CN108375381B - Bionic polarization sensor multi-source error calibration method based on extended Kalman filtering - Google Patents
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Abstract
The invention discloses a bionic polarization sensor multi-source error calibration method based on extended Kalman filtering, which comprises the following steps: (1) multi-source error analysis of the bionic polarized light sensor; (2) establishing a system state model by taking multi-source errors such as installation errors, scale factors and the like and polarization azimuth angles as system state quantities; (3) establishing a system measurement model by taking the light intensity measured value containing the multi-source error as an output; (4) building an experimental environment and collecting sensor data; (5) designing an extended Kalman filter, and estimating installation errors, scale factors and polarization azimuth angles; (6) and compensating the polarization sensor measurement value containing the multisource error according to the installation error and the scale factor estimated value. The method is independent of a high-precision measuring instrument, low in cost, high in operability, easy to implement, high in precision and suitable for simultaneous calibration and compensation of multi-source errors of the bionic polarization navigation system.
Description
Technical Field
The invention relates to the technical field of calibration and compensation of a bionic polarization navigation system, in particular to a bionic polarization sensor multi-source error calibration method based on extended Kalman filtering.
Background
Navigation is a technical means for guiding a moving body or vehicle from a certain departure place to a destination along a set path, and with the continuous development of modern navigation technology, the navigation technology has been developed from experience skill to special science. In recent years, navigation technology is continuously developing towards low cost, intellectualization, anti-interference and the like. Meanwhile, as the working environment of the navigation equipment is increasingly complex and diversified, the requirements on the precision and the performance of the navigation system are higher and higher. In practical application, in the face of a complex task scene, a navigation system with high research sensitivity, strong anti-interference performance and high working reliability has extremely urgent practical requirements.
With the continuous progress of science and technology, biologists have conducted intensive research on the structure of biological organs, and find that many insects, such as bees and solenopsis invigorates to navigate by using sky polarized light information. The strategy of the Sahara desert ants navigating by using sky polarized light is as follows: path integration, visual navigation and system search, and through analyzing the physiological structure characteristics of the solenopsis invicta, the solenopsis invicta perceives the external polarization mode by compound eyes to acquire accurate position and direction information. Further research shows that organisms such as insects, migratory birds and the like can assist navigation in activities such as foraging, migrating, homing, predation and the like by means of atmospheric polarized light; these findings provide a new idea and a new method for improving the traditional navigation mode, the bionic polarized light has the fusion complementary characteristic compared with the traditional navigation mode, and the combined navigation mode with high precision and interference resistance has scientific and engineering reference significance for realizing the high-precision and interference-resistant combined navigation mode.
Through long-term research, people can design bionic polarization navigation sensors which accord with biological characteristics. However, the polarization sensor has the characteristics of compact structure and function integration, and the accuracy of the error analysis and calibration of the sensor needs to be improved. In order to solve the problem, a novel polarization sensor error calibration method needs to be designed.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at error interference of a polarization sensor in a polarization navigation system, the calibration method aiming at multisource errors such as installation errors of the polarization sensor and transmission response coefficients of a photodiode, namely scale factors is provided, the calibration process is realized by means of extended Kalman filtering, the problem that the real-time calibration accuracy of the multisource errors of the polarization sensor is not high is solved, and the precision and the anti-interference capability of polarization navigation are improved.
The technical solution of the invention is as follows: a multi-source error calibration method of a bionic polarization sensor based on extended Kalman filtering comprises the following implementation steps:
firstly, multi-source error analysis of a bionic polarization sensor:
in the practical application of the bionic polarization sensor, the precision of the actual output data of the sensor is restricted by multisource errors, and the precision mainly comprises three types, namely, the installation error of the polarization sensor, measurement noise and a transmission response coefficient, namely a scale factor, of a multichannel photodiode.
Polarization sensor mounting errors are mainly caused by the imprecise mounting of the polarizer and photodiode. Theoretically, the polarization plates in the polarization sensor are arranged perpendicular to each other in the polarization direction, and the output signal of the polarization sensor is related to whether the polarization plates are arranged perpendicular to the polarization direction; the photodiode is susceptible to the conversion of an optical signal into an electrical signal by whether it is mounted on the same horizontal plane. The response of the polaroid and the photodiode to the optical signal collected by the polarization sensor is different, and the photodiode converts the optical signal into an electrical signal and then has additive drift error; after passing through the amplifying circuit, a voltage amplitude multiplicative error exists; the errors are collectively called as the transmission response coefficient of the multichannel photodiode, namely the scale factor.
Secondly, selecting multi-source errors such as installation errors and scale factors and a polarization azimuth angle as system state variables to establish a state model of the bionic polarization navigation system:
according to the opposite channel signal processing method of the polarization sensor, 9 state quantities are selected as calibration parameters, and the parameters to be estimated of the polarization sensor are considered as follows:
X＝[ε1 ε2 ε3 ε4 ε5 K1 K2 K3 φ]T
wherein epsiloni(i-1, 2, … 5) is the installation error angle of the polarizing film of the 3 groups of bionic sensors, K1～K3Is a scale factor of 3 groups of bionic sensors, phi is a polarization azimuth angle of the polarization sensor;
establishing a state equation of the bionic polarization navigation system as follows:
Xk＝f(Xk-1)+Wk-1
wherein f (X)k-1)＝[ε1,k-1 ε2,k-1 ε3,k-1 ε4,k-1 ε5,k-1 K1,k-1 K2,k-1 K3,k-1 φk-1+ψk-1]Tψk-1Is the angle of rotation of the turntable at each time in data acquisition; wk-1Is system noise, white Gaussian noise, Wk-1The covariance matrix of is Qk-1(ii) a k-1 represents the k-1 th time;
thirdly, selecting the output value of the polarization sensor containing the multisource error, namely a light intensity measured value; establishing a measurement model of the bionic polarization navigation system as measurement:
processing the opposite channel signal according to the polarization sensor; the measurement equation of the bionic polarization navigation system is as follows:
Yk＝h(Xk)+Vk，
wherein
d is the degree of atmospheric polarization; vkIs to measure the noise, the noise being white Gaussian noise, VkThe covariance matrix of (1) is Rk；
And step four, building a polarized light test experimental environment based on the step two and the step three, and collecting the measurement data of the polarized sensor:
according to the experimental measurement requirements, a standard polarized light source is selected as a light source, and a bionic polarization navigation sensor to be measured is fixed on a rotary table of a tooth partition table; the turntable rotates at uniform speed, and the degree of each rotation is psikAnd the rotation degree of the experimental turntable in each measurement period is not less than 360 degrees, and the output measurement value of the opposite channel of the polarization sensor is sampled at equal intervals in the rotation process and is recorded as the output value of the bionic polarization sensor.
Fifthly, designing an extended Kalman filter, estimating installation errors, scale factors and polarization azimuth angles:
(1) updating the time;
setting initialization state quantity
And state quantity
Of the covariance matrix P0|0；
Secondly, calculating the one-step prediction,
wherein
In order to be able to predict the state in one step,
a state estimated for a previous time;
calculating state transition matrix phik-1，
Fourthly, calculating and predicting covariance Pk|k-1，
Pk-1|k-1Estimating a covariance matrix of the state for the previous time instance;
(2) measurement update
Firstly, calculate the measurement transfer matrix Hk，
② calculating filter gain matrix Mk，
State estimation value
Fourthly, updating covariance matrix P of state quantityk，Pk＝(I9-ΜkHk)Pk|k-1，I9Is an identity matrix of 9 dimensions.
And sixthly, compensating the actual measurement value of the bionic polarization sensor according to the installation error, the scale factor and the polarization azimuth angle estimation value:
assuming that the sensor is a six-channel sensor, the installation angles of the lenses are 0, 2 pi/3 and 4 pi/3 respectively, the total light intensity of partial polarized light received by the polarization sensor is I, the polarization degree is d, and the included angle between the E-vector direction of the linear polarized light and the reference coordinate direction is phi; converted by photoelectric converter to output electric signal P according to Malus' law1,P2,P3：
Introducing a log-removing transformation:
the following can be obtained:
the degree of polarization d and the azimuthal angle of polarization φ are:
calculating the estimated values of installation error and scale factor in the first to fifth steps
Substituting the measured value into a bionic polarization sensor measurement model to obtain a compensated measured value
Then calculating a polarization angle phi of the bionic polarization sensor;
obtaining compensated measurement values taking into account installation errors and scale factors
Comprises the following steps:
then compensated measured value
Substituting the polarization azimuth angle phi into a solution formula to obtain a compensated polarization azimuth angle phi:
compared with the prior art, the invention has the advantages that:
the invention relates to a bionic polarization sensor multi-source error calibration method based on extended Kalman filtering, which is an optimization and improvement of a multi-element error calibration method aiming at polarization sensor installation errors and photodiode transmission response coefficients, namely scale factors and the like in the existing polarization navigation, and compared with the existing traditional calibration method, the method has the advantages of fast response, strong operability, high precision, good anti-interference performance and the like; the method also has wide applicability, a Global Navigation Satellite System (GNSS) is not applicable to high-rise buildings and luxurious forests, and the Inertial Navigation System (INS) has larger and larger error accumulation along with the increase of time. The bionic polarized light navigation has great potential and wide application prospect in the aspects of unmanned aerial vehicles, bionic robot navigation and the like. Through demarcating polarization sensor, promote polarization sensor precision, can compensate the not enough of other sensors in the integrated navigation, to improving the precision and the autonomy of integrated navigation system and having realistic meaning. Meanwhile, the calibration method of the invention is utilized to provide reliable service for obtaining the polarization navigation information in the integrated navigation system, and the cost of the navigation equipment can be reduced.
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FIG. 1 is a design flow chart of a bionic polarization sensor multi-source error calibration method based on extended Kalman filtering;
FIG. 2 is an experimental calibration environment diagram of the multi-source error calibration method of the bionic polarization sensor based on extended Kalman filtering;
description of reference numerals:
1-integrating sphere; 2-a scaffold;
3-a polarizing plate; 4-a lens;
5-rotating the platform; 6-power interface;
Detailed Description
The invention relates to a bionic polarization sensor multi-source error calibration method based on extended Kalman filtering, which comprises the following design steps: firstly, multi-source error analysis of the bionic polarization sensor is carried out. And secondly, establishing a system state model by using multi-source errors such as installation errors and scale factors and a polarization azimuth angle as system state quantities. And thirdly, establishing a system measurement model by taking the light intensity measured value containing the multi-source error as an output. Then, based on the steps, an experimental environment is built, and polarization sensor data are collected. Next, an extended kalman filter is designed, and the installation error, the scale factor, and the degree of polarization are estimated. And finally, compensating the measured value of the polarization sensor containing the multisource error according to the installation error and the scale factor estimated value. The specific implementation steps are as follows:
firstly, multi-source error analysis of a bionic polarization sensor:
in the practical application of the bionic polarization sensor, the precision of the actual output data of the sensor is restricted by multisource errors, and the precision mainly comprises three types, namely, the installation error of the polarization sensor, measurement noise and a transmission response coefficient, namely a scale factor, of a multichannel photodiode.
Polarization sensor mounting errors are mainly caused by the imprecise mounting of the polarizer and photodiode. Theoretically, the polarization plates in the polarization sensor are arranged perpendicular to each other in the polarization direction, and the output signal of the polarization sensor is related to whether the polarization plates are arranged perpendicular to the polarization direction; the photodiode is susceptible to the conversion of an optical signal into an electrical signal by whether it is mounted on the same horizontal plane. The response of the polaroid and the photodiode to the optical signal collected by the polarization sensor is different, and the photodiode converts the optical signal into an electrical signal and then has additive drift error; after passing through the amplifying circuit, a voltage amplitude multiplicative error exists; the errors are collectively called as the transmission response coefficient of the multichannel photodiode, namely the scale factor.
Secondly, selecting multi-source errors such as installation errors and scale factors and a polarization azimuth angle as system state variables to establish a state model of the bionic polarization navigation system as follows:
according to the opposite channel signal processing method of the polarization sensor, the total light intensity of partial polarized light received by the polarization sensor is assumed to be I, the polarization degree is assumed to be d, the included angle between the E-vector direction of the linear polarized light and the reference coordinate direction is assumed to be phi, and the included angle between the polarization direction of the polaroid in each channel and the reference coordinate system direction is assumed to be phin(n-1, 2), so after passing through the polarizers in the horizontal and vertical channels, the intensity I'nIs composed of two parts, respectively natural light I1And linearly polarized light I2. From Malus' law:
I2＝Idcos2(φ-φn)
the intensity of light passing through the nth polarizer:
combining to obtain:
the electrical signals converted by the photoelectric converter are respectively:
and (3) outputting after logarithmic transformation:
the main sources of signal error and noise of the sensor: internal errors and environmental errors. The internal errors mainly include device errors and mounting errors, and the mounting errors epsilon of the polaroid and the transmission response coefficient of the photodiode, namely the scale factor expression are considered to be changed into:
the sensor is assumed to be a six-channel sensor, and the lenses are respectively provided with photoelectric signals with the angles of 0, 2 pi/3 and 4 pi/3
Obtaining:
order to
Obtaining:
wherein the content of the first and second substances,
is the electrical signal value, K, of the opposite channel of the 3 polarization sensors1～K3Is the transmission response coefficient of the photodiode of the opposite channel of the 3 polarization sensors, namely the scale factor epsilon1～ε5And (5) installing an error angle.
According to the opposite channel signal processing method of the polarization sensor, 9 state quantities are selected as calibration parameters, and the parameters to be estimated of the polarization sensor are considered as follows:
X＝[ε1 ε2 ε3 ε4 ε5 K1 K2 K3 φ]T
wherein epsiloni(i-1, 2, … 5) is the installation error angle of the polarizing film of the 3 groups of bionic sensors, K1～K3Is a scale factor of 3 groups of bionic sensors, phi is the polarization orientation of the polarization sensorAn angle;
establishing a state equation of the bionic polarization navigation system as follows:
Xk＝f(Xk-1)+Wk-1
wherein f (X)k-1)＝[ε1,k-1 ε2,k-1 ε3,k-1 ε4,k-1 ε5,k-1 K1,k-1 K2,k-1 K3,k-1 φk-1+ψk-1]Tψk-1Is the angle of rotation of the turntable at each time in data acquisition; wk-1Is system noise, white Gaussian noise, Wk-1The covariance matrix of is Qk-1(ii) a k-1 represents the k-1 th time;
thirdly, selecting the output value of the polarization sensor containing the multisource error, namely a light intensity measured value; establishing a measurement model of the bionic polarization navigation system as measurement:
processing the opposite channel signal according to the polarization sensor; the measurement equation of the bionic polarization navigation system is as follows:
Yk＝h(Xk)+Vk
d is the degree of atmospheric polarization; vkIs to measure the noise, the noise being white Gaussian noise, VkThe covariance matrix of (1) is Rk；
And step four, building a polarized light test experimental environment based on the step two and the step three, and collecting the measurement data of the polarized sensor:
as shown in fig. 2, the device comprises an integrating sphere 1, a bracket 2, a polarizer 3, a lens 4, a rotary platform 5 and a power interface 6; wherein: integrating sphere 1 is kept flat on the ground by support 2 as fixed support, and integrating sphere 1 effect is the standard polarized light source that provides no interference, and power supply interface 6 is on integrating sphere 1 surface, gives the luminous power supply of fixed light source in integrating sphere 1. According to the experimental measurement requirement, a bionic polarization navigation sensor to be measured is fixed on a rotary platform 5, a polaroid 3 is fixed at a light outlet of an integrating sphere 1, and a lens 4 collects light passing through the polaroid 3Strong data; the rotary platform 5 rotates at a constant speed, and the degree of rotation is psi every timekAnd the rotation degree of the experimental rotating platform 5 in each measurement period is not less than 360 degrees, and the output measurement value of the opposite channel of the polarization sensor is sampled at equal intervals in the rotation process and is recorded as the output value of the bionic polarization sensor.
Fifthly, designing an extended Kalman filter, estimating installation errors, scale factors and polarization azimuth angles:
(1) updating the time;
firstly, initializing state quantities
And state quantity
Of the covariance matrix P0|0In which P is0|0＝I9，I9Is a 9 multiplied by 9 unit matrix;
secondly, the prediction is carried out in one step,
wherein
A predicted state for one step;
calculating state transition matrix phik-1，
Predicting covariance Pk|k-1，
(2) Measurement update
Firstly, calculate the measurement transfer matrix Hk，
② calculating filter gain matrix Mk，
Update state estimation value
Fourthly, updating the state quantity
Covariance P ofk，Pk＝(I9-ΜkHk)Pk|k-1。
And sixthly, compensating the actual measurement value of the bionic polarization sensor according to the installation error, the scale factor and the polarization azimuth angle estimation value:
assuming that the sensor is a six-channel sensor, the installation angles of the lenses are 0, 2 pi/3 and 4 pi/3 respectively, the total light intensity of partial polarized light received by the polarization sensor is I, the polarization degree is d, and the included angle between the E-vector direction of the linear polarized light and the reference coordinate direction is phi; converted by photoelectric converter to output electric signal P according to Malus' law1,P2,P3：
Introducing a log-removing transformation:
the following can be obtained:
the degree of polarization d and the azimuthal angle of polarization φ are:
calculating the estimated values of installation error and scale factor in the first to fifth steps
Substituting the measured value into a bionic polarization sensor measurement model to obtain a compensated measured value
Then calculating a polarization angle phi of the bionic polarization sensor;
obtaining compensated measurement values taking into account installation errors and scale factors
Comprises the following steps:
then compensated measured value
Substituting the polarization azimuth angle phi into a solution formula to obtain a compensated polarization azimuth angle phi:
those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (1)
1. A bionic polarization sensor multi-source error calibration method based on extended Kalman filtering is characterized in that: the method comprises the following steps:
(1) multi-source error analysis of the bionic polarization sensor;
(2) establishing a bionic polarization navigation system state model taking a multi-source error comprising an installation error and a scale factor and a polarization azimuth angle as system state quantities;
(3) selecting the output value of the polarization sensor containing the multisource error, namely a light intensity measured value, as a measurement value to establish a measurement model of the bionic polarization navigation system;
(4) building a polarized light test experimental environment based on the steps (1) to (3), and collecting the measurement data of the polarized sensor;
(5) designing an extended Kalman filter, and estimating installation errors, scale factors and polarization azimuth angles;
(6) compensating the actual measurement value of the bionic polarization sensor according to the installation error, the scale factor and the polarization azimuth angle estimation value;
wherein, the multi-source error analysis of the bionic polarization sensor in the step (1) comprises the following steps:
in the practical application of the bionic polarization sensor, the precision of the actual output data of the sensor is restricted by multisource errors, and the precision mainly comprises three types, namely, the installation error of the polarization sensor, measurement noise and a multichannel photodiode transmission response coefficient, namely a scale factor;
the installation error of the polarization sensor is mainly caused by the inaccurate installation of the polaroid and the photodiode; theoretically, the polarization plates in the polarization sensor are arranged perpendicular to each other in the polarization direction, and the output signal of the polarization sensor is related to whether the polarization plates are arranged perpendicular to the polarization direction; the photodiode converts an optical signal into an electrical signal and is easily influenced by whether the photodiode is arranged on the same horizontal plane or not;
the response of the polaroid and the photodiode to the optical signal collected by the polarization sensor is different, and the photodiode converts the optical signal into an electrical signal and then has additive drift error; after passing through the amplifying circuit, a voltage amplitude multiplicative error exists; the errors are collectively called as a multichannel photodiode transmission response coefficient, namely a scale factor;
selecting a multi-source error comprising an installation error and a scale factor and a polarization azimuth angle as a system state variable to establish a bionic polarization navigation system state model; according to the opposite channel signal processing method of the polarization sensor, 9 state quantities are selected as calibration parameters, and the parameters to be estimated of the polarization sensor are considered as follows:
X＝[ε1 ε2 ε3 ε4 ε5 K1 K2 K3 φ]T
wherein epsiloniWhere i is 1,2, … 5 is the installation error angle of the polarizing film of the 3 groups of bionic sensors, K1～K3Is a scale factor of 3 groups of bionic sensors, phi is a polarization azimuth angle of the polarization sensor;
establishing a state equation of the bionic polarization navigation system as follows:
Xk＝f(Xk-1)+Wk-1
wherein, f (X)k-1)＝[ε1,k-1 ε2,k-1 ε3,k-1 ε4,k-1 ε5,k-1 K1,k-1 K2,k-1 K3,k-1 φk-1+ψk-1]T，ψk-1Is the angle of rotation of the turntable at each time in data acquisition; wk-1Is system noise, white Gaussian noise, Wk-1The covariance matrix of is Qk-1(ii) a k-1 represents the k-1 th time;
selecting the output value of the polarization sensor containing the multisource error, namely the light intensity measured value; establishing a measurement model of the bionic polarization navigation system as measurement;
processing the opposite channel signal according to the polarization sensor; the measurement equation of the bionic polarization navigation system is as follows:
Yk＝h(Xk)+Vk
wherein the content of the first and second substances,
wherein d is the degree of atmospheric polarization; vkIs to measure the noise, the noise being white Gaussian noise, VkThe covariance matrix of (1) is Rk；
Constructing a polarized light test experimental environment in the step (4), and collecting the measurement data of the polarized sensor;
according to the experimental measurement requirements, a standard polarized light source is selected as a light source, and a bionic polarization navigation sensor to be measured is fixed on a rotary table of a tooth partition table; the turntable rotates at uniform speed, and the degree of each rotation is psikThe rotation degree of the experimental turntable is not less than 360 degrees in each measurement period, and output measurement values of opposite channels of the polarization sensor are sampled at equal intervals in the rotation process and are recorded as output values of the bionic polarization sensor;
and (5) designing an extended Kalman filter, estimating installation errors, scale factors and polarization azimuth angles:
(1) updating the time;
setting initialization state quantity
And state quantity
Of the covariance matrix P0|0；
Secondly, calculating the one-step prediction,
wherein
In order to be able to predict the state in one step,
a state estimated for a previous time;
calculating state transition matrix phik-1，
Fourthly, calculating and predicting covariance Pk|k-1，
Pk-1|k-1Estimating a covariance matrix of the state for the previous time instance;
(2) measurement update
Firstly, calculate the measurement transfer matrix Hk，
② calculating filter gain matrix Mk，
State estimation value
Fourthly, updating covariance matrix P of state quantityk，Pk＝(I9-ΜkHk)Pk|k-1，I9An identity matrix of 9 dimensions;
compensating the actual measurement value of the bionic polarization sensor according to the installation error, the scale factor and the estimated value of the polarization azimuth angle in the step (6);
specifically, the sensor is a six-channel sensor, the lens is respectively provided with angles of 0, 2 pi/3 and 4 pi/3, the total light intensity of partial polarized light received by the polarization sensor is I, the polarization degree is d, and the included angle between the E-vector direction of the linear polarized light and the reference coordinate direction is phi; converted by photoelectric converter to output electric signal P according to Malus' law1,P2,P3：
Introducing a log-removing transformation:
the following can be obtained:
the degree of polarization d and the azimuthal angle of polarization φ are:
calculating the installation error and the scale factor estimated value in the steps (1) to (5)
Substituting the measured value into a bionic polarization sensor measurement model to obtain a compensated measured value
Then calculating a polarization angle phi of the bionic polarization sensor;
obtaining compensated measurement values taking into account installation errors and scale factors
Comprises the following steps:
then compensated measured value
Substituting the polarization azimuth angle phi into a solution formula to obtain a compensated polarization azimuth angle phi;
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| CN109556633B (en) * | 2018-11-26 | 2020-11-20 | 北方工业大学 | Bionic polarization sensor multi-source error calibration method based on adaptive EKF |
| CN110046368B (en) * | 2018-11-26 | 2023-06-13 | 北方工业大学 | Bionic polarization sensor multisource error calibration method based on self-adaptive UKF |
| CN110779514B (en) * | 2019-10-28 | 2021-04-06 | 北京信息科技大学 | Hierarchical Kalman fusion method and device for auxiliary attitude determination of bionic polarization navigation |
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| CN111238467B (en) * | 2020-02-07 | 2021-09-03 | 西北工业大学 | Bionic polarized light assisted unmanned combat aircraft autonomous navigation method |
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