The algorithm of kalman filter integrating GNSS and ins for orbit determination of a satellite and recording medium storing program for executing the same

Abstract

The present invention relates to a Kalman filter algorithm method for coupling a Global Navigation Satellite System (GNSS) receiver and an Inertial Measurement Unit (IMU) for determining the orbit of a low Earth orbit (LEO) satellite. More specifically, the invention provides a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite capable of designing a GNSS / INS integrated Kalman filter algorithm that estimates errors by using the difference between the position or velocity of the GNSS receiver and the position or velocity of the INS calculated by the IMU sensor as a measurement model, and using the position error, velocity error, attitude error, gyroscope error, and acceleration error of the INS as a state variable model, for precise position calculation that could not be processed because semiconductors capable of fast computation processing suitable for a space environment capable of processing two signals from a satellite GNSS receiver and an IMU sensor have not been developed. The invention also provides a recording medium storing a program for implementing the same.

Description

Technology Field

[0001] The present invention relates to a Kalman filter algorithm method for integrating a Global Navigation Satellite System (GNSS) receiver and an Inertial Navigation System (INS). More specifically, it relates to a method for designing a distributed federated Kalman filter algorithm that reduces computational load by estimating position error, velocity error, attitude error, acceleration error, and gyro error separately, thereby replacing a centralized Kalman filter that estimates position error, velocity error, attitude error, acceleration error, and gyro error as a single group and estimating them individually. Background Technology

[0003] As the service market for low-orbit satellites expands, the demand for commercial practical satellites, military satellites, satellite constellations, and scientific satellites is surging. Low-orbit satellites with diverse missions, such as weather, disaster, communications, and surveillance and reconnaissance, require orbit determination technology that precisely measures position, velocity, time, attitude, and angle to ensure data reliability according to the mission objectives.

[0004] However, low-orbit satellites orbit at high speeds of about 7-8 km / s, and while the GNSS receivers that are now essential provide stable position references for a long time, their reception sensitivity is weak (-130 dBw to -160 dBw), making them vulnerable to jamming and disturbances and resulting in lower precision. Additionally, while IMUs (especially MEMS-based ones) have the advantages of being small and low-power, cumulative error (bias drift) and performance degradation in high-acceleration and rotational environments are causing vulnerability issues in satellite orbit operation.

[0005] In particular, semiconductors applied in space are vulnerable to radiation and temperature changes, and semiconductors suitable for space have so far faced difficulties in high-speed computation due to slow processing speeds and limitations in handling large volumes of high-speed calculations.

[0006] The Kalman filter algorithm is being applied to CPUs capable of high-speed computational processing to correct cumulative errors and improve signal quality of IMU sensors used in daily life, and

[0007] Generally, the INS error behavior model, which serves as the state variable model for the GNSS / INS integrated Kalman filter, includes position error, velocity error, attitude error, gyro error, and acceleration error. The state variable of a single Kalman filter to which this error behavior model is applied consists of 15 orders, as shown in Figure 1.

[0008] This design method is called a traditional centralizing Kalman filter.

[0009] The centralizing Kalman filter is simple to configure and design, but the computational load is very large as shown in Figure 2 based on the 15th order. Nevertheless, it can be sufficiently handled by the computational power of onboard computers equipped with commercial high-performance CPUs that we use in everyday life.

[0010] However, space-grade onboard computers operated on satellites lack computational performance and have limited processing speeds compared to commercially available CPUs, and onboard computers that execute only GNSS functions using space-grade CPUs are only capable of processing for space use. Furthermore, when INS and Kalman filters must be additionally executed using IMU sensors, applying high-performance CPUs or dual-CPUs leads to problems such as increased product costs and reduced reliability due to increased hardware complexity.

[0011] Therefore, since low-orbit satellites operate continuously for long periods, distributed federated Kalman filter algorithm methods capable of effectively processing computations such as deep coupling—which are used to precisely acquire position, velocity, attitude, angular velocity, and acceleration—and operating them on space-grade CPU computing resources have not been sufficiently presented.

[0013] Korean registered patent [10-2026653] discloses a method for verifying the performance of a navigation receiver using a ground test device (EGSE) for verifying the precision navigation performance of a satellite navigation receiver for low orbit satellites. Prior art literature

[0015] Korean Registered Patent [10-2026653] (Registration Date: September 24, 2019) The problem to be solved

[0016] Accordingly, the present invention has been devised to solve the problems described above. The objective of the present invention is to provide a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite capable of designing a GNSS / INS integrated Kalman filter algorithm that estimates errors by using the difference between the position or velocity of the GNSS receiver and the position or velocity of the INS calculated by the IMU sensor as a measurement model, and the position error, velocity error, attitude error, gyroscope error, and acceleration error of the INS as a state variable model, for precise position calculation that could not be processed because a semiconductor capable of fast computation processing suitable for a space environment capable of processing two signals from a satellite GNSS receiver and an IMU sensor has not been developed so far, and to provide a recording medium storing a program for implementing the same.

[0018] The purposes of the embodiments of the present invention are not limited to those mentioned above, and other unmentioned purposes will be clearly understood by those skilled in the art from the description below. means of solving the problem

[0020] A GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention for achieving the above-mentioned purpose is formed in the form of a program executed by a computational processing means including a computer, and in a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit that processes data from a GNSS (Global Navigation Satellite System) receiver and an IMU (Inertial Measurement Unit) for determining a satellite orbit, comprising: a state variable model separation step (S10) for separating a position error state variable model, a velocity error state variable model, an attitude error state variable model, an acceleration error state variable model, and a gyro error state variable model of an INS; A differentiation model generation step (S20) of calculating a position error measurement model using the difference between the position information of the GNSS receiver and the INS (Inertial Navigation System) position information calculated based on the IMU data, obtaining a velocity error measurement model by taking a first derivative of the position error measurement model, obtaining an acceleration error measurement model by taking a second derivative, and obtaining an acceleration error measurement model by taking a third derivative;and an independent position error estimation Kalman filter is configured such that the position error measurement model and the position error state variable model correspond as a pair, an independent velocity error estimation Kalman filter is configured such that the velocity error measurement model and the velocity error state variable model correspond as a pair, an independent attitude error estimation Kalman filter is configured such that the acceleration error measurement model and the attitude error state variable model correspond as a pair, an independent acceleration error estimation Kalman filter is configured such that the acceleration error measurement model and the acceleration error state variable model correspond as a pair, and an independent gyro error estimation Kalman filter is configured such that the acceleration error measurement model and the gyro error state variable model correspond as a pair, respectively, and the position error covariance propagation of the position error estimation Kalman filter is expanded by receiving the velocity error covariance of the velocity error estimation Kalman filter, and the velocity error estimation Kalman filter's The velocity error covariance propagation is characterized by receiving and expanding the attitude error covariance of the attitude error estimation Kalman filter and the acceleration error covariance of the acceleration error estimation Kalman filter, and the attitude error covariance propagation of the attitude error estimation Kalman filter receives and expands the gyro error covariance of the gyro error estimation Kalman filter to estimate the position error, velocity error, attitude error, acceleration error, and gyro error, and includes an error estimation step (S30).

[0021] In addition, the differential model generation step (S20) is characterized by modeling the difference of the INS position information as a cubic function and using a recursive linear regression method on the time series of the position error measurements to obtain the velocity error measurements, attitude error measurements, and acceleration error measurements.

[0022] In addition, according to one embodiment of the present invention, a computer-readable recording medium is provided that stores a program for implementing a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of the satellite. Effects of the invention

[0024] According to a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite according to one embodiment of the present invention and a recording medium storing a program for implementing the same, the method has the effect of providing a method to design a distributed combined Kalman filter by stepwise decomposing the position error, velocity error, attitude error, and gyro error included in the INS error behavior model, which is a state variable model of the GNSS / INS integrated Kalman filter.

[0025] In addition, it has the effect of providing a method to design a distributed combined Kalman filter by obtaining velocity error measurements, attitude error measurements, and gyro error measurements through the numerical differentiation method of the position error measurement time series of the GNSS / INS integrated Kalman filter.

[0026] In addition, by designing the GNSS / INS integrated Kalman filter as a stepped distributed federated type and reducing it in a reduced order, it is possible to significantly reduce the amount of computation compared to a centralized type. Brief explanation of the drawing

[0028] Figure 1 is a configuration diagram of a centralized Kalman filter integrating GNSS / INS. Figure 2 shows the computational amount of a centralized Kalman filter integrating GNSS / INS. FIG. 3 is a flowchart of a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite according to an embodiment of the present invention. Figure 4 is an example diagram of a 15th-order state variable model of INS error. Figure 5 is an example of a 15th-order state variable model decomposed of INS errors. FIG. 6 is a design configuration diagram of a distributed federated Kalman filter integrating GNSS / INS of a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention. FIG. 7 shows the computational amount of a distributed federated Kalman filter integrating GNSS / INS in a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention. FIG. 8 is an example diagram of a cubic function model of INS position error in a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention. FIG. 9 is a flowchart of the operation of a distributed federated Kalman filter integrating GNSS / INS in a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite according to an embodiment of the present invention. Specific details for implementing the invention

[0029] The present invention is capable of various modifications and may have various embodiments, and specific embodiments are illustrated in the drawings and described in detail. However, this is not intended to limit the invention to specific embodiments, and it should be understood that the invention includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention.

[0030] When it is stated that one component is "connected" or "joined" to another component, it should be understood that while it may be directly connected or joined to that other component, there may also be other components in between.

[0031] On the other hand, when it is stated that one component is "directly connected" or "directly coupled" to another component, it should be understood that there are no other components in between.

[0032] The terms used in this specification are used merely to describe specific embodiments and are not intended to limit the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, terms such as “comprising” or “having” are intended to specify the existence of the features, numbers, processes, operations, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, processes, operations, components, parts, or combinations thereof.

[0033] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an ideal or overly formal sense unless explicitly defined in this application.

[0034] The present invention will be described in more detail below with reference to the attached drawings. Prior to this, terms and words used in this specification and claims should not be interpreted as being limited to their ordinary or dictionary meanings. Based on the principle that the inventor can appropriately define the concepts of terms to best describe their invention, they should be interpreted in a meaning and concept consistent with the technical spirit of the present invention. Furthermore, unless otherwise defined, technical and scientific terms used shall have the meaning commonly understood by those skilled in the art to which this invention pertains. Descriptions of known functions and configurations that could unnecessarily obscure the essence of the present invention in the following description and attached drawings are omitted. The drawings presented below are provided as examples to ensure that the spirit of the present invention is sufficiently conveyed to those skilled in the art. Accordingly, the present invention is not limited to the drawings presented below and may be embodied in other forms. Additionally, throughout the specification, the same reference numerals indicate the same components. It should be noted that the same components in the drawings are represented by the same reference numerals wherever possible.

[0036] FIG. 1 is a configuration diagram of a centralized Kalman filter integrating GNSS / INS, FIG. 2 is the computational amount of a centralized Kalman filter integrating GNSS / INS, FIG. 3 is a flowchart of a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention, FIG. 4 is an example diagram of a 15th-order state variable model of an INS error, FIG. 5 is an example diagram of a 15th-order state variable model decomposed of an INS error, FIG. 6 is a design configuration diagram of a distributed federated Kalman filter integrating GNSS / INS in the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention, FIG. 7 is the computational amount of a distributed federated Kalman filter integrating GNSS / INS in the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to an embodiment of the present invention, and FIG. 8 is a GNSS / IMU integrated for determining a satellite orbit according to an embodiment of the present invention Figure 9 is an example of a cubic function model of INS position error in the Kalman filter algorithm method, and is a flowchart of a distributed federated Kalman filter operation that integrates GNSS / INS in the GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite according to an embodiment of the present invention.

[0038] The present invention will be described in detail below with reference to the accompanying drawings. In describing the present invention, detailed descriptions of disclosed technologies related to the present invention will be omitted if it is determined that such detailed descriptions may unnecessarily obscure the essence of the invention.

[0040] The present invention relates to an integrated Kalman filter algorithm for GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) for determining the precise orbit of a low Earth orbit (LEO) satellite. In particular, to overcome the limited computational resources of an onboard computer (OBC) operating in a space environment and hardware limitations caused by radiation, a decentralized federate structure is proposed that dramatically improves computational efficiency by separating high-dimensional state variables and reducing them to a reduced order.

[0041] Unlike traditional centralizing Kalman filters, the decentralizing federate Kalman filter in the present invention separates position error, velocity error, attitude error, gyro error, and acceleration error into five third-order Kalman filters, and links each Kalman filter in a stepwise manner.

[0042] Unlike a single centralized Kalman filter, this distributed combined Kalman filter transmits estimation information between five separate Kalman filters through the covariance of state variables, and for each Kalman filter, uses not only the position error measurement but also the velocity error measurement, acceleration error measurement, and acceleration error measurement derived from the position error measurement.

[0043] The present invention aims to provide a method for designing a decentralizing federate Kalman filter integrated with GNSS / INS, with reduced computational load through an optimization algorithm of a software method rather than a hardware method.

[0044] In addition, the present invention aims to provide a method for designing a distributed federated Kalman filter by decomposing an INS error behavior model into multiple stages and reducing them in order to reduce the computational load of a GNSS / INS integrated Kalman filter, and linking Kalman filters for each of the decomposed stages.

[0045] In addition, the present invention aims to provide a design method for obtaining velocity error measurements, acceleration error measurements, and acceleration error measurements for a velocity error estimation Kalman filter, attitude error estimation Kalman filter, accelerometer error estimation Kalman filter, and gyro error estimation Kalman filter, respectively, from position error measurements of GNSS and INS.

[0047] As illustrated in FIG. 3, the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to one embodiment of the present invention is formed in the form of a program executed by a computational processing means including a computer, and the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit that processes data from a GNSS (Global Navigation Satellite System) receiver and an IMU (Inertial Measurement Unit) for determining a satellite orbit includes a state variable model separation step (S10), a differential model generation step (S20), and an error estimation step (S30).

[0048] The state variable model separation step (S10) separates the position error state variable model, velocity error state variable model, attitude error state variable model, acceleration error state variable model and gyro error state variable model of the INS.

[0049] Figure 4 is a 15th-order state variable model including position error, velocity error, attitude error, acceleration error, and gyro error of the INS based on the ECEF (Earth Centered Earth Fixed) coordinate system used for satellite orbit determination.

[0050] The gyro error and acceleration error included the most important bias in the model. As shown in Fig. 5, this model can be separated into independent position error state variable models, velocity error state variable models, attitude error state variable models, acceleration error state variable models, and gyro error state variable models, each without mutual coupling elements.

[0051] Unlike the centralized Kalman filter's state variable model, the position error state variable model in each of the five separated state variable models is configured such that the velocity error is converted into an input component, the velocity error state variable model is configured such that the position error, attitude error, and acceleration error are converted into input components, and the attitude error state variable model is configured such that the gyroscope error is converted into an input component.

[0052] In this way, the 15th-order state variable model is separated into five 3rd-order state variable models and input models for the design of a variance-coordinated Kalman filter. Each separated state variable model has a reduce-order effect that reduces computational load, and each input model also serves as a medium that transmits the covariance information of the Kalman filter in a stepwise manner.

[0054] The differential model generation step (S20) calculates a position error measurement model using the difference between the position information of the GNSS receiver and the INS (Inertial Navigation System) position information calculated based on the IMU data, obtains a velocity error measurement model by taking a first derivative of the position error measurement model, obtains an acceleration error measurement model by taking a second derivative, and obtains an acceleration error measurement model by taking a third derivative.

[0055] The difference between the GNSS position and the INS position is the position error measurement of the Kalman filter for position error estimation.

[0056] The velocity error measurement can be obtained by differentiating the time series of the position error measurement once, the acceleration error measurement by differentiating twice, and the acceleration error measurement by differentiating three times.

[0057] INS position based on the ECEF coordinate system as shown in Fig. 1 and GNSS position The difference is a measurement of position error. This is because GNSS position accuracy is known to be within 15m SEP, and since it is very high compared to INS, where the position error increases by at least 1.8km / Hr depending on the performance of the gyroscope / accelerometer inertial sensor and time, the difference represents the position error of INS at the level of GNSS position accuracy.

[0058] The measurement model for position error measurements is It becomes, and here am.

[0059] If you differentiate the position error measurement model once Therefore, the speed error measurement model is It becomes, here am.

[0060] If you differentiate the position error measurement model twice Since it is, of Fig. 4 From, the acceleration error measurement model is

[0061] It becomes, here And, am.

[0062] Attitude error and acceleration error included in the acceleration error measurement model are the main factors causing acceleration measurement error, and are residual values This can be considered as measurement noise. The reason for this is position error ( ) and speed error( This is because ) is maintained at the level of GNSS positional and velocity accuracy in a steady state, so it is within tens of μg.

[0063] If you differentiate the position error measurement model three times Since it is, of Fig. 4 In the relationship equation Simplified by substituting From, the acceleration error measurement model is It becomes, here am.

[0064] The gyro error included in the acceleration error measurement model is a major factor causing acceleration measurement error, and the residual value To summarize It can be considered as measurement noise. The reason for this is that position error and velocity error in the steady state GNSS position accuracy ( ) and speed accuracy( It is maintained at the level of ), and the amount of acceleration (in weightless constant velocity motion in satellite orbit) ) and angular momentum( ), and attitude error( ) and acceleration error( This is because ) converges to 0.

[0065] In this way, the velocity error measurement model obtained by taking the first derivative of the position error measurement model can form an independent Kalman filter by corresponding as a pair with the velocity error state variable model, and the acceleration error measurement model obtained by taking the second derivative can form an independent Kalman filter by corresponding as a pair with the attitude error and acceleration error state variable models. In addition, the acceleration error measurement model obtained by taking the third derivative can form an independent Kalman filter by corresponding as a pair with the gyro error state variable model.

[0067] The covariance propagation step (S30) configures an independent position error estimation Kalman filter such that the position error measurement model and the position error state variable model correspond as a pair, configures an independent velocity error estimation Kalman filter such that the velocity error measurement model and the velocity error state variable model correspond as a pair, configures an independent attitude error estimation Kalman filter such that the acceleration error measurement model and the attitude error state variable model correspond as a pair, configures an independent acceleration error estimation Kalman filter such that the acceleration error measurement model and the acceleration error state variable model correspond as a pair, and configures an independent gyro error estimation Kalman filter such that the acceleration error measurement model and the gyro error state variable model correspond as a pair, respectively.

[0068] The propagation of the position error covariance of the above position error estimation Kalman filter receives and expands the velocity error covariance of the above velocity error estimation Kalman filter, the propagation of the velocity error covariance of the above velocity error estimation Kalman filter receives and expands the attitude error covariance of the above attitude error estimation Kalman filter and the acceleration error covariance of the above acceleration error estimation Kalman filter, and the propagation of the attitude error covariance of the above attitude error estimation Kalman filter receives and expands the gyro error covariance of the above gyro error estimation Kalman filter to estimate the position error, velocity error, attitude error, acceleration error, and gyro error.

[0069] By constructing a position error state variable model and a position error measurement model that take the velocity error component of the position error differential equation as input, the position error can be estimated by performing calculations to propagate and update the position error covariance of the position error estimation Kalman filter and calculating the Kalman filter gain.

[0070] By constructing a velocity error state variable model and a velocity error measurement model that take the attitude error, acceleration error, and gravity error components of the velocity error differential equation as inputs, the velocity error can be estimated by calculating the velocity error covariance of the velocity error estimation Kalman filter and the Kalman filter gain, thereby estimating the velocity error.

[0071] By constructing an attitude error state variable model that takes the gyro error component of the attitude error differential equation as input and an acceleration error measurement model coupled with the attitude error, the attitude error can be estimated by calculating the attitude error covariance of the attitude error estimation Kalman filter, and calculating the Kalman filter gain.

[0072] By constructing an accelerometer bias state variable model that takes the white noise component of the acceleration error differential equation as input and an acceleration error measurement model combined with the attitude error acceleration error, it is possible to estimate the gyro error by calculating the gain of the Kalman filter and the calculation of the acceleration error covariance of the acceleration error estimation Kalman filter, and the gyro error.

[0073] By constructing a gyrobias state variable model that takes the white noise component of the gyro error differential equation as input and an acceleration error measurement model coupled with the gyro error, the gyro error can be estimated by performing calculations to propagate and update the gyro error covariance of the gyro error estimation Kalman filter and calculating the Kalman filter gain.

[0074] The aforementioned position error estimation Kalman filter, velocity error estimation Kalman filter, attitude error estimation Kalman filter, acceleration error estimation Kalman filter, and gyro error estimation Kalman filter are each independent variance-type Kalman filters; the position error estimation Kalman filter receives the velocity error covariance and links with it, the velocity error estimation Kalman filter receives the attitude error and acceleration error covariance and links with it, and the attitude error estimation Kalman filter receives the gyro error covariance and links with it so that they are combined in a stepwise manner.

[0076] FIG. 6 is an overall configuration diagram of a distributed federated Kalman filter design integrating GNSS / INS, wherein the covariance due to gyro noise of the gyro error estimation Kalman filter (600) is

[0077] And,

[0078] The covariance propagation formula am.

[0079] Here is gyro white noise.

[0080] And Kalman filter gain is,

[0081] Covariance update is am.

[0083] The covariance due to accelerometer noise in the acceleration error estimation Kalman filter (700) is And,

[0084] The covariance propagation formula am.

[0085] Here is accelerometer white noise.

[0086] And Kalman filter gain is,

[0087] Covariance update is am.

[0089] The covariance transfer equation by gyro error for the covariance propagation of the Kalman filter (800) for estimating attitude error is

[0090] And,

[0091] The covariance propagation formula is,

[0092] Here Is It is the transition matrix.

[0093] And Kalman filter gain

[0094] is,

[0095] Covariance update is am.

[0097] The covariance transfer equation due to attitude error for covariance propagation of the Kalman filter (900) for estimating velocity error is

[0098] And,

[0099] The covariance propagation formula is,

[0100] Here Is It is the transition matrix.

[0101] And Kalman filter gain is,

[0102] Covariance update is am.

[0104] The covariance transfer equation due to velocity error for covariance propagation of the position error estimating Kalman filter (1000) is

[0105] And,

[0106] The covariance propagation formula am.

[0107] And Kalman filter gain is,

[0108] Covariance update is am.

[0110] The above-mentioned Kalman filter for gyro error estimation (600), Kalman filter for acceleration error estimation (700), Kalman filter for attitude error estimation (800), Kalman filter for velocity error estimation (900), and Kalman filter for position error estimation (1000) , , , , Each of these should be tuned for performance optimization as process noise of the state variable model.

[0111] The above-mentioned Kalman filter for gyro error estimation (600), Kalman filter for acceleration error estimation (700), Kalman filter for attitude error estimation (800), Kalman filter for velocity error estimation (900), and Kalman filter for position error estimation (1000)

[0112] The above position error estimation Kalman filter (600), acceleration error estimation Kalman filter (700), attitude error estimation Kalman filter (800), velocity error estimation Kalman filter (900) and position error estimation Kalman filter (1000) , , , Each of these must be tuned for performance optimization as measurement noise of the measurement model.

[0113] class It is tuned based on the noise levels of GNSS position and velocity, and

[0114] and The tuning of is the residual component of the measurement model and Each can be considered.

[0115] As described above, the 15×15 system matrix of the centralized Kalman filter in Fig. 1 has 225 elements, whereas the 3×3 system matrix of the distributed federated Kalman filter of the present invention designed in Fig. 6 has 45 elements, so the amount of computation for one matrix multiplication and addition / subtraction is greatly reduced.

[0116] To explain in more detail, the computational amount between matrix elements in the multiplication of two n-order square matrices is n 3 And, the amount of computation for addition and subtraction is n 2 It is (n - 1). Also, the computational cost for addition and subtraction between matrix elements in square matrix addition and subtraction expressions is n×n, and the computational costs for multiplication and addition and subtraction between matrix elements in inverse matrix expressions are 4n each. 3 It is / 3. Based on this, operations on a 3rd-order determinant are 1 / 5 of the addition and subtraction operations on a 15th-order determinant. 2 (=1 / 25) and 1 / 5 for multiplication and inverse matrix operations 3 It decreases to the level of (=1 / 125).

[0117] The computational amount of the distributed federated Kalman filter of the present invention is summarized as shown in Figure 7. Compared to the computational amount of the centralized Kalman filter of Figure 2, even though measurement calculation and covariance transfer functions are added, the multiplication is 4.7% and the addition and subtraction are 3.8%, showing an effect of reducing the computational amount by more than 20 times.

[0119] The invention described above is most suitable for satellites in the field of GNSS / INS integrated technology to which the invention belongs, where hardware resources are inevitably limited. Since there may be application fields where price increases due to high-performance hardware are a problem with conventional general designs, various modifications and changes are possible within the scope of the technical concept of the invention, so it is not limited to the design implementation described above and the attached drawings.

[0121] The differential model generation step (S20) of the GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite according to one embodiment of the present invention may be characterized by modeling the difference of the INS position information as a cubic function and using a recursive linear regression method on the time series of the position error measurements to obtain the velocity error measurements, attitude error measurements, and acceleration error measurements.

[0122] The numerical derivative of the time series of position error measurements can be obtained by modeling the position error measurements as a third-order nonlinear function using recursive linear regression (RLR).

[0123] To explain in more detail, first, the coefficients of a cubic function are estimated using the RLR method from the position error measurement, the velocity error measurement is calculated by differentiating the cubic function with the estimated coefficients once, the acceleration error measurement is calculated by differentiating the cubic function twice, and the acceleration error measurement is obtained by differentiating the cubic function three times.

[0124] There may be various ways to differentiate the time series of the position error measurement (100), but as shown in FIG. 8, the INS position error is modeled as a cubic function by considering the characteristics that the INS position error is proportional to the cube of time due to the gyro error, proportional to the square of time due to the attitude error, and proportional to the first square due to the velocity error, and a linear regression method can be used.

[0125] Modeling the INS position error as a cubic function is because the bias of the angular velocity (deg / sec) characteristic, which is the main error of the gyroscope, is integrated, causing the attitude error (deg) to increase as a linear function; this linear attitude error is combined with the input acceleration (m / s²) and integrated, causing a velocity error as a quadratic function, and therefore the position error accumulated from the velocity error increases as a cubic function.

[0126] Since numerically differentiating the time series of position error measurements without any conditions is sensitive to measurement errors and noise, the position error derivative value can be continuously updated from periodic GNSS and INS position measurements by applying the recursive linear regression method among curve-fitting techniques based on the condition of the cubic function characteristic of the INS position error.

[0128] At this time, a Recursive Linear Regression (RLR) measure estimator (200), a Recursive Linear Regression (RLR) measure first-order derivative (300), a Recursive Linear Regression (RLR) measure second-order derivative (400), and a Recursive Linear Regression (RLR) measure third-order derivative (500) may be used.

[0129] For example, INS position error If we model it as a cubic function and apply the recursive linear regression method

[0130]

[0131] It is the same as.

[0132] Here, the measurement time interval is set to 1 second since the GNSS output is typically 1Hz, and the measurement section is Sample of position error measurements (100) Uses.

[0133] at And,

[0134] ,

[0135] ,

[0136] It becomes.

[0137] Here It must be tuned for optimization with the estimated gain.

[0138] The result obtained by the recursive linear regression method Using at

[0139]

[0140] It is the same as.

[0142] To summarize, it can be expressed as a flowchart like Figure 9.

[0143] Compared to the pressure-luminous Kalman filter, the variance-coupled Kalman filter algorithm calculates velocity error, acceleration error, and acceleration error measurements using RLR, and can newly apply an acceleration error measurement model combining attitude error and acceleration error, and an acceleration error measurement model including gyro error.

[0144] In addition, the position error state variable, velocity error state variable, attitude error state variable, gyro error state variable, and acceleration error state variable models are separated to propagate the covariance of the Kalman filter. The attitude error covariance is propagated by receiving the 3×3 covariance matrix of the gyro error, the velocity error covariance is propagated by receiving the 3×3 covariance matrix of the acceleration error and the attitude error respectively, and the position error covariance is propagated by receiving the 3×3 covariance matrix of the velocity error. In this method, the Kalman filters for position error, velocity error, and attitude error are linked in a stepwise manner through the covariance, and the estimation information is linked in a stepwise manner. This method can drastically reduce the amount of computation compared to a pressure-luminous Kalman filter that operates as a single bundle of 15×15 covariance matrices.

[0146] Although a GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to one embodiment of the present invention has been described above, it is obvious that a computer-readable recording medium storing a program for implementing the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit and a program stored on the computer-readable recording medium for implementing the GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit can also be implemented.

[0147] That is, those skilled in the art will readily understand that the GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite described above may be provided by being tangibly implemented as a program of instructions for implementing it, and included in a computer-readable recording medium. In other words, it may be implemented in the form of program instructions that can be executed through various computer means and recorded on a computer-readable recording medium. The computer-readable recording medium may include program instructions, data files, data structures, etc., either individually or in combination. The program instructions recorded on the computer-readable recording medium may be those specifically designed and configured for the present invention, or they may be those known and available to those skilled in computer software. Examples of the above computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes; optical media such as CD-ROMs and DVDs; magneto-optical media such as floptical disks; and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and USB memory. Examples of program instructions include machine code, such as that generated by a compiler, as well as high-level language code that can be executed by a computer using an interpreter, etc. The above hardware devices may be configured to operate as one or more software modules to perform the operation of the present invention, and vice versa.

[0150] The present invention is not limited to the embodiments described above, and its scope of application is diverse. Furthermore, it is understood that various modifications are possible without departing from the essence of the invention as claimed in the claims. Explanation of the symbols

[0153] 100: Position error measurement 200: Recursive Linear Regression Measure Estimator 300: Recursive linear regression measure first-order derivative 400: Recursive linear regression measure second-order derivative 500: Recursive linear regression measure 3rd derivative 600: Gyro error estimation Kalman filter 700: Acceleration Error Estimation Kalman Filter 800: Attitude Error Estimation Kalman Filter 900: Velocity Error Estimation Kalman Filter 1000: Position error estimation Kalman filter S10: State variable model separation step S20: Differential model generation step S30: Error estimation step

Claims

Claim 1 A GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit, comprising a program executed by a computational processing means including a computer, and processing data from a GNSS (Global Navigation Satellite System) receiver and an IMU (Inertial Measurement Unit) for determining the satellite orbit, comprising: a state variable model separation step (S10) for separating a position error state variable model, a velocity error state variable model, an attitude error state variable model, an acceleration error state variable model, and a gyro error state variable model of the INS; and a differential model generation step (S20) for calculating a position error measurement model using the difference between the position information of the GNSS receiver and the INS (Inertial Navigation System) position information calculated based on the IMU data, obtaining a velocity error measurement model by taking a first derivative of the position error measurement model, obtaining an acceleration error measurement model by taking a second derivative, and obtaining an acceleration error measurement model by taking a third derivative.and an independent position error estimation Kalman filter is configured such that the position error measurement model and the position error state variable model correspond as a pair, an independent velocity error estimation Kalman filter is configured such that the velocity error measurement model and the velocity error state variable model correspond as a pair, an independent attitude error estimation Kalman filter is configured such that the acceleration error measurement model and the attitude error state variable model correspond as a pair, an independent acceleration error estimation Kalman filter is configured such that the acceleration error measurement model and the acceleration error state variable model correspond as a pair, and an independent gyro error estimation Kalman filter is configured such that the acceleration error measurement model and the gyro error state variable model correspond as a pair, respectively, and the position error covariance propagation of the position error estimation Kalman filter is expanded by receiving the velocity error covariance of the velocity error estimation Kalman filter, and the velocity error estimation Kalman filter's An error estimation step (S30) comprising: propagating the velocity error covariance by receiving and expanding the attitude error covariance of the attitude error estimating Kalman filter and the acceleration error covariance of the acceleration error estimating Kalman filter, and propagating the attitude error covariance of the attitude error estimating Kalman filter by receiving and expanding the gyro error covariance of the gyro error estimating Kalman filter to estimate position error, velocity error, attitude error, acceleration error, and gyro error; comprising a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite.; Claim 2 A GNSS / IMU integrated Kalman filter algorithm method for determining a satellite orbit according to claim 1, wherein the differential model generation step (S20) models the difference of the INS position information as a cubic function and obtains velocity error measurements, attitude error measurements, and acceleration error measurements using a recursive linear regression method on the time series of position error measurements. Claim 3 A computer-readable recording medium storing a program for implementing a GNSS / IMU integrated Kalman filter algorithm method for determining the orbit of a satellite as described in any one of claims 1 to 2.

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