixed Gaussian distribution through early statistics of a distance measurement error and an azimuth angle measurement error;
the mobile target carrying terminal comprises an Ultra Wide Band (UWB) part and an Inertial Sensor Unit (ISU) part, compares a true value with a measured value according to an actual scene to obtain a measurement error, and adopts mixed Gaussian distribution to approximate according to the statistical characteristic of the measurement error;
the statistical characteristic of the acceleration in the state equation can be modeled according to the walking speed of a normal person, and the person can be approximated by adopting mixed Gaussian distribution with the collection number of 3 because the person has motion states of acceleration, deceleration, uniform speed and the like in the walking process.
(2) Performing local linearization on a nonlinear observation equation to obtain a suboptimal importance function and a weight coefficient at any moment, wherein two parameters, namely values of a mean value and a variance are obtained by recursion;
(3) measuring the distance between the current moment of the moving target and an observation node, the motion azimuth angle of the current moment of the moving target and the distance between the current moment of the moving target and the position of the previous moment, and obtaining optimal estimation by adopting particle filtering based on a suboptimal importance function on a measured value;
(4) and positioning and tracking the moving target according to the distance and the azimuth angle between the filtered moving target and the observation point, and updating two parameters, namely the mean value and the variance.
The observation equation is a nonlinear function, statistical characteristics of state variables passing through the observation equation are difficult to analyze, and therefore the importance function is obtained by locally linearizing the observation equation, and the importance function is enabled to gradually converge to the required filter distribution under the general assumption condition.
The particle filter adopts a particle filter algorithm based on an importance function, and the degradation phenomenon in the particle filter can be improved and the efficiency and the precision of the algorithm can be improved by adopting the derived suboptimal importance function and weight coefficient.
The technical solution of the present invention is further specifically analyzed and described as shown in fig. 3 to 4.
Establishing a state equation and an observation equation of the motion of the moving target:
ηk＝Fηk-1+wk(1)
ξk＝h(ηk)+vk(2) in the equation of state (1), the state,
wherein, ηkIs a state variable, xp(k) And yp(k) Distance measurement values in x-axis direction and y-axis direction at time k, xv(k) And yv(k) The movement speeds in the x-axis direction and the y-axis direction at the moment k; f is a state transition matrix, wkIs an acceleration, wxp(k) And wyp(k) Ranging noise in x-and y-directions at time k, wxv(k) And wyv(k) The speed noises in the x-axis direction and the y-axis direction at the moment k are respectively; is an accelerationCoefficient matrix of terms, vkξ for measurement errorkIs an observed quantity.
In the observation of the equation (2),
wherein,
as shown in FIG. 3, α (k) is the angular measurement of the Inertial Sensor Unit (ISU), α (k) ∈ [0, 2 π](ii) a L (k) is an Ultra Wideband (UWB) ranging value; v. ofkFor measuring errors, wherein vθ(k) Noise at heading angle, vL(k) Noise of the ranging value. Will measure the error vkAcceleration w in (1)kAre approximated using a mixed gaussian distribution.
The observation equation (2) relates to solving nonlinear operations such as inverse cosine and square of an angle, so that in order to obtain the statistical characteristic of a random variable passing through a nonlinear system, the random variable needs to be subjected to local linearization, thereby reducing the calculated amount, obtaining an importance function and laying a foundation for efficient particle filtering. The linearization is carried out on the (2),
wherein, the constant h (F η)k-1) Is CkMemory for recordingIs DkThen (3) is
Record againThen (4) is
Assuming that the observed noise follows a mixed Gaussian distribution, i.e.
The relationship of the accelerations at adjacent moments is modeled as:
wk＝wk-1+ek(7)
in the process of normal walking of the user, the user has the states of acceleration, deceleration and uniform motion. The increment of the acceleration shows different distribution in different states, and the increment e of the acceleration at adjacent momentskThe modelling is also a Gaussian mixture model, i.e.
So as to derive the weight coefficient as,
wherein,
the suboptimal density function is:
wherein,
and (4) performing optimal estimation on the measured value by adopting particle filtering according to the weight coefficients and the suboptimal density functions obtained in the steps (9) and (10), so as to obtain the coordinates of the moving target at the current moment. And iteratively updating the important statistic according to (11) - (14). The mean value and the variance are statistics in the weight coefficient in the particle filtering process, the mean value and the variance have memorability, values required by the current moment can be obtained through iteration according to values of the previous moment, and the recursive process is linear operation, so that the calculated amount is greatly reduced. Meanwhile, the filtering adopts a particle filtering algorithm based on an importance function, so that the degradation phenomenon in the particle filtering can be improved, and the efficiency and the precision of the algorithm are improved.
The invention adopts a particle filtering method based on the suboptimal importance function, and obtains the suboptimal importance function and the weight coefficient by modeling the acceleration of the object motion and the measurement noise as random vectors obeying mixed Gaussian distribution and carrying out local linearization on a nonlinear observation equation, thereby improving the particle degradation phenomenon in the particle filtering, realizing the optimal estimation of the state vector and improving the positioning precision.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.
Claims (6)
1. An indoor positioning method based on particle filtering under the condition of non-Gaussian noise is characterized in that: modeling acceleration in a state equation and measurement noise in an observation equation into a Gaussian mixture random variable, performing local linearization on the observation equation, and obtaining a suboptimal importance function, thereby performing particle filtering to obtain the optimal estimation of the state quantity, wherein the method specifically comprises the following steps:
(1) establishing a state equation and an observation equation of the motion of the moving target, approximating the probability distribution of the acceleration vector in the state equation by mixed Gaussian distribution, and approximating the distribution of the distance measurement noise and the inertia measurement noise in the observation equation by the mixed Gaussian distribution;
(2) performing local linearization on a nonlinear observation equation to obtain a suboptimal importance function and a weight coefficient at any moment, wherein two parameters, namely values of a mean value and a variance are obtained by recursion;
(3) measuring the distance between the current moment of the moving target and an observation node, the motion azimuth angle of the current moment of the moving target and the distance between the current moment of the moving target and the position of the previous moment, and obtaining optimal estimation by adopting particle filtering based on a suboptimal importance function on a measured value;
(4) and positioning and tracking the moving target according to the distance and the azimuth angle between the filtered moving target and the observation point, and updating two parameters, namely the mean value and the variance.
2. The method of claim 1, wherein the indoor positioning method based on particle filtering under the non-gaussian noise condition comprises: in the step (1), an acceleration term of the state equation is modeled into a random vector which obeys mixed Gaussian distribution, and a noise term in the observation equation is modeled into a random vector which obeys mixed Gaussian distribution through advanced statistics of a distance measurement error and an azimuth angle measurement error.
3. The method of claim 1, wherein the indoor positioning method based on particle filtering under the non-gaussian noise condition comprises: the mobile target carrying terminal in the step (1) comprises an Ultra Wide Band (UWB) part and an Inertial Sensor Unit (ISU), a true value and a measured value are compared according to an actual scene to obtain a measurement error, and the actual value and the measured value are approximated by adopting mixed Gaussian distribution according to the statistical characteristic of the measurement error.
4. The indoor positioning method based on particle filtering under the condition of non-Gaussian noise according to claim 1 or 2, characterized in that: the acceleration of the state equation is modeled according to the acceleration, deceleration and uniform motion states in the walking process of a normal person, and is approximated by adopting mixed Gaussian distribution with the collection number of 3.
5. The method of claim 1, wherein the indoor positioning method based on particle filtering under the non-gaussian noise condition comprises: the mean value and the variance are statistics in the weight coefficient in the particle filtering process, have memory, can obtain a value required by the current moment through iteration according to a value of the previous moment, and the recursive process is linear operation.
6. The method of claim 3, wherein the indoor positioning method based on particle filtering under the non-Gaussian noise condition comprises: the ultra-wideband (UWB) anchor node is single, and positions a single user.
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| US11474486B2 (en) * | 2019-03-11 | 2022-10-18 | Mitsubishi Electric Research Laboratories, Inc. | Model-based control with uncertain motion model |
| CN110440794B (en) * | 2019-07-26 | 2021-07-30 | 杭州微萤科技有限公司 | Positioning correction method for IMU navigation |
| CN110567441B (en) * | 2019-07-29 | 2021-09-28 | 广东星舆科技有限公司 | Particle filter-based positioning method, positioning device, mapping and positioning method |
| CN111761583B (en) * | 2020-07-08 | 2022-04-08 | 温州大学 | Intelligent robot motion positioning method and system |
| CN114077245A (en) * | 2020-08-21 | 2022-02-22 | 苏州三六零机器人科技有限公司 | SLAM method and device for multiple data sources, sweeping robot and readable medium |
| CN114040325B (en) * | 2021-11-05 | 2022-08-19 | 西北工业大学 | Single-anchor node network cooperative positioning method under inertial navigation assistance |
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