Complex sea condition sea target positioning and tracking method with limited dependent variable constraint

Abstract

A complex sea condition sea target positioning and tracking method constrained by dependent variables belongs to the technical field of intelligent maritime affair monitoring and ship navigation, and comprises the following steps: S1, constructing a sea target positioning and tracking state model including a state equation based on uniform linear motion and two observation equations adapted to AIS / GNSS and radar; s2, establishing a limited dependent variable observation model, and quantitatively observing nonlinear correlation between loss / truncation and the real state of the target; s3, performing prior prediction of the current target state and the covariance based on the historical state; s4, fusing the prediction state and actual observation (including censored data) to complete state and error covariance updating; and S5, introducing a Bernoulli random variable to calculate an observation state adaptive weight. Through combination of the limited dependent variable model and the filtering method, the problems of trajectory breakage and target missing detection of a traditional tracking method caused by incomplete observation data under complex sea conditions are solved, and the method is directly integrated to a shipborne radar monitoring system and a maritime affair supervision platform.

Description

Technical Field

[0001] This invention relates to the field of intelligent maritime monitoring and ship navigation technology, and more specifically, to a method for locating and tracking maritime targets in complex sea conditions under constrained dependent variables. Background Technology

[0002] With the continuous upgrading of global maritime shipping, offshore operations, and maritime regulatory needs, higher precision and reliability requirements are being placed on the real-time positioning and continuous tracking of maritime targets. Among existing maritime target positioning and tracking systems, AIS can provide dynamic information about vessels with installed equipment (such as position and heading), microwave radar has all-weather detection capabilities, and optical cameras can provide visual details of targets. All of these observation systems can be used for positioning and tracking maritime targets.

[0003] In the field of maritime target positioning and tracking methods, most rely on Kalman filtering, particle filtering, and their improved forms, achieving trajectory tracking through state estimation of target observation data. These methods effectively reduce measurement errors and ensure tracking stability under ideal sea conditions with complete observation data (e.g., calm sea surface, good visibility). However, their application has significant limitations in actual complex sea conditions: wave impacts can easily obscure the target, and low visibility environments such as darkness, rain, snow, and fog can directly weaken or interrupt the target observation signal, ultimately leading to the loss or truncation of target observation data. Existing tracking methods lack effective mechanisms for handling "loss or truncation of observation data," resulting in positioning and tracking failures, and causing problems such as missed target detection and trajectory breaks.

[0004] To improve target tracking performance under complex sea conditions, existing research has focused on two main approaches: first, enhancing hardware performance to improve the anti-interference capability of observation signals; and second, optimizing algorithms, such as adjusting filtering parameters and adding simple data completion modules. However, none of these methods address the core issue of "complete loss or truncation of observation data." That is, when observation data cannot be effectively acquired, simple parameter adjustments or data completion cannot accurately reflect the true motion of the target, leading to a significant decrease in tracking accuracy.

[0005] The restricted dependent variable model originated in the field of economics. Its core value lies in solving the incomplete observation problems commonly found in economic data, such as censoring and missing data. Through accurate modeling and effective fitting of restricted data, it achieves accurate inferences about the true economic state. Research has found that the core mechanism of this model is highly compatible with the technical pain points of maritime target positioning and tracking under complex sea conditions. That is, the loss and truncation of observation data caused by complex sea conditions is essentially a typical scenario of "observation restriction," and the model's advantage in processing incomplete observation data can precisely address the core shortcomings of existing tracking methods. Currently, this model has not yet been introduced into the field of maritime target positioning and tracking, and there is a lack of adaptation and algorithm integration solutions for complex maritime environments.

[0006] Therefore, it is necessary to address the problem that existing shipborne target positioning and tracking methods fail under complex sea conditions due to incomplete observation data. This paper proposes a new method for maritime target positioning and tracking that introduces and constructs a constrained dependent variable model to effectively process incomplete observation data and ultimately improve the accuracy and reliability of target positioning and tracking under complex sea conditions. Summary of the Invention

[0007] To address the technical challenges of traditional tracking methods in complex sea conditions for maritime shipping, maritime supervision, and nearshore operations, where target observation data is easily lost or truncated due to wave obstruction, low visibility (fog, rain, snow), and equipment detection limitations, leading to trajectory breaks and missed detections, this invention proposes a complex sea target positioning and tracking method constrained by dependent variables. This method can be directly adapted to engineering applications in ship navigation, maritime monitoring, and other systems, as detailed below.

[0008] A method for locating and tracking maritime targets in complex sea states with constrained dependent variables includes the following steps:

[0009] S1, Construction of the State Model for Maritime Target Positioning and Tracking: For maritime targets such as ships and floating objects in a two-dimensional plane, a state model is constructed based on the assumption of uniform linear motion. The state vector contains position and velocity components. At the same time, it is adapted to the scenario of maritime multi-source sensors and establishes two types of observation models, corresponding to the direct position observation of AIS / GNSS and the range and azimuth observation of radar, respectively, to provide basic model support for subsequent tracking.

[0010] S2, Establishment of the Constrained Dependent Variable Observation Model: To address the problem of lost or truncated observation data caused by wave obstruction and low visibility, a constrained dependent variable model is introduced to construct a nonlinear observation censoring model; the correlation between observation constraints and the true state of the target is quantified, the nonlinear functions of potential observations, censored observations and the true state are clarified, and the observation Jacobian matrix is ​​obtained by differentiation to adapt to the characteristics of maritime observation.

[0011] S3, State Prediction and State Covariance Estimation: Based on the target's historical state information, make prior estimates of the target's state and covariance at the current moment; infer the possible state of the target through the state prediction equation, and calculate the state covariance matrix from the previous moment to the current moment. Even during periods of lost observation data, the continuity of the target trajectory can be maintained, providing a prior basis for subsequent state correction.

[0012] S4, State Update and Error Covariance Update: When the observation data is reacquired, the previously predicted state is fused with the actual observation data including censored data; by constructing the relative distance vector between the estimated measurement value and the censoring threshold, the state error covariance matrix is ​​minimized to achieve target state correction, solving the problem of correction failure of traditional methods when the observation is incomplete;

[0013] S5, Calculation of observation state adaptation weights: Introducing Bernoulli random variables, the optimal observation state adaptation weights are calculated based on the distance between the potential observation and the censoring threshold, quantifying the probability of occurrence of the two observation scenarios; substituting the weights into the covariance matrix formula enhances the robustness and adaptability of the tracking method under complex sea conditions.

[0014] Furthermore, in step S1, the state model is constructed as follows:

[0015] For a tracking model of a moving target in a two-dimensional plane, if the target moves in a straight line, the state vector consists of velocity and position. ,in, and They are respectively Directional velocity and Directional velocity, and They are respectively Directional displacement and If the direction of displacement is considered, then the state equation is:

[0016]

[0017] in, This represents the k-th time. The time interval between samples The state transition matrix for linear motion of the target. State noise, , The state estimation error covariance;

[0018] The two types of observation models are established as follows:

[0019] If the position information of a moving target is directly observed using AIS or GNSS sensors, then the observation vector is: Therefore, the observation equation is:

[0020]

[0021] in, State noise, For the observation transfer matrix using AIS and GNSS sensors, , For observation error covariance;

[0022] If radar is used to observe the range and azimuth information of a moving target, then the observation vector is: ,in:

[0023]

[0024] Therefore, the observation equation is:

[0025]

[0026] in, State noise, To use the observation transfer function of a radar sensor, , This represents the observation error covariance.

[0027] Furthermore, in step S2, the nonlinear observation censoring model is constructed as follows:

[0028]

[0029] in, yes The state vector at time t is direction and velocity and position in direction ; for The potential observation vector at time t; for The censored observation vector at time step is the actual observation vector; This is the censoring threshold vector;

[0030] The observation and the state satisfy a nonlinear relationship, that is, the observation function is:

[0031]

[0032] and For state noise and observation noise, satisfying and ;

[0033] Differentiating the observation equation, we obtain the observation Jacobian matrix as follows:

[0034] .

[0035] Further, step S3 is as follows: Given the initial value of the state vector. Initial values ​​of the error covariance matrix ;

[0036] The prior estimate of the state probability distribution is:

[0037]

[0038] in, for The state estimation vector and the state prediction equation are:

[0039]

[0040] for The estimated vector; the measured value and The state covariance matrix before time step is:

[0041]

[0042] This is an estimate of the error covariance of the previous state.

[0043] Furthermore, step S4 is detailed as follows:

[0044] Depend on The correction steps for obtaining the current estimate from all observations prior to time are as follows:

[0045]

[0046] in, Abbreviated as Because the observation model is nonlinear, i.e., based on the predicted state... The measured relationship is as follows:

[0047]

[0048] Thus, the estimated measurement value is obtained. With censoring threshold Relative distance vector between , The element for:

[0049]

[0050] therefore for:

[0051]

[0052] Regarding the aforementioned The state error covariance matrix Minimize:

[0053] .

[0054] Furthermore, step S5 is detailed as follows:

[0055] Introducing a Bernoulli random variable, when the measurement is not censored, i.e., the target is not obscured and is within radar detection range, the variable... When the measured value equals the censoring threshold, i.e., the target is occluded or outside the detection range, the variable... The measurement model can be written as:

[0056]

[0057] For the At any moment, the measurement passes probability of formation To represent the state; because the Bernoulli random matrix is ​​a diagonal matrix. Therefore, the measured value can be given by the following formula:

[0058]

[0059] We can obtain:

[0060]

[0061] make Then the covariance matrix of the state estimate is:

[0062]

[0063] Taking the trace of the above equation, we get:

[0064]

[0065] Then adjust the above formula Find the derivative, and set it to zero:

[0066]

[0067] This yields the optimal observation state adaptation weights:

[0068]

[0069] The probability of a measurement not being censored is a function of the distance between the potential measurement and the censoring threshold. The expectation can be written as:

[0070]

[0071] The equality sign in the formula holds under the following two assumptions: Assumption 1 is Assume that 2 is the measurement error covariance matrix. Since it is a diagonal matrix, we can obtain:

[0072]

[0073] use and Representing the standard Gaussian distribution The probability density function and probability distribution function are given, and the inverse Mills ratio is defined as:

[0074]

[0075] for ,because It is white noise and has , ,as well as

[0076]

[0077] therefore, for:

[0078]

[0079] Similarly, we can obtain for:

[0080]

[0081] Substituting the obtained optimal observation state adaptation weights into the equation yields:

[0082]

[0083] The step ends when the number of iterations meets the preset value; otherwise, the current data is saved. , And then begin the next update iteration.

[0084] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0085] 1. Targeted solutions to the core pain point of lost / trunculated observation data under complex sea conditions: By customizing the restricted dependent variable model, the correlation between "restricted observation" and the true state of the target is quantified, avoiding the trajectory breakage and missed detection problems caused by incomplete observations in traditional filtering methods.

[0086] 2. Strong engineering adaptability: It is compatible with commonly used maritime observation methods such as AIS, GNSS, and radar, supports linear / nonlinear observation scenarios, and can be directly integrated into existing equipment such as shipborne radar monitoring systems and maritime supervision platforms.

[0087] 3. Improved tracking accuracy and stability: Combining the state prediction capability of extended Kalman filtering with the advantages of incomplete data processing of restricted dependent variable models, it achieves "continuous inference when observations are lost and accurate correction when observations are recovered", balancing continuity and accuracy.

[0088] 4. Excellent robustness: The system introduces observation state adaptation weights to quantify the probability of observation censoring, adapting to the randomness of maritime scenarios such as wave obstruction and visibility fluctuations, thereby enhancing the tracking reliability in complex environments. Attached Figure Description

[0089] Figure 1 This is a flowchart of the maritime target positioning and tracking method of the present invention.

[0090] Figure 2 This is a flowchart of the maritime target positioning and tracking algorithm of the present invention.

[0091] Figure 3 This is a comparison of the positioning and tracking trajectories in a scenario with limited observation, according to an embodiment of the present invention.

[0092] Figure 4 For Figure 3 The magnified details of area A are shown in the image.

[0093] Figure 5 For Figure 3 The magnified details of the area marked B.

[0094] Figure 6 This is a comparison of positioning and tracking errors in observation-limited scenarios according to embodiments of the present invention. Detailed Implementation

[0095] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0096] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0097] like Figures 1-2As shown, a method for locating and tracking maritime targets in complex sea states under constrained dependent variable models is described below. The specific steps are as follows:

[0098] Step S1, Construction of the maritime target positioning and tracking state model:

[0099] In practical maritime applications, the motion status of maritime targets such as ships and buoys needs to meet the requirements of real-time monitoring and continuous tracking. For example, collision avoidance monitoring of surrounding vessels in ocean shipping and positioning and tracking of work platforms in near-shore operations both require decision support based on the target's actual position and velocity data. This step focuses on maritime moving targets (such as ships and floating objects) in a two-dimensional plane, and combines commonly used observation methods in the maritime field to construct a state model and observation model that fits the actual engineering situation.

[0100] For a tracking model of a moving target in a two-dimensional plane, if the target moves in a straight line, the state vector consists of velocity and position. ,in, and They are respectively Directional velocity and Directional velocity, and They are respectively Directional displacement and Directional displacement. Therefore, the state equation is:

[0101]

[0102] in, This represents the k-th time. The time interval between samples The state transition matrix for linear motion of the target. State noise, , Let be the state estimation error covariance.

[0103] For this moving target, the following two types of observation models can be constructed:

[0104] If the position information of a moving target is directly observed using methods such as AIS or GNSS, then the observation vector is: Therefore, the observation equation is:

[0105]

[0106] in, State noise, For observation transfer matrices using sensors such as AIS and GNSS, , This represents the observation error covariance.

[0107] If radar or other methods are used to observe the range and azimuth information of moving targets, then the observation vector is: ,in:

[0108]

[0109] Therefore, the observation equation is:

[0110]

[0111] in, State noise, To use the observation transfer function of sensors such as radar, , This represents the observation error covariance.

[0112] This invention focuses on more complex nonlinear observation scenarios in practical applications. Maritime monitoring scenarios, in which radar and other sensors are the core observation methods, constitute the majority and are more prone to data loss due to sea conditions. Linear observation can be treated as a special form of nonlinear observation to ensure the method's versatility and engineering adaptability.

[0113] Step S2, Establishment of the restricted dependent variable observation model:

[0114] In actual maritime operations, radar and other observation equipment often face two typical observation problems: First, the impact of violent waves can cause targets to be obscured by wave crests, preventing the radar from acquiring effective observation data (i.e., observation loss); second, in low-visibility environments, the radar's detection range is limited, and observation data is truncated when targets exceed the detection threshold (e.g., if the radar's maximum detection range is 10km, the observation value for targets outside this range is forcibly set to 10km). To address these two frequently occurring incomplete observation problems in practical engineering, this invention introduces a restricted dependent variable model, and through customized modifications, adapts it to the observation characteristics of maritime scenarios, constructing a nonlinear observation censoring motion tracking model as follows:

[0115]

[0116] in, yes The state vector at time t is direction and velocity and position in direction ; for The potential observation vector at time t; for The censored observation vector at time step is the actual observation vector; This is the censoring threshold vector;

[0117] The observation and the state satisfy a nonlinear relationship, that is, the observation function is:

[0118]

[0119] and For state noise and observation noise, satisfying and .

[0120] Differentiating the observation equation, we obtain the observation Jacobian matrix as follows:

[0121]

[0122] This model solves the core problem that traditional models cannot quantify the relationship between "observation loss / truncation" and "target's true state" by accurately simulating the observation censoring characteristics of maritime scenarios, thus providing theoretical support for stable tracking under complex sea conditions.

[0123] Step S3, State Prediction and State Covariance Estimation:

[0124] When observation data is lost or truncated, such as when the target is obscured by waves for a few seconds, the current position needs to be inferred based on the target's historical motion state to avoid target loss due to trajectory breakage. The core purpose of this step is to predict the possible state of the target at the current moment using the effective observation information from the previous moment, providing a priori basis for subsequent state correction.

[0125] Given initial values ​​of the state vector Initial values ​​of the error covariance matrix ;

[0126] In the state prediction step, the prior estimate of the state probability distribution is:

[0127]

[0128] in, for The state estimation vector and the state prediction equation are:

[0129]

[0130] for The estimated vector. Measurements and The state covariance matrix before time step is:

[0131]

[0132] This is an estimate of the error covariance of the previous state.

[0133] The core significance of this step is that even if there is no effective observation data in a short period of time, the target position can be continuously inferred based on historical status, avoiding tracking failure due to observation interruption, and adapting to the high-frequency demand of "short-term observation loss" in maritime scenarios.

[0134] Step S4, State Update and Error Covariance Update:

[0135] When the radar regains valid observation data, such as when the target moves out of the wave crest obscuring area or visibility temporarily improves, it needs to be corrected by combining the predicted state with the new observation data to ensure the accuracy of the target position estimation. This step minimizes the state error covariance matrix. This achieves optimal fusion between predicted states and actual observations. Specifically, it is achieved by... The correction steps for obtaining the current estimate from all observations prior to time are as follows:

[0136]

[0137] in, Abbreviated as Because the observation model is nonlinear, i.e., based on the predicted state... The measured relationship is as follows:

[0138]

[0139] Thus, the estimated measurement value is obtained. With censoring threshold Relative distance vector between , The element for:

[0140]

[0141] therefore for:

[0142]

[0143] Regarding the aforementioned The state error covariance matrix Minimize:

[0144]

[0145] This step, by integrating "predicted state" with "actual observation (which may contain censoring)," solves the problem of correction failure in traditional methods when observation data is incomplete, ensuring the continuity and accuracy of target state estimation under complex sea conditions.

[0146] Step S5, Calculation of observation state adaptation weights:

[0147] To quantify the probabilities of "uncensored observation" and "censored observation" and to reflect the randomness of observation states in maritime scenarios, such as the uncertainty of wave obstruction, this step introduces a Bernoulli random variable to simulate the occurrence of censored measurements versus actual measurements. When the measurement is uncensored (the target is not obstructed and is within radar detection range), the variable... When the measured value equals the censoring threshold (the target is occluded or outside the detection range), the variable... The measurement model can be written as:

[0148]

[0149] For the At any moment, the measurement passes probability of formation To represent the state. Because the Bernoulli random matrix is ​​a diagonal matrix. Therefore, the measured value can be given by the following formula:

[0150]

[0151] We can obtain:

[0152]

[0153] make Then the covariance matrix of the state estimate is:

[0154]

[0155] Taking the trace of the above equation, we get:

[0156]

[0157] Then adjust the above formula Find the derivative, and set it to zero:

[0158]

[0159] This yields the optimal observation state adaptation weights:

[0160]

[0161] The probability of a measurement not being censored is a function of the distance between the potential measurement and the censoring threshold. The expectation can be written as:

[0162]

[0163] The equality sign in the formula holds under the following two assumptions: Assumption 1 is Assume that 2 is the measurement error covariance matrix. It is a diagonal matrix. Therefore:

[0164]

[0165] use and Representing the standard Gaussian distribution Given the probability density function (PDF) and probability distribution function (CDF), the inverse Mills ratio (IMR) is defined as:

[0166]

[0167] for ,because It is white noise and has , ,as well as

[0168]

[0169] therefore, for:

[0170]

[0171] Similarly, we can obtain for:

[0172]

[0173] Substituting the obtained optimal observation state adaptation weights into the equation yields:

[0174]

[0175] The step ends when the number of iterations meets the preset value; otherwise, the current data is saved. , And then begin the next update iteration.

[0176] Ultimately, a method for locating and tracking maritime targets in complex sea states, constrained by a limited dependent variable model, was obtained. This method can be directly integrated into engineering equipment such as shipborne radar monitoring systems and maritime surveillance platforms to achieve continuous and high-precision tracking of targets under complex sea states.

[0177]

[0178] This invention enables the engineering application of target positioning and tracking under complex sea conditions. The method significantly reduces trajectory breakage rates and improves maritime safety monitoring capabilities in scenarios with surge obstruction and low visibility.

[0179] Example:

[0180] For a maritime ship observation experiment using radar sensors, the radar sensors are positioned at the origin (0,0). A moving target at sea moves towards the radar position with varying speed in a straight line from a distance. The ideal trajectory of the target, the trajectory observed by the radar, the target tracking trajectory achieved using traditional methods such as extended Kalman filtering, and the target tracking trajectory achieved using the algorithm of this patent are compared. Figure 3 As shown. In the early stage of the target's movement, as... Figure 3 Region A in the middle (after magnification, as shown) Figure 4 As shown), the radar sensor is working normally, and both the traditional method and the method of this patent can achieve good tracking results; when the target moves to the area around y=20m, such as Figure 3 Region B in the middle (after local magnification, as shown) Figure 5 (As shown) Due to external factors such as ocean waves, radar detection data of the target is truncated. Although the actual trajectory of the target continues to move towards the origin, the observed trajectory of the target moves randomly near the truncated position. In this scenario, traditional methods exhibit large tracking errors, while the method of this patent can adaptively identify it as a scenario with a limited dependent variable, and continue to achieve stable predictive tracking of the target. Figure 6 This displays a quantitative evaluation curve of the root mean square error (MSE) along the y-direction, compared with... Figure 5 As can be seen, at y=20m, due to the truncation of radar detection data, both traditional methods and direct measurement results show a large MSE, while the method of this patent can still maintain a low MSE.

[0181] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for locating and tracking maritime targets in complex sea states with constrained dependent variables, characterized in that, Includes the following steps: S1, Construction of the State Model for Maritime Target Positioning and Tracking: For maritime targets such as ships and floating objects in a two-dimensional plane, a state model is constructed based on the assumption of uniform linear motion. The state vector contains position and velocity components. At the same time, it is adapted to the scenario of maritime multi-source sensors and establishes two types of observation models, corresponding to the direct position observation of AIS / GNSS and the range and azimuth observation of radar, respectively, to provide basic model support for subsequent tracking. S2, Establishment of the Constrained Dependent Variable Observation Model: To address the problem of lost or truncated observation data caused by wave obstruction and low visibility, a constrained dependent variable model is introduced to construct a nonlinear observation censoring model; the correlation between observation constraints and the true state of the target is quantified, the nonlinear functions of potential observations, censored observations and the true state are clarified, and the observation Jacobian matrix is ​​obtained by differentiation to adapt to the characteristics of maritime observation. S3, State Prediction and State Covariance Estimation: Based on the target's historical state information, make prior estimates of the target's state and covariance at the current moment; infer the possible state of the target through the state prediction equation, and calculate the state covariance matrix from the previous moment to the current moment. Even during periods of lost observation data, the continuity of the target trajectory can be maintained, providing a prior basis for subsequent state correction. S4, State Update and Error Covariance Update: When the observation data is reacquired, the previous predicted state is merged with the actual observation data including censored data; By constructing a relative distance vector between the estimated measurement value and the censoring threshold, and minimizing the state error covariance matrix, target state correction is achieved, solving the problem of correction failure in traditional methods when observations are incomplete. S5, Calculation of observation state adaptation weights: Introducing Bernoulli random variables, the optimal observation state adaptation weights are calculated based on the distance between the potential observation and the censoring threshold, quantifying the probability of occurrence of the two observation scenarios; substituting the weights into the covariance matrix formula enhances the robustness and adaptability of the tracking method under complex sea conditions.

2. The method for locating and tracking maritime targets in complex sea states under constrained dependent variables as described in claim 1, characterized in that, In step S1, the state model is constructed as follows: For a tracking model of a moving target in a two-dimensional plane, if the target moves in a straight line, the state vector consists of velocity and position. ,in, and They are respectively Directional velocity and Directional velocity, and They are respectively Directional displacement and If the direction of displacement is given, then the state equation is: in, This represents the k-th time. The time interval between samples The state transition matrix for linear motion of the target. State noise, , The state estimation error covariance; The two types of observation models are established as follows: If the position information of a moving target is directly observed using AIS or GNSS sensors, then the observation vector is: Therefore, the observation equation is: in, State noise, This is the observation transfer matrix using AIS and GNSS sensors. , For observation error covariance; If radar is used to observe the range and azimuth information of a moving target, then the observation vector is: ,in: Therefore, the observation equation is: in, State noise, To use the observation transfer function of a radar sensor, , This represents the observation error covariance.

3. The method for locating and tracking maritime targets in complex sea states under constrained dependent variables as described in claim 2, characterized in that, In step S2, the nonlinear observation censoring model is constructed as follows: in, yes The state vector at time t is direction and velocity and position in direction ; for The potential observation vector at time t; for The censored observation vector at time step is the actual observation vector; This is the censoring threshold vector; The observation and the state satisfy a nonlinear relationship, that is, the observation function is: and For state noise and observation noise, satisfying and ; Differentiating the observation equation, we obtain the observation Jacobian matrix as follows: 。 4. The method for locating and tracking maritime targets in complex sea states under constrained dependent variables according to claim 3, characterized in that, Step S3 is as follows: Given the initial value of the state vector. Initial values ​​of the error covariance matrix ; The prior estimate of the state probability distribution is: in, for The state estimation vector and the state prediction equation are: for The estimated vector; the measured value and The state covariance matrix before time step is: This is an estimate of the covariance of the error in the previous state.

5. The method for locating and tracking maritime targets in complex sea states under constrained dependent variables according to claim 4, characterized in that, Step S4 is as follows: Depend on The correction steps for obtaining the current estimate from all observations prior to time are as follows: in, Abbreviated as Because the observation model is nonlinear, i.e., based on the predicted state... The measured relationship is as follows: Thus, the estimated measurement value is obtained. With censoring threshold Relative distance vector between , The element for: therefore for: Regarding the aforementioned The state error covariance matrix Minimize: 。 6. The method for locating and tracking maritime targets in complex sea states with constrained dependent variables as described in claim 5, characterized in that, Step S5 is as follows: Introducing a Bernoulli random variable, when the measurement is not censored, i.e., the target is not obscured and is within radar detection range, the variable... When the measured value equals the censoring threshold, i.e., the target is occluded or outside the detection range, the variable... The measurement model can be written as: For the At any moment, the measurement passes probability of formation To represent the state; because the Bernoulli random matrix is ​​a diagonal matrix. Therefore, the measured value can be given by the following formula: We can obtain: make Then the covariance matrix of the state estimate is: Taking the trace of the above equation, we get: Then adjust the above formula Find the derivative, and set it to zero: This yields the optimal observation state adaptation weights: The probability of a measurement not being censored is a function of the distance between the potential measurement and the censoring threshold. The expectation can be written as: The equality sign in the formula holds under the following two assumptions: Assumption 1 is Assume that 2 is the measurement error covariance matrix. Since it is a diagonal matrix, we can obtain: use and Representing the standard Gaussian distribution The probability density function and probability distribution function are given, and the inverse Mills ratio is defined as: for ,because It is white noise and has , ,as well as therefore, for: Similarly, we can obtain for: Substituting the obtained optimal observation state adaptation weights into the equation yields: The step ends when the number of iterations meets the preset value; Otherwise, save the current data. , And then begin the next update iteration.

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